````text
Token                Input ID      Label
---------------------------------------------
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'system'                   8948       -100
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','                          11       -100
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','                          11       -100
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','                          11       -100
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'tr'                        376       -100
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'consider'                24712       -100
'ed'                        291       -100
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':'                          25       -100
' Thought'                35187       -100
' and'                      323       -100
' Solution'               12478       -100
'.'                          13       -100
' In'                       758       -100
' the'                      279       -100
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','                          11       -100
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'thought'                 60565       -100
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'n'                          77       -100
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','                          11       -100
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','                          11       -100
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','                          11       -100
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','                          11       -100
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' In'                       758       -100
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','                          11       -100
' based'                   3118       -100
' on'                       389       -100
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','                          11       -100
' explor'                 47439       -100
'ations'                    804       -100
','                          11       -100
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' from'                     504       -100
' the'                      279       -100
' Thought'                35187       -100
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','                          11       -100
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' present'                 3042       -100
' the'                      279       -100
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' that'                     429       -100
' you'                      498       -100
' deem'                   81477       -100
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' The'                      576       -100
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','                          11       -100
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','                          11       -100
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','                          11       -100
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':'                          25       -100
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'begin'                    7265       -100
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':'                          25       -100
'<|im_end|>'             151645       -100
'\n'                        198       -100
'<|im_start|>'           151644       -100
'user'                      872       -100
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'Generate'                31115       -100
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' Python'                 13027       -100
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' given'                   2661       -100
' prompt'                  9934       -100
'.'                          13       -100
' The'                      576       -100
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' the'                      279       -100
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'.'                          13       -100
' Simply'                 28424       -100
' call'                    1618       -100
' the'                      279       -100
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' after'                   1283       -100
' the'                      279       -100
' definition'              7271       -100
'.Today'                  72672       -100
','                          11       -100
' Wet'                    44856       -100
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' is'                       374       -100
' given'                   2661       -100
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'1'                          16       -100
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'.\n\n'                     382       -100
'W'                          54       -100
'et'                        295       -100
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','                          11       -100
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'according'               73846       -100
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')'                           8       -100
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'.'                          13       -100
' Now'                     4695       -100
' Wet'                    44856       -100
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'.\n\n\n'                  4192       -100
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'Input'                    2505       -100
'-----\n\n'               70674       -100
'The'                       785       -100
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' ('                        320       -100
'1'                          16       -100
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')'                           8       -100
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'_{'                      15159       -100
'i'                          72       -100
'},'                       2137       -100
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'0'                          15       -100
'0'                          15       -100
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')'                           8       -100
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' guaranteed'             19323       -100
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' share'                   4332       -100
' the'                      279       -100
' same'                    1852       -100
' position'                2309       -100
'.\n\n\n'                  4192       -100
'-----'                   15081       -100
'Output'                   5097       -100
'-----\n\n'               70674       -100
'Output'                   5097       -100
' one'                      825       -100
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'\xa0'                     4102       -100
'—'                        2293       -100
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' which'                    892       -100
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'.'                          13       -100
' \n\n\n'                 14731       -100
'-----'                   15081       -100
'Examples'                40381       -100
'-----\n'                 34764       -100
'Input'                    2505       -100
'\n'                        198       -100
'5'                          20       -100
'\n'                        198       -100
'1'                          16       -100
' '                         220       -100
'1'                          16       -100
'\n'                        198       -100
'1'                          16       -100
' '                         220       -100
'5'                          20       -100
'\n'                        198       -100
'3'                          18       -100
' '                         220       -100
'3'                          18       -100
'\n'                        198       -100
'5'                          20       -100
' '                         220       -100
'1'                          16       -100
'\n'                        198       -100
'5'                          20       -100
' '                         220       -100
'5'                          20       -100
'\n\n'                      271       -100
'Output'                   5097       -100
'\n'                        198       -100
'6'                          21       -100
'\n\n'                      271       -100
'Input'                    2505       -100
'\n'                        198       -100
'3'                          18       -100
'\n'                        198       -100
'1'                          16       -100
' '                         220       -100
'1'                          16       -100
'\n'                        198       -100
'2'                          17       -100
' '                         220       -100
'3'                          18       -100
'\n'                        198       -100
'3'                          18       -100
' '                         220       -100
'5'                          20       -100
'\n\n'                      271       -100
'Output'                   5097       -100
'\n'                        198       -100
'0'                          15       -100
'\n\n\n\n'                 1022       -100
'-----'                   15081       -100
'Note'                     9112       -100
'-----\n\n'               70674       -100
'In'                        641       -100
' the'                      279       -100
' first'                   1156       -100
' sample'                  6077       -100
' following'               2701       -100
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' of'                       315       -100
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' attack'                  3359       -100
' each'                    1817       -100
' other'                   1008       -100
':'                          25       -100
' ('                        320       -100
'1'                          16       -100
','                          11       -100
' '                         220       -100
'3'                          18       -100
'),'                        701       -100
' ('                        320       -100
'1'                          16       -100
','                          11       -100
' '                         220       -100
'5'                          20       -100
'),'                        701       -100
' ('                        320       -100
'2'                          17       -100
','                          11       -100
' '                         220       -100
'3'                          18       -100
'),'                        701       -100
' ('                        320       -100
'2'                          17       -100
','                          11       -100
' '                         220       -100
'4'                          19       -100
'),'                        701       -100
' ('                        320       -100
'3'                          18       -100
','                          11       -100
' '                         220       -100
'4'                          19       -100
')'                           8       -100
' and'                      323       -100
' ('                        320       -100
'3'                          18       -100
','                          11       -100
' '                         220       -100
'5'                          20       -100
').'                        568       -100
' P'                        393       -100
'airs'                     4720       -100
' ('                        320       -100
'1'                          16       -100
','                          11       -100
' '                         220       -100
'2'                          17       -100
'),'                        701       -100
' ('                        320       -100
'1'                          16       -100
','                          11       -100
' '                         220       -100
'4'                          19       -100
'),'                        701       -100
' ('                        320       -100
'2'                          17       -100
','                          11       -100
' '                         220       -100
'5'                          20       -100
')'                           8       -100
' and'                      323       -100
' ('                        320       -100
'4'                          19       -100
','                          11       -100
' '                         220       -100
'5'                          20       -100
')'                           8       -100
' do'                       653       -100
' not'                      537       -100
' attack'                  3359       -100
' each'                    1817       -100
' other'                   1008       -100
' because'                 1576       -100
' they'                     807       -100
' do'                       653       -100
' not'                      537       -100
' share'                   4332       -100
' the'                      279       -100
' same'                    1852       -100
' diagonal'               37236       -100
'.\n'                       624       -100
'<|im_end|>'             151645       -100
'\n'                        198       -100
'<|im_start|>'           151644       -100
'assistant'               77091       -100
'\n'                        198       -100
'<think>'                151667     151667
'\n\n'                      271        271
'</think>'               151668     151668
'\n\n'                      271        271
'<'                          27         27
'|'                          91         91
'begin'                    7265       7265
'_of'                      3575       3575
'_th'                      5854       5854
'ought'                    2450       2450
'|'                          91         91
'>\n\n'                    1339       1339
'Okay'                    32313      32313
','                          11         11
' let'                     1077       1077
"'s"                        594        594
' see'                     1490       1490
'.'                          13         13
' The'                      576        576
' problem'                 3491       3491
' is'                       374        374
' to'                       311        311
' count'                   1760       1760
' the'                      279        279
' number'                  1372       1372
' of'                       315        315
' pairs'                  13530      13530
' of'                       315        315
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' that'                     429        429
' attack'                  3359       3359
' each'                    1817       1817
' other'                   1008       1008
' on'                       389        389
' a'                        264        264
' '                         220        220
'1'                          16         16
'0'                          15         15
'0'                          15         15
'0'                          15         15
'x'                          87         87
'1'                          16         16
'0'                          15         15
'0'                          15         15
'0'                          15         15
' grid'                    5827       5827
'.'                          13         13
' B'                        425        425
'ishops'                  50109      50109
' attack'                  3359       3359
' if'                       421        421
' they'                     807        807
' are'                      525        525
' on'                       389        389
' the'                      279        279
' same'                    1852       1852
' diagonal'               37236      37236
'.'                          13         13
' So'                      2055       2055
' each'                    1817       1817
' diagonal'               37236      37236
' can'                      646        646
' contribute'             16792      16792
' some'                    1045       1045
' pairs'                  13530      13530
','                          11         11
' and'                      323        323
' the'                      279        279
' total'                   2790       2790
' is'                       374        374
' the'                      279        279
' sum'                     2629       2629
' over'                     916        916
' all'                      678        678
' diagon'                 84018      84018
'als'                      1127       1127
' of'                       315        315
' the'                      279        279
' combination'            10601      10601
' of'                       315        315
' bishops'                65623      65623
' in'                       304        304
' that'                     429        429
' diagonal'               37236      37236
' taken'                   4429       4429
' two'                     1378       1378
' at'                       518        518
' a'                        264        264
' time'                     882        882
'.\n\n'                     382        382
'First'                    5338       5338
','                          11         11
' I'                        358        358
' need'                    1184       1184
' to'                       311        311
' figure'                  7071       7071
' out'                      700        700
' how'                     1246       1246
' to'                       311        311
' group'                   1874       1874
' the'                      279        279
' bishops'                65623      65623
' into'                    1119       1119
' their'                    862        862
' respective'             19511      19511
' diagon'                 84018      84018
'als'                      1127       1127
'.'                          13         13
' There'                   2619       2619
' are'                      525        525
' two'                     1378       1378
' types'                   4494       4494
' of'                       315        315
' diagon'                 84018      84018
'als'                      1127       1127
':'                          25         25
' the'                      279        279
' ones'                    6174       6174
' that'                     429        429
' slope'                  30232      30232
' from'                     504        504
' top'                     1909       1909
'-left'                    7950       7950
' to'                       311        311
' bottom'                  5622       5622
'-right'                   6701       6701
' ('                        320        320
'let'                      1149       1149
"'s"                        594        594
' call'                    1618       1618
' them'                    1105       1105
' positive'                6785       6785
' diagon'                 84018      84018
'als'                      1127       1127
'),'                        701        701
' and'                      323        323
' the'                      279        279
' ones'                    6174       6174
' that'                     429        429
' slope'                  30232      30232
' from'                     504        504
' top'                     1909       1909
'-right'                   6701       6701
' to'                       311        311
' bottom'                  5622       5622
'-left'                    7950       7950
' ('                        320        320
'negative'                42224      42224
' diagon'                 84018      84018
'als'                      1127       1127
').\n\n'                   3593       3593
'For'                      2461       2461
' a'                        264        264
' positive'                6785       6785
' diagonal'               37236      37236
','                          11         11
' the'                      279        279
' key'                     1376       1376
' is'                       374        374
' x'                        856        856
' -'                        481        481
' y'                        379        379
'.'                          13         13
' Because'                 9211       9211
' along'                   3156       3156
' such'                    1741       1741
' a'                        264        264
' diagonal'               37236      37236
','                          11         11
' the'                      279        279
' difference'              6672       6672
' x'                        856        856
' -'                        481        481
' y'                        379        379
' remains'                 8458       8458
' constant'                6783       6783
'.'                          13         13
' For'                     1752       1752
' example'                 3110       3110
','                          11         11
' ('                        320        320
'1'                          16         16
','                          11         11
'1'                          16         16
')'                           8          8
' has'                      702        702
' x'                        856        856
'-y'                      12034      12034
'='                          28         28
'0'                          15         15
','                          11         11
' ('                        320        320
'2'                          17         17
','                          11         11
'2'                          17         17
')'                           8          8
' also'                    1083       1083
' '                         220        220
'0'                          15         15
','                          11         11
' etc'                     4992       4992
'.'                          13         13
' So'                      2055       2055
' all'                      678        678
' bishops'                65623      65623
' on'                       389        389
' the'                      279        279
' same'                    1852       1852
' positive'                6785       6785
' diagonal'               37236      37236
' will'                     686        686
' have'                     614        614
' the'                      279        279
' same'                    1852       1852
' x'                        856        856
'-y'                      12034      12034
' value'                    897        897
'.\n\n'                     382        382
'For'                      2461       2461
' the'                      279        279
' negative'                8225       8225
' diagon'                 84018      84018
'als'                      1127       1127
','                          11         11
' the'                      279        279
' sum'                     2629       2629
' x'                        856        856
' +'                        488        488
' y'                        379        379
' is'                       374        374
' constant'                6783       6783
'.'                          13         13
' Like'                    8909       8909
' ('                        320        320
'1'                          16         16
','                          11         11
'5'                          20         20
')'                           8          8
' and'                      323        323
' ('                        320        320
'2'                          17         17
','                          11         11
'4'                          19         19
')'                           8          8
' both'                    2176       2176
' sum'                     2629       2629
' to'                       311        311
' '                         220        220
'6'                          21         21
'.'                          13         13
' So'                      2055       2055
' bishops'                65623      65623
' on'                       389        389
' the'                      279        279
' same'                    1852       1852
' negative'                8225       8225
' diagonal'               37236      37236
' will'                     686        686
' have'                     614        614
' the'                      279        279
' same'                    1852       1852
' x'                        856        856
'+y'                      43010      43010
'.\n\n'                     382        382
'So'                       4416       4416
' the'                      279        279
' plan'                    3119       3119
' is'                       374        374
':\n\n'                    1447       1447
'1'                          16         16
'.'                          13         13
' For'                     1752       1752
' each'                    1817       1817
' bishop'                 53206      53206
','                          11         11
' compute'                12564      12564
' both'                    2176       2176
' x'                        856        856
'-y'                      12034      12034
' and'                      323        323
' x'                        856        856
'+y'                      43010      43010
'.\n'                       624        624
'2'                          17         17
'.'                          13         13
' For'                     1752       1752
' each'                    1817       1817
' of'                       315        315
' these'                   1493       1493
' two'                     1378       1378
' values'                  2750       2750
','                          11         11
' group'                   1874       1874
' the'                      279        279
' bishops'                65623      65623
' by'                       553        553
' them'                    1105       1105
'.\n'                       624        624
'3'                          18         18
'.'                          13         13
' For'                     1752       1752
' each'                    1817       1817
' group'                   1874       1874
' with'                     448        448
' k'                        595        595
' bishops'                65623      65623
','                          11         11
' add'                      912        912
' k'                        595        595
'*('                       6599       6599
'k'                          74         74
'-'                          12         12
'1'                          16         16
')/'                       5620       5620
'2'                          17         17
' to'                       311        311
' the'                      279        279
' total'                   2790       2790
' count'                   1760       1760
'.'                          13         13
' Because'                 9211       9211
' each'                    1817       1817
' pair'                    6716       6716
' in'                       304        304
' the'                      279        279
' group'                   1874       1874
' contributes'            42972      42972
' to'                       311        311
' the'                      279        279
' total'                   2790       2790
'.\n\n'                     382        382
'Wait'                    14190      14190
','                          11         11
' right'                   1290       1290
'.'                          13         13
' Because'                 9211       9211
' for'                      369        369
' any'                      894        894
' group'                   1874       1874
' of'                       315        315
' size'                    1379       1379
' k'                        595        595
','                          11         11
' the'                      279        279
' number'                  1372       1372
' of'                       315        315
' pairs'                  13530      13530
' is'                       374        374
' C'                        356        356
'(k'                       5969       5969
','                          11         11
'2'                          17         17
')'                           8          8
' which'                    892        892
' is'                       374        374
' k'                        595        595
'*('                       6599       6599
'k'                          74         74
'-'                          12         12
'1'                          16         16
')/'                       5620       5620
'2'                          17         17
'.\n\n'                     382        382
'So'                       4416       4416
' the'                      279        279
' steps'                   7354       7354
' are'                      525        525
':\n\n'                    1447       1447
'-'                          12         12
' Iterate'                54340      54340
' over'                     916        916
' all'                      678        678
' bishops'                65623      65623
'.\n'                       624        624
'-'                          12         12
' For'                     1752       1752
' each'                    1817       1817
','                          11         11
' calculate'              11047      11047
' the'                      279        279
' two'                     1378       1378
' keys'                    6894       6894
':'                          25         25
' x'                        856        856
'-y'                      12034      12034
' and'                      323        323
' x'                        856        856
'+y'                      43010      43010
'.\n'                       624        624
'-'                          12         12
' Use'                     5443       5443
' dictionaries'           57514      57514
' to'                       311        311
' count'                   1760       1760
' the'                      279        279
' number'                  1372       1372
' of'                       315        315
' bishops'                65623      65623
' in'                       304        304
' each'                    1817       1817
' diagonal'               37236      37236
' ('                        320        320
'both'                    21028      21028
' positive'                6785       6785
' and'                      323        323
' negative'                8225       8225
').\n'                     4292       4292
'-'                          12         12
' Then'                    5005       5005
','                          11         11
' for'                      369        369
' each'                    1817       1817
' count'                   1760       1760
' in'                       304        304
' the'                      279        279
' dictionaries'           57514      57514
','                          11         11
' compute'                12564      12564
' the'                      279        279
' combinations'           27459      27459
' and'                      323        323
' sum'                     2629       2629
' them'                    1105       1105
' all'                      678        678
'.\n\n'                     382        382
'Wait'                    14190      14190
','                          11         11
' but'                      714        714
' the'                      279        279
' problem'                 3491       3491
' states'                  5302       5302
' that'                     429        429
' two'                     1378       1378
' bishops'                65623      65623
' attack'                  3359       3359
' each'                    1817       1817
' other'                   1008       1008
' if'                       421        421
' they'                     807        807
' share'                   4332       4332
' the'                      279        279
' same'                    1852       1852
' diagonal'               37236      37236
'.'                          13         13
' But'                     1988       1988
' each'                    1817       1817
' bishop'                 53206      53206
' is'                       374        374
' part'                     949        949
' of'                       315        315
' two'                     1378       1378
' diagon'                 84018      84018
'als'                      1127       1127
' ('                        320        320
'positive'                30487      30487
' and'                      323        323
' negative'                8225       8225
').'                        568        568
' However'                 4354       4354
','                          11         11
' two'                     1378       1378
' bishops'                65623      65623
' can'                      646        646
' only'                    1172       1172
' attack'                  3359       3359
' each'                    1817       1817
' other'                   1008       1008
' if'                       421        421
' they'                     807        807
' are'                      525        525
' on'                       389        389
' the'                      279        279
' same'                    1852       1852
' positive'                6785       6785
' diagonal'               37236      37236
' OR'                      2726       2726
' the'                      279        279
' same'                    1852       1852
' negative'                8225       8225
' diagonal'               37236      37236
'.'                          13         13
' So'                      2055       2055
' each'                    1817       1817
' pair'                    6716       6716
' is'                       374        374
' counted'                29994      29994
' once'                    3055       3055
' if'                       421        421
' they'                     807        807
' share'                   4332       4332
' either'                  2987       2987
' of'                       315        315
' the'                      279        279
' two'                     1378       1378
' diagon'                 84018      84018
'als'                      1127       1127
'.\n\n'                     382        382
'But'                      3983       3983
' how'                     1246       1246
' do'                       653        653
' we'                       582        582
' avoid'                   5648       5648
' double'                  1990       1990
'-count'                  26580      26580
'ing'                       287        287
'?'                          30         30
' For'                     1752       1752
' example'                 3110       3110
','                          11         11
' two'                     1378       1378
' bishops'                65623      65623
' could'                   1410       1410
' be'                       387        387
' on'                       389        389
' the'                      279        279
' same'                    1852       1852
' positive'                6785       6785
' and'                      323        323
' same'                    1852       1852
' negative'                8225       8225
' diagonal'               37236      37236
'.'                          13         13
' But'                     1988       1988
' that'                     429        429
"'s"                        594        594
' impossible'             11997      11997
' unless'                  7241       7241
' they'                     807        807
' are'                      525        525
' the'                      279        279
' same'                    1852       1852
' point'                   1459       1459
','                          11         11
' which'                    892        892
' isn'                     4436       4436
"'t"                        944        944
' allowed'                 5420       5420
' here'                    1588       1588
'.'                          13         13
' Because'                 9211       9211
' if'                       421        421
' two'                     1378       1378
' bishops'                65623      65623
' are'                      525        525
' on'                       389        389
' the'                      279        279
' same'                    1852       1852
' x'                        856        856
'-y'                      12034      12034
' and'                      323        323
' same'                    1852       1852
' x'                        856        856
'+y'                      43010      43010
','                          11         11
' then'                    1221       1221
' solving'                21828      21828
' x'                        856        856
'1'                          16         16
' +'                        488        488
' y'                        379        379
'1'                          16         16
' ='                        284        284
' x'                        856        856
'2'                          17         17
' +'                        488        488
' y'                        379        379
'2'                          17         17
' and'                      323        323
' x'                        856        856
'1'                          16         16
' -'                        481        481
' y'                        379        379
'1'                          16         16
' ='                        284        284
' x'                        856        856
'2'                          17         17
' -'                        481        481
' y'                        379        379
'2'                          17         17
' would'                   1035       1035
' give'                    2968       2968
' x'                        856        856
'1'                          16         16
' ='                        284        284
' x'                        856        856
'2'                          17         17
' and'                      323        323
' y'                        379        379
'1'                          16         16
' ='                        284        284
' y'                        379        379
'2'                          17         17
','                          11         11
' which'                    892        892
' can'                      646        646
"'t"                        944        944
' happen'                  3537       3537
' since'                   2474       2474
' the'                      279        279
' positions'               9892       9892
' are'                      525        525
' unique'                  4911       4911
'.'                          13         13
' So'                      2055       2055
' no'                       902        902
' two'                     1378       1378
' bishops'                65623      65623
' can'                      646        646
' be'                       387        387
' on'                       389        389
' both'                    2176       2176
' the'                      279        279
' same'                    1852       1852
' positive'                6785       6785
' and'                      323        323
' same'                    1852       1852
' negative'                8225       8225
' diagonal'               37236      37236
'.'                          13         13
' So'                      2055       2055
' for'                      369        369
' each'                    1817       1817
' pair'                    6716       6716
' of'                       315        315
' bishops'                65623      65623
','                          11         11
' they'                     807        807
' are'                      525        525
' counted'                29994      29994
' either'                  2987       2987
' once'                    3055       3055
' ('                        320        320
'if'                        333        333
' they'                     807        807
' share'                   4332       4332
' either'                  2987       2987
' positive'                6785       6785
' or'                       476        476
' negative'                8225       8225
' diagonal'               37236      37236
')'                           8          8
' or'                       476        476
' not'                      537        537
' at'                       518        518
' all'                      678        678
'.'                          13         13
' Therefore'              15277      15277
','                          11         11
' the'                      279        279
' sum'                     2629       2629
' of'                       315        315
' the'                      279        279
' combinations'           27459      27459
' from'                     504        504
' both'                    2176       2176
' positive'                6785       6785
' and'                      323        323
' negative'                8225       8225
' diagon'                 84018      84018
'als'                      1127       1127
' will'                     686        686
' give'                    2968       2968
' the'                      279        279
' correct'                 4396       4396
' total'                   2790       2790
'.\n\n'                     382        382
'So'                       4416       4416
' the'                      279        279
' approach'                5486       5486
' is'                       374        374
' correct'                 4396       4396
'.'                          13         13
' So'                      2055       2055
' now'                     1431       1431
','                          11         11
' the'                      279        279
' code'                    2038       2038
' steps'                   7354       7354
':\n\n'                    1447       1447
'Read'                     4418       4418
' n'                        308        308
'.\n\n'                     382        382
'Then'                    12209      12209
' for'                      369        369
' each'                    1817       1817
' of'                       315        315
' the'                      279        279
' n'                        308        308
' bishops'                65623      65623
','                          11         11
' read'                    1349       1349
' x'                        856        856
'_i'                       5318       5318
' and'                      323        323
' y'                        379        379
'_i'                       5318       5318
'.\n\n'                     382        382
'Compute'                 46254      46254
' for'                      369        369
' each'                    1817       1817
' bishop'                 53206      53206
':\n\n'                    1447       1447
'sum'                      1242       1242
'_diag'                   61304      61304
' ='                        284        284
' x'                        856        856
' +'                        488        488
' y'                        379        379
'\n'                        198        198
'diff'                    13490      13490
'_diag'                   61304      61304
' ='                        284        284
' x'                        856        856
' -'                        481        481
' y'                        379        379
'\n\n'                      271        271
'We'                       1654       1654
' need'                    1184       1184
' to'                       311        311
' track'                   3754       3754
' the'                      279        279
' number'                  1372       1372
' of'                       315        315
' bishops'                65623      65623
' in'                       304        304
' each'                    1817       1817
' sum'                     2629       2629
'_diag'                   61304      61304
' and'                      323        323
' each'                    1817       1817
' diff'                    3638       3638
'_diag'                   61304      61304
'.\n\n'                     382        382
'So'                       4416       4416
' two'                     1378       1378
' dictionaries'           57514      57514
':'                          25         25
' one'                      825        825
' for'                      369        369
' sums'                   36398      36398
','                          11         11
' one'                      825        825
' for'                      369        369
' diffs'                  86947      86947
'.\n\n'                     382        382
'Then'                    12209      12209
','                          11         11
' for'                      369        369
' each'                    1817       1817
' key'                     1376       1376
' in'                       304        304
' sums'                   36398      36398
','                          11         11
' add'                      912        912
' C'                        356        356
'(count'                  11512      11512
','                          11         11
' '                         220        220
'2'                          17         17
')'                           8          8
' to'                       311        311
' the'                      279        279
' total'                   2790       2790
'.\n\n'                     382        382
'Same'                    19198      19198
' for'                      369        369
' the'                      279        279
' diffs'                  86947      86947
'.\n\n'                     382        382
'So'                       4416       4416
' the'                      279        279
' code'                    2038       2038
' will'                     686        686
' be'                       387        387
':\n\n'                    1447       1447
'Initialize'               9928       9928
' sum'                     2629       2629
'_counts'                 25977      25977
' and'                      323        323
' diff'                    3638       3638
'_counts'                 25977      25977
' as'                       438        438
' default'                 1638       1638
' dicts'                  97599      97599
' ('                        320        320
'or'                        269        269
' regular'                 5792       5792
' dicts'                  97599      97599
','                          11         11
' initialized'            17271      17271
' to'                       311        311
' '                         220        220
'0'                          15         15
').\n\n'                   3593       3593
'For'                      2461       2461
' each'                    1817       1817
' x'                        856        856
','                          11         11
' y'                        379        379
':\n\n'                    1447       1447
'sum'                      1242       1242
'_key'                     3097       3097
' ='                        284        284
' x'                        856        856
' +'                        488        488
' y'                        379        379
'\n\n'                      271        271
'diff'                    13490      13490
'_key'                     3097       3097
' ='                        284        284
' x'                        856        856
' -'                        481        481
' y'                        379        379
'\n\n'                      271        271
'sum'                      1242       1242
'_counts'                 25977      25977
'['                          58         58
'sum'                      1242       1242
'_key'                     3097       3097
']'                          60         60
' +='                      1421       1421
' '                         220        220
'1'                          16         16
'\n\n'                      271        271
'diff'                    13490      13490
'_counts'                 25977      25977
'['                          58         58
'diff'                    13490      13490
'_key'                     3097       3097
']'                          60         60
' +='                      1421       1421
' '                         220        220
'1'                          16         16
'\n\n'                      271        271
'Then'                    12209      12209
','                          11         11
' total'                   2790       2790
' ='                        284        284
' sum'                     2629       2629
'('                           7          7
' ('                        320        320
'c'                          66         66
'*('                       6599       6599
'c'                          66         66
'-'                          12         12
'1'                          16         16
')//'                     27151      27151
'2'                          17         17
')'                           8          8
' for'                      369        369
' c'                        272        272
' in'                       304        304
' sum'                     2629       2629
'_counts'                 25977      25977
'.values'                 10656      10656
'()'                        368        368
' )'                        873        873
' +'                        488        488
' sum'                     2629       2629
'('                           7          7
' ('                        320        320
'c'                          66         66
'*('                       6599       6599
'c'                          66         66
'-'                          12         12
'1'                          16         16
')//'                     27151      27151
'2'                          17         17
')'                           8          8
' for'                      369        369
' c'                        272        272
' in'                       304        304
' diff'                    3638       3638
'_counts'                 25977      25977
'.values'                 10656      10656
'()'                        368        368
' )\n\n'                   5125       5125
'That'                     4792       4792
"'s"                        594        594
' the'                      279        279
' answer'                  4226       4226
'.\n\n'                     382        382
'But'                      3983       3983
' since'                   2474       2474
' n'                        308        308
' can'                      646        646
' be'                       387        387
' up'                       705        705
' to'                       311        311
' '                         220        220
'2'                          17         17
'0'                          15         15
'0'                          15         15
','                          11         11
'0'                          15         15
'0'                          15         15
'0'                          15         15
','                          11         11
' and'                      323        323
' for'                      369        369
' each'                    1817       1817
' of'                       315        315
' them'                    1105       1105
' we'                       582        582
' process'                 1882       1882
' two'                     1378       1378
' dictionaries'           57514      57514
','                          11         11
' this'                     419        419
' should'                  1265       1265
' be'                       387        387
' efficient'              11050      11050
' enough'                  3322       3322
'.'                          13         13
' Because'                 9211       9211
' even'                    1496       1496
' with'                     448        448
' '                         220        220
'2'                          17         17
'0'                          15         15
'0'                          15         15
','                          11         11
'0'                          15         15
'0'                          15         15
'0'                          15         15
' entries'                10695      10695
','                          11         11
' the'                      279        279
' dictionaries'           57514      57514
' can'                      646        646
' handle'                  3705       3705
' that'                     429        429
'.'                          13         13
' And'                     1597       1597
' the'                      279        279
' sum'                     2629       2629
' is'                       374        374
' O'                        506        506
'(m'                       1255       1255
'),'                        701        701
' where'                   1380       1380
' m'                        296        296
' is'                       374        374
' the'                      279        279
' number'                  1372       1372
' of'                       315        315
' keys'                    6894       6894
' in'                       304        304
' each'                    1817       1817
' dictionary'             10997      10997
','                          11         11
' which'                    892        892
' is'                       374        374
' at'                       518        518
' most'                    1429       1429
' '                         220        220
'2'                          17         17
'0'                          15         15
'0'                          15         15
','                          11         11
'0'                          15         15
'0'                          15         15
'0'                          15         15
' *'                        353        353
' '                         220        220
'2'                          17         17
' in'                       304        304
' the'                      279        279
' worst'                  11785      11785
' case'                    1142       1142
','                          11         11
' which'                    892        892
' is'                       374        374
' manageable'             70028      70028
'.\n\n'                     382        382
'Testing'                 16451      16451
' the'                      279        279
' first'                   1156       1156
' example'                 3110       3110
':\n\n'                    1447       1447
'Input'                    2505       2505
' '                         220        220
'5'                          20         20
':\n\n'                    1447       1447
'Positions'               45793      45793
' are'                      525        525
' ('                        320        320
'1'                          16         16
','                          11         11
'1'                          16         16
'),'                        701        701
' ('                        320        320
'1'                          16         16
','                          11         11
'5'                          20         20
'),'                        701        701
' ('                        320        320
'3'                          18         18
','                          11         11
'3'                          18         18
'),'                        701        701
' ('                        320        320
'5'                          20         20
','                          11         11
'1'                          16         16
'),'                        701        701
' ('                        320        320
'5'                          20         20
','                          11         11
'5'                          20         20
').\n\n'                   3593       3593
'Looking'                 22464      22464
' at'                       518        518
' sum'                     2629       2629
'_diag'                   61304      61304
':\n\n'                    1447       1447
'('                           7          7
'1'                          16         16
'+'                          10         10
'1'                          16         16
')='                      11730      11730
'2'                          17         17
','                          11         11
' ('                        320        320
'1'                          16         16
'+'                          10         10
'5'                          20         20
')='                      11730      11730
'6'                          21         21
','                          11         11
' ('                        320        320
'3'                          18         18
'+'                          10         10
'3'                          18         18
')='                      11730      11730
'6'                          21         21
','                          11         11
' ('                        320        320
'5'                          20         20
'+'                          10         10
'1'                          16         16
')='                      11730      11730
'6'                          21         21
','                          11         11
' ('                        320        320
'5'                          20         20
'+'                          10         10
'5'                          20         20
')='                      11730      11730
'1'                          16         16
'0'                          15         15
'.\n\n'                     382        382
'So'                       4416       4416
' sum'                     2629       2629
'_counts'                 25977      25977
':\n\n'                    1447       1447
'2'                          17         17
':'                          25         25
' '                         220        220
'1'                          16         16
'\n\n'                      271        271
'6'                          21         21
':'                          25         25
' '                         220        220
'3'                          18         18
' ('                        320        320
'positions'               27436      27436
' '                         220        220
'1'                          16         16
','                          11         11
'5'                          20         20
';'                          26         26
' '                         220        220
'3'                          18         18
','                          11         11
'3'                          18         18
';'                          26         26
'5'                          20         20
','                          11         11
'1'                          16         16
'?)\n\n'                  57777      57777
'Wait'                    14190      14190
' wait'                    3783       3783
','                          11         11
' ('                        320        320
'1'                          16         16
','                          11         11
'5'                          20         20
')'                           8          8
' sum'                     2629       2629
' is'                       374        374
' '                         220        220
'6'                          21         21
','                          11         11
' ('                        320        320
'3'                          18         18
','                          11         11
'3'                          18         18
')'                           8          8
' sum'                     2629       2629
' is'                       374        374
' '                         220        220
'6'                          21         21
','                          11         11
' ('                        320        320
'5'                          20         20
','                          11         11
'1'                          16         16
')'                           8          8
' sum'                     2629       2629
' is'                       374        374
' '                         220        220
'6'                          21         21
'.'                          13         13
' So'                      2055       2055
' sum'                     2629       2629
' '                         220        220
'6'                          21         21
' has'                      702        702
' count'                   1760       1760
' '                         220        220
'3'                          18         18
'.\n\n'                     382        382
'Then'                    12209      12209
','                          11         11
' sum'                     2629       2629
' contribution'           18527      18527
' is'                       374        374
' '                         220        220
'3'                          18         18
' choose'                  5157       5157
' '                         220        220
'2'                          17         17
' ='                        284        284
' '                         220        220
'3'                          18         18
'.\n\n'                     382        382
'The'                       785        785
' other'                   1008       1008
' sum'                     2629       2629
' counts'                 14579      14579
' are'                      525        525
' '                         220        220
'2'                          17         17
':'                          25         25
'1'                          16         16
','                          11         11
' '                         220        220
'1'                          16         16
'0'                          15         15
':'                          25         25
'1'                          16         16
'.'                          13         13
' So'                      2055       2055
' sum'                     2629       2629
' contribution'           18527      18527
' is'                       374        374
' '                         220        220
'3'                          18         18
'.\n\n'                     382        382
'For'                      2461       2461
' the'                      279        279
' diff'                    3638       3638
'_diag'                   61304      61304
':\n\n'                    1447       1447
'('                           7          7
'1'                          16         16
'-'                          12         12
'1'                          16         16
')='                      11730      11730
'0'                          15         15
','                          11         11
' ('                        320        320
'1'                          16         16
'-'                          12         12
'5'                          20         20
')'                           8          8
'=-'                      10829      10829
'4'                          19         19
','                          11         11
' ('                        320        320
'3'                          18         18
'-'                          12         12
'3'                          18         18
')='                      11730      11730
'0'                          15         15
','                          11         11
' ('                        320        320
'5'                          20         20
'-'                          12         12
'1'                          16         16
')='                      11730      11730
'4'                          19         19
','                          11         11
' ('                        320        320
'5'                          20         20
'-'                          12         12
'5'                          20         20
')='                      11730      11730
'0'                          15         15
'.\n\n'                     382        382
'diff'                    13490      13490
'_counts'                 25977      25977
':\n\n'                    1447       1447
'0'                          15         15
':'                          25         25
'3'                          18         18
' ('                        320        320
'positions'               27436      27436
' '                         220        220
'1'                          16         16
','                          11         11
'1'                          16         16
';'                          26         26
'3'                          18         18
','                          11         11
'3'                          18         18
';'                          26         26
'5'                          20         20
','                          11         11
'5'                          20         20
')\n\n'                     692        692
'-'                          12         12
'4'                          19         19
':'                          25         25
'1'                          16         16
'\n\n'                      271        271
'4'                          19         19
':'                          25         25
'1'                          16         16
'.\n\n'                     382        382
'So'                       4416       4416
' diff'                    3638       3638
' contribution'           18527      18527
' is'                       374        374
' '                         220        220
'3'                          18         18
' choose'                  5157       5157
' '                         220        220
'2'                          17         17
' ='                        284        284
' '                         220        220
'3'                          18         18
'.\n\n'                     382        382
'So'                       4416       4416
' total'                   2790       2790
' sum'                     2629       2629
' is'                       374        374
' '                         220        220
'3'                          18         18
' ('                        320        320
'sum'                      1242       1242
')'                           8          8
' +'                        488        488
' '                         220        220
'3'                          18         18
' ('                        320        320
'diff'                    13490      13490
')'                           8          8
' ='                        284        284
' '                         220        220
'6'                          21         21
'.'                          13         13
' Which'                  15920      15920
' matches'                 9071       9071
' the'                      279        279
' first'                   1156       1156
' example'                 3110       3110
"'s"                        594        594
' output'                  2550       2550
'.\n\n'                     382        382
'Yes'                      9454       9454
','                          11         11
' that'                     429        429
"'s"                        594        594
' correct'                 4396       4396
'.\n\n'                     382        382
'Another'                 14037      14037
' example'                 3110       3110
':\n\n'                    1447       1447
'Input'                    2505       2505
' '                         220        220
'3'                          18         18
':\n\n'                    1447       1447
'('                           7          7
'1'                          16         16
','                          11         11
'1'                          16         16
'),'                        701        701
' ('                        320        320
'2'                          17         17
','                          11         11
'3'                          18         18
'),'                        701        701
' ('                        320        320
'3'                          18         18
','                          11         11
'5'                          20         20
').\n\n'                   3593       3593
'sum'                      1242       1242
'_diag'                   61304      61304
':\n\n'                    1447       1447
'1'                          16         16
'+'                          10         10
'1'                          16         16
'='                          28         28
'2'                          17         17
' ('                        320        320
'count'                    1830       1830
' '                         220        220
'1'                          16         16
')\n\n'                     692        692
'2'                          17         17
'+'                          10         10
'3'                          18         18
'='                          28         28
'5'                          20         20
' ('                        320        320
'count'                    1830       1830
' '                         220        220
'1'                          16         16
')\n\n'                     692        692
'3'                          18         18
'+'                          10         10
'5'                          20         20
'='                          28         28
'8'                          23         23
' ('                        320        320
'count'                    1830       1830
' '                         220        220
'1'                          16         16
').'                        568        568
' Sum'                     8116       8116
' contribution'           18527      18527
' '                         220        220
'0'                          15         15
'.\n\n'                     382        382
'diff'                    13490      13490
'_diag'                   61304      61304
':\n\n'                    1447       1447
'1'                          16         16
'-'                          12         12
'1'                          16         16
'='                          28         28
'0'                          15         15
' ('                        320        320
'count'                    1830       1830
'1'                          16         16
')\n\n'                     692        692
'2'                          17         17
'-'                          12         12
'3'                          18         18
' ='                        284        284
' -'                        481        481
'1'                          16         16
' ('                        320        320
'count'                    1830       1830
'1'                          16         16
')\n\n'                     692        692
'3'                          18         18
'-'                          12         12
'5'                          20         20
' ='                        284        284
' -'                        481        481
'2'                          17         17
' ('                        320        320
'count'                    1830       1830
'1'                          16         16
').'                        568        568
' So'                      2055       2055
' diff'                    3638       3638
' contribution'           18527      18527
' '                         220        220
'0'                          15         15
'.\n\n'                     382        382
'Total'                    7595       7595
' '                         220        220
'0'                          15         15
'.'                          13         13
' Correct'                39970      39970
'.\n\n'                     382        382
'So'                       4416       4416
' the'                      279        279
' code'                    2038       2038
' should'                  1265       1265
' work'                     975        975
'.\n\n'                     382        382
'Now'                      7039       7039
','                          11         11
' coding'                 10822      10822
' this'                     419        419
' in'                       304        304
' Python'                 13027      13027
'.\n\n'                     382        382
'The'                       785        785
' code'                    2038       2038
' should'                  1265       1265
' read'                    1349       1349
' from'                     504        504
' stdin'                  31369      31369
'.'                          13         13
' Then'                    5005       5005
','                          11         11
' compute'                12564      12564
' the'                      279        279
' sum'                     2629       2629
' and'                      323        323
' diff'                    3638       3638
' counts'                 14579      14579
'.\n\n'                     382        382
'Implement'               62980      62980
' as'                       438        438
':\n\n'                    1447       1447
'Read'                     4418       4418
' n'                        308        308
'.\n\n'                     382        382
'sum'                      1242       1242
'_counts'                 25977      25977
' ='                        284        284
' defaultdict'            42908      42908
'(int'                     1548       1548
')\n\n'                     692        692
'diff'                    13490      13490
'_counts'                 25977      25977
' ='                        284        284
' defaultdict'            42908      42908
'(int'                     1548       1548
')\n\n'                     692        692
'for'                      1958       1958
' _'                        716        716
' in'                       304        304
' range'                   2088       2088
'(n'                       1445       1445
'):\n\n'                   7731       7731
'   '                       262        262
' x'                        856        856
','                          11         11
' y'                        379        379
' ='                        284        284
' map'                     2415       2415
'(int'                     1548       1548
','                          11         11
' input'                   1946       1946
'().'                      1005       1005
'split'                    6960       6960
'())\n\n'                 12367      12367
'   '                       262        262
' s'                        274        274
' ='                        284        284
' x'                        856        856
' +'                        488        488
' y'                        379        379
'\n\n'                      271        271
'   '                       262        262
' d'                        294        294
' ='                        284        284
' x'                        856        856
' -'                        481        481
' y'                        379        379
'\n\n'                      271        271
'   '                       262        262
' sum'                     2629       2629
'_counts'                 25977      25977
'[s'                      11880      11880
']'                          60         60
' +='                      1421       1421
' '                         220        220
'1'                          16         16
'\n\n'                      271        271
'   '                       262        262
' diff'                    3638       3638
'_counts'                 25977      25977
'[d'                      21427      21427
']'                          60         60
' +='                      1421       1421
' '                         220        220
'1'                          16         16
'\n\n'                      271        271
'total'                    5035       5035
' ='                        284        284
' '                         220        220
'0'                          15         15
'\n\n'                      271        271
'for'                      1958       1958
' c'                        272        272
' in'                       304        304
' sum'                     2629       2629
'_counts'                 25977      25977
'.values'                 10656      10656
'():\n\n'                 39974      39974
'   '                       262        262
' total'                   2790       2790
' +='                      1421       1421
' c'                        272        272
' *'                        353        353
' ('                        320        320
'c'                          66         66
'-'                          12         12
'1'                          16         16
')'                           8          8
' //'                       442        442
' '                         220        220
'2'                          17         17
'\n\n'                      271        271
'for'                      1958       1958
' c'                        272        272
' in'                       304        304
' diff'                    3638       3638
'_counts'                 25977      25977
'.values'                 10656      10656
'():\n\n'                 39974      39974
'   '                       262        262
' total'                   2790       2790
' +='                      1421       1421
' c'                        272        272
' *'                        353        353
' ('                        320        320
'c'                          66         66
'-'                          12         12
'1'                          16         16
')'                           8          8
' //'                       442        442
' '                         220        220
'2'                          17         17
'\n\n'                      271        271
'print'                    1350       1350
'(total'                  22842      22842
')\n\n'                     692        692
'Yes'                      9454       9454
','                          11         11
' that'                     429        429
"'s"                        594        594
' straightforward'        30339      30339
'.\n\n'                     382        382
'Testing'                 16451      16451
' with'                     448        448
' the'                      279        279
' first'                   1156       1156
' example'                 3110       3110
':\n\n'                    1447       1447
'sum'                      1242       1242
'_counts'                 25977      25977
' for'                      369        369
' '                         220        220
'6'                          21         21
' is'                       374        374
' '                         220        220
'3'                          18         18
' ('                        320        320
'from'                     1499       1499
' ('                        320        320
'1'                          16         16
','                          11         11
'5'                          20         20
'),'                        701        701
' ('                        320        320
'3'                          18         18
','                          11         11
'3'                          18         18
'),'                        701        701
' ('                        320        320
'5'                          20         20
','                          11         11
'1'                          16         16
')).'                      4579       4579
' So'                      2055       2055
' '                         220        220
'3'                          18         18
'*'                           9          9
'2'                          17         17
'/'                          14         14
'2'                          17         17
' ='                        284        284
'3'                          18         18
'.\n\n'                     382        382
'diff'                    13490      13490
'_counts'                 25977      25977
' for'                      369        369
' '                         220        220
'0'                          15         15
' is'                       374        374
' '                         220        220
'3'                          18         18
' ('                        320        320
'1'                          16         16
','                          11         11
'1'                          16         16
';'                          26         26
'3'                          18         18
','                          11         11
'3'                          18         18
';'                          26         26
'5'                          20         20
','                          11         11
'5'                          20         20
')'                           8          8
' →'                      11397      11397
' '                         220        220
'3'                          18         18
'.'                          13         13
' So'                      2055       2055
' total'                   2790       2790
' '                         220        220
'6'                          21         21
'.\n\n'                     382        382
'Another'                 14037      14037
' example'                 3110       3110
','                          11         11
' as'                       438        438
' before'                  1573       1573
'.\n\n'                     382        382
'But'                      3983       3983
' the'                      279        279
' code'                    2038       2038
' reads'                  15804      15804
' from'                     504        504
' stdin'                  31369      31369
'.'                          13         13
' So'                      2055       2055
' the'                      279        279
' function'                 729        729
' should'                  1265       1265
' be'                       387        387
' written'                 5326       5326
' to'                       311        311
' read'                    1349       1349
' inputs'                 11127      11127
','                          11         11
' process'                 1882       1882
','                          11         11
' and'                      323        323
' output'                  2550       2550
'.\n\n'                     382        382
'But'                      3983       3983
' the'                      279        279
' problem'                 3491       3491
' says'                    2727       2727
' to'                       311        311
' generate'                6923       6923
' an'                       458        458
' executable'             32156      32156
' Python'                 13027      13027
' function'                 729        729
' that'                     429        429
' reads'                  15804      15804
' stdin'                  31369      31369
' and'                      323        323
' prints'                 23473      23473
' the'                      279        279
' output'                  2550       2550
'.\n\n'                     382        382
'So'                       4416       4416
' the'                      279        279
' code'                    2038       2038
' would'                   1035       1035
' be'                       387        387
':\n\n'                    1447       1447
'import'                    474        474
' sys'                     5708       5708
'\n'                        198        198
'from'                     1499       1499
' collections'            15302      15302
' import'                  1159       1159
' defaultdict'            42908      42908
'\n\n'                      271        271
'def'                       750        750
' main'                    1887       1887
'():\n'                    3932       3932
'   '                       262        262
' n'                        308        308
' ='                        284        284
' int'                      526        526
'(sys'                    18140      18140
'.stdin'                  43184      43184
'.readline'               31800      31800
'())\n'                    2398       2398
'   '                       262        262
' sum'                     2629       2629
'_counts'                 25977      25977
' ='                        284        284
' defaultdict'            42908      42908
'(int'                     1548       1548
')\n'                       340        340
'   '                       262        262
' diff'                    3638       3638
'_counts'                 25977      25977
' ='                        284        284
' defaultdict'            42908      42908
'(int'                     1548       1548
')\n'                       340        340
'   '                       262        262
' for'                      369        369
' _'                        716        716
' in'                       304        304
' range'                   2088       2088
'(n'                       1445       1445
'):\n'                      982        982
'       '                   286        286
' x'                        856        856
','                          11         11
' y'                        379        379
' ='                        284        284
' map'                     2415       2415
'(int'                     1548       1548
','                          11         11
' sys'                     5708       5708
'.stdin'                  43184      43184
'.readline'               31800      31800
'().'                      1005       1005
'split'                    6960       6960
'())\n'                    2398       2398
'       '                   286        286
' sum'                     2629       2629
'_key'                     3097       3097
' ='                        284        284
' x'                        856        856
' +'                        488        488
' y'                        379        379
'\n'                        198        198
'       '                   286        286
' diff'                    3638       3638
'_key'                     3097       3097
' ='                        284        284
' x'                        856        856
' -'                        481        481
' y'                        379        379
'\n'                        198        198
'       '                   286        286
' sum'                     2629       2629
'_counts'                 25977      25977
'['                          58         58
'sum'                      1242       1242
'_key'                     3097       3097
']'                          60         60
' +='                      1421       1421
' '                         220        220
'1'                          16         16
'\n'                        198        198
'       '                   286        286
' diff'                    3638       3638
'_counts'                 25977      25977
'['                          58         58
'diff'                    13490      13490
'_key'                     3097       3097
']'                          60         60
' +='                      1421       1421
' '                         220        220
'1'                          16         16
'\n'                        198        198
'   '                       262        262
' total'                   2790       2790
' ='                        284        284
' '                         220        220
'0'                          15         15
'\n'                        198        198
'   '                       262        262
' for'                      369        369
' cnt'                    13195      13195
' in'                       304        304
' sum'                     2629       2629
'_counts'                 25977      25977
'.values'                 10656      10656
'():\n'                    3932       3932
'       '                   286        286
' total'                   2790       2790
' +='                      1421       1421
' cnt'                    13195      13195
' *'                        353        353
' ('                        320        320
'cnt'                     15853      15853
' -'                        481        481
'1'                          16         16
')'                           8          8
' //'                       442        442
'2'                          17         17
'\n'                        198        198
'   '                       262        262
' for'                      369        369
' cnt'                    13195      13195
' in'                       304        304
' diff'                    3638       3638
'_counts'                 25977      25977
'.values'                 10656      10656
'():\n'                    3932       3932
'       '                   286        286
' total'                   2790       2790
' +='                      1421       1421
' cnt'                    13195      13195
' *'                        353        353
' ('                        320        320
'cnt'                     15853      15853
' -'                        481        481
'1'                          16         16
')'                           8          8
' //'                       442        442
'2'                          17         17
'\n'                        198        198
'   '                       262        262
' print'                   1173       1173
'(total'                  22842      22842
')\n\n'                     692        692
'main'                     3817       3817
'()\n\n'                   2822       2822
'But'                      3983       3983
' in'                       304        304
' the'                      279        279
' problem'                 3491       3491
' statement'               5114       5114
','                          11         11
' the'                      279        279
' function'                 729        729
' should'                  1265       1265
' be'                       387        387
' called'                  2598       2598
' after'                   1283       1283
' definition'              7271       7271
'.'                          13         13
' So'                      2055       2055
' that'                     429        429
"'s"                        594        594
' correct'                 4396       4396
'.\n\n'                     382        382
'Yes'                      9454       9454
','                          11         11
' that'                     429        429
"'s"                        594        594
' the'                      279        279
' code'                    2038       2038
'.'                          13         13
' It'                      1084       1084
' should'                  1265       1265
' handle'                  3705       3705
' all'                      678        678
' cases'                   5048       5048
'.\n\n'                     382        382
'Edge'                    11656      11656
' Cases'                  46024      46024
':\n\n'                    1447       1447
'n'                          77         77
'='                          28         28
'1'                          16         16
':'                          25         25
' output'                  2550       2550
' '                         220        220
'0'                          15         15
'.\n\n'                     382        382
'n'                          77         77
'='                          28         28
'2'                          17         17
','                          11         11
' same'                    1852       1852
' sum'                     2629       2629
' or'                       476        476
' same'                    1852       1852
' diff'                    3638       3638
':'                          25         25
' output'                  2550       2550
' '                         220        220
'1'                          16         16
'.\n\n'                     382        382
'But'                      3983       3983
' the'                      279        279
' code'                    2038       2038
' works'                   4278       4278
'.\n\n'                     382        382
'Another'                 14037      14037
' case'                    1142       1142
':'                          25         25
' bishops'                65623      65623
' in'                       304        304
' same'                    1852       1852
' sum'                     2629       2629
' but'                      714        714
' different'               2155       2155
' diffs'                  86947      86947
'.'                          13         13
' So'                      2055       2055
' they'                     807        807
' contribute'             16792      16792
' '                         220        220
'1'                          16         16
' pair'                    6716       6716
'.'                          13         13
' Or'                      2521       2521
' same'                    1852       1852
' diff'                    3638       3638
' but'                      714        714
' different'               2155       2155
' sum'                     2629       2629
','                          11         11
' contribute'             16792      16792
' '                         220        220
'1'                          16         16
'.\n\n'                     382        382
'So'                       4416       4416
' code'                    2038       2038
' seems'                   4977       4977
' correct'                 4396       4396
'.\n\n'                     382        382
'<'                          27         27
'|'                          91         91
'end'                       408        408
'_of'                      3575       3575
'_th'                      5854       5854
'ought'                    2450       2450
'|'                          91         91
'>\n\n'                    1339       1339
'<'                          27         27
'|'                          91         91
'begin'                    7265       7265
'_of'                      3575       3575
'_solution'               50274      50274
'|'                          91         91
'>\n\n'                    1339       1339
'To'                       1249       1249
' solve'                  11625      11625
' this'                     419        419
' problem'                 3491       3491
','                          11         11
' we'                       582        582
' need'                    1184       1184
' to'                       311        311
' determine'               8253       8253
' the'                      279        279
' number'                  1372       1372
' of'                       315        315
' pairs'                  13530      13530
' of'                       315        315
' bishops'                65623      65623
' that'                     429        429
' attack'                  3359       3359
' each'                    1817       1817
' other'                   1008       1008
' on'                       389        389
' a'                        264        264
' '                         220        220
'1'                          16         16
'0'                          15         15
'0'                          15         15
'0'                          15         15
'x'                          87         87
'1'                          16         16
'0'                          15         15
'0'                          15         15
'0'                          15         15
' grid'                    5827       5827
'.'                          13         13
' B'                        425        425
'ishops'                  50109      50109
' attack'                  3359       3359
' each'                    1817       1817
' other'                   1008       1008
' if'                       421        421
' they'                     807        807
' are'                      525        525
' on'                       389        389
' the'                      279        279
' same'                    1852       1852
' diagonal'               37236      37236
','                          11         11
' either'                  2987       2987
' from'                     504        504
' top'                     1909       1909
'-left'                    7950       7950
' to'                       311        311
' bottom'                  5622       5622
'-right'                   6701       6701
' ('                        320        320
'positive'                30487      30487
' diagonal'               37236      37236
')'                           8          8
' or'                       476        476
' from'                     504        504
' top'                     1909       1909
'-right'                   6701       6701
' to'                       311        311
' bottom'                  5622       5622
'-left'                    7950       7950
' ('                        320        320
'negative'                42224      42224
' diagonal'               37236      37236
').\n\n'                   3593       3593
'###'                     14374      14374
' Approach'               53084      53084
'\n'                        198        198
'1'                          16         16
'.'                          13         13
' **'                      3070       3070
'Ident'                   28301      28301
'ify'                      1437       1437
' Di'                      7767       7767
'agon'                     6113       6113
'als'                      1127       1127
'**:'                     95518      95518
' Each'                    8886       8886
' bishop'                 53206      53206
' can'                      646        646
' be'                       387        387
' part'                     949        949
' of'                       315        315
' two'                     1378       1378
' diagon'                 84018      84018
'als'                      1127       1127
':\n'                       510        510
'  '                        256        256
' -'                        481        481
' **'                      3070       3070
'Positive'                35490      35490
' Di'                      7767       7767
'agonal'                  23450      23450
'**:'                     95518      95518
' Character'              15633      15633
'ized'                     1506       1506
' by'                       553        553
' the'                      279        279
' difference'              6672       6672
' \\('                    17767      17767
'x'                          87         87
' -'                        481        481
' y'                        379        379
'\\'                         59         59
'),'                        701        701
' which'                    892        892
' remains'                 8458       8458
' constant'                6783       6783
' for'                      369        369
' all'                      678        678
' positions'               9892       9892
' on'                       389        389
' the'                      279        279
' same'                    1852       1852
' positive'                6785       6785
' diagonal'               37236      37236
'.\n'                       624        624
'  '                        256        256
' -'                        481        481
' **'                      3070       3070
'Negative'                38489      38489
' Di'                      7767       7767
'agonal'                  23450      23450
'**:'                     95518      95518
' Character'              15633      15633
'ized'                     1506       1506
' by'                       553        553
' the'                      279        279
' sum'                     2629       2629
' \\('                    17767      17767
'x'                          87         87
' +'                        488        488
' y'                        379        379
'\\'                         59         59
'),'                        701        701
' which'                    892        892
' remains'                 8458       8458
' constant'                6783       6783
' for'                      369        369
' all'                      678        678
' positions'               9892       9892
' on'                       389        389
' the'                      279        279
' same'                    1852       1852
' negative'                8225       8225
' diagonal'               37236      37236
'.\n\n'                     382        382
'2'                          17         17
'.'                          13         13
' **'                      3070       3070
'Count'                    2507       2507
' B'                        425        425
'ishops'                  50109      50109
' on'                       389        389
' Each'                    8886       8886
' Di'                      7767       7767
'agonal'                  23450      23450
'**:'                     95518      95518
' Use'                     5443       5443
' two'                     1378       1378
' dictionaries'           57514      57514
' to'                       311        311
' count'                   1760       1760
' the'                      279        279
' number'                  1372       1372
' of'                       315        315
' bishops'                65623      65623
' on'                       389        389
' each'                    1817       1817
' positive'                6785       6785
' and'                      323        323
' negative'                8225       8225
' diagonal'               37236      37236
'.'                          13         13
' The'                      576        576
' key'                     1376       1376
' for'                      369        369
' positive'                6785       6785
' diagon'                 84018      84018
'als'                      1127       1127
' is'                       374        374
' \\('                    17767      17767
'x'                          87         87
' -'                        481        481
' y'                        379        379
'\\)'                     57758      57758
' and'                      323        323
' for'                      369        369
' negative'                8225       8225
' diagon'                 84018      84018
'als'                      1127       1127
' is'                       374        374
' \\('                    17767      17767
'x'                          87         87
' +'                        488        488
' y'                        379        379
'\\'                         59         59
').\n\n'                   3593       3593
'3'                          18         18
'.'                          13         13
' **'                      3070       3070
'Calculate'               47866      47866
' P'                        393        393
'airs'                     4720       4720
'**:'                     95518      95518
' For'                     1752       1752
' each'                    1817       1817
' diagonal'               37236      37236
' ('                        320        320
'both'                    21028      21028
' positive'                6785       6785
' and'                      323        323
' negative'                8225       8225
'),'                        701        701
' if'                       421        421
' there'                   1052       1052
' are'                      525        525
' \\('                    17767      17767
'k'                          74         74
'\\)'                     57758      57758
' bishops'                65623      65623
' on'                       389        389
' a'                        264        264
' diagonal'               37236      37236
','                          11         11
' the'                      279        279
' number'                  1372       1372
' of'                       315        315
' attacking'              22818      22818
' pairs'                  13530      13530
' is'                       374        374
' given'                   2661       2661
' by'                       553        553
' the'                      279        279
' combination'            10601      10601
' formula'                14806      14806
' \\('                    17767      17767
'C'                          34         34
'(k'                       5969       5969
','                          11         11
' '                         220        220
'2'                          17         17
')'                           8          8
' ='                        284        284
' k'                        595        595
' \\'                      1124       1124
'times'                   15136      15136
' ('                        320        320
'k'                          74         74
' -'                        481        481
' '                         220        220
'1'                          16         16
')'                           8          8
' /'                        608        608
' '                         220        220
'2'                          17         17
'\\'                         59         59
').'                        568        568
' Sum'                     8116       8116
' these'                   1493       1493
' values'                  2750       2750
' for'                      369        369
' all'                      678        678
' diagon'                 84018      84018
'als'                      1127       1127
' to'                       311        311
' get'                      633        633
' the'                      279        279
' total'                   2790       2790
' number'                  1372       1372
' of'                       315        315
' attacking'              22818      22818
' pairs'                  13530      13530
'.\n\n'                     382        382
'###'                     14374      14374
' Solution'               12478      12478
' Code'                    6119       6119
'\n'                        198        198
'```'                     73594      73594
'python'                  12669      12669
'\n'                        198        198
'import'                    474        474
' sys'                     5708       5708
'\n'                        198        198
'from'                     1499       1499
' collections'            15302      15302
' import'                  1159       1159
' defaultdict'            42908      42908
'\n\n'                      271        271
'def'                       750        750
' main'                    1887       1887
'():\n'                    3932       3932
'   '                       262        262
' n'                        308        308
' ='                        284        284
' int'                      526        526
'(sys'                    18140      18140
'.stdin'                  43184      43184
'.readline'               31800      31800
'())\n'                    2398       2398
'   '                       262        262
' sum'                     2629       2629
'_counts'                 25977      25977
' ='                        284        284
' defaultdict'            42908      42908
'(int'                     1548       1548
')\n'                       340        340
'   '                       262        262
' diff'                    3638       3638
'_counts'                 25977      25977
' ='                        284        284
' defaultdict'            42908      42908
'(int'                     1548       1548
')\n'                       340        340
'   '                       262        262
' for'                      369        369
' _'                        716        716
' in'                       304        304
' range'                   2088       2088
'(n'                       1445       1445
'):\n'                      982        982
'       '                   286        286
' x'                        856        856
','                          11         11
' y'                        379        379
' ='                        284        284
' map'                     2415       2415
'(int'                     1548       1548
','                          11         11
' sys'                     5708       5708
'.stdin'                  43184      43184
'.readline'               31800      31800
'().'                      1005       1005
'split'                    6960       6960
'())\n'                    2398       2398
'       '                   286        286
' sum'                     2629       2629
'_key'                     3097       3097
' ='                        284        284
' x'                        856        856
' +'                        488        488
' y'                        379        379
'\n'                        198        198
'       '                   286        286
' diff'                    3638       3638
'_key'                     3097       3097
' ='                        284        284
' x'                        856        856
' -'                        481        481
' y'                        379        379
'\n'                        198        198
'       '                   286        286
' sum'                     2629       2629
'_counts'                 25977      25977
'['                          58         58
'sum'                      1242       1242
'_key'                     3097       3097
']'                          60         60
' +='                      1421       1421
' '                         220        220
'1'                          16         16
'\n'                        198        198
'       '                   286        286
' diff'                    3638       3638
'_counts'                 25977      25977
'['                          58         58
'diff'                    13490      13490
'_key'                     3097       3097
']'                          60         60
' +='                      1421       1421
' '                         220        220
'1'                          16         16
'\n'                        198        198
'   '                       262        262
' total'                   2790       2790
' ='                        284        284
' '                         220        220
'0'                          15         15
'\n'                        198        198
'   '                       262        262
' for'                      369        369
' cnt'                    13195      13195
' in'                       304        304
' sum'                     2629       2629
'_counts'                 25977      25977
'.values'                 10656      10656
'():\n'                    3932       3932
'       '                   286        286
' total'                   2790       2790
' +='                      1421       1421
' cnt'                    13195      13195
' *'                        353        353
' ('                        320        320
'cnt'                     15853      15853
' -'                        481        481
' '                         220        220
'1'                          16         16
')'                           8          8
' //'                       442        442
' '                         220        220
'2'                          17         17
'\n'                        198        198
'   '                       262        262
' for'                      369        369
' cnt'                    13195      13195
' in'                       304        304
' diff'                    3638       3638
'_counts'                 25977      25977
'.values'                 10656      10656
'():\n'                    3932       3932
'       '                   286        286
' total'                   2790       2790
' +='                      1421       1421
' cnt'                    13195      13195
' *'                        353        353
' ('                        320        320
'cnt'                     15853      15853
' -'                        481        481
' '                         220        220
'1'                          16         16
')'                           8          8
' //'                       442        442
' '                         220        220
'2'                          17         17
'\n'                        198        198
'   '                       262        262
' print'                   1173       1173
'(total'                  22842      22842
')\n\n'                     692        692
'main'                     3817       3817
'()\n'                      741        741
'``'                      13874      13874
'`\n\n'                   19324      19324
'###'                     14374      14374
' Explanation'            71287      71287
'\n'                        198        198
'1'                          16         16
'.'                          13         13
' **'                      3070       3070
'Reading'                 31899      31899
' Input'                   5571       5571
'**:'                     95518      95518
' The'                      576        576
' input'                   1946       1946
' is'                       374        374
' read'                    1349       1349
' from'                     504        504
' standard'                5297       5297
' input'                   1946       1946
'.'                          13         13
' The'                      576        576
' first'                   1156       1156
' line'                    1555       1555
' contains'                5610       5610
' the'                      279        279
' number'                  1372       1372
' of'                       315        315
' bishops'                65623      65623
','                          11         11
' followed'                8110       8110
' by'                       553        553
' their'                    862        862
' positions'               9892       9892
'.\n'                       624        624
'2'                          17         17
'.'                          13         13
' **'                      3070       3070
'Tracking'                37119      37119
' Di'                      7767       7767
'agon'                     6113       6113
'als'                      1127       1127
'**:'                     95518      95518
' Two'                     9043       9043
' dictionaries'           57514      57514
','                          11         11
' `'                       1565       1565
'sum'                      1242       1242
'_counts'                 25977      25977
'`'                          63         63
' and'                      323        323
' `'                       1565       1565
'diff'                    13490      13490
'_counts'                 25977      25977
'`,'                       7808       7808
' are'                      525        525
' used'                    1483       1483
' to'                       311        311
' count'                   1760       1760
' the'                      279        279
' number'                  1372       1372
' of'                       315        315
' bishops'                65623      65623
' on'                       389        389
' each'                    1817       1817
' negative'                8225       8225
' and'                      323        323
' positive'                6785       6785
' diagonal'               37236      37236
','                          11         11
' respectively'           15576      15576
'.\n'                       624        624
'3'                          18         18
'.'                          13         13
' **'                      3070       3070
'Calcul'                  57908      57908
'ating'                    1095       1095
' P'                        393        393
'airs'                     4720       4720
'**:'                     95518      95518
' For'                     1752       1752
' each'                    1817       1817
' diagonal'               37236      37236
' ('                        320        320
'sum'                      1242       1242
' and'                      323        323
' difference'              6672       6672
'),'                        701        701
' we'                       582        582
' calculate'              11047      11047
' the'                      279        279
' number'                  1372       1372
' of'                       315        315
' pairs'                  13530      13530
' using'                   1667       1667
' the'                      279        279
' combination'            10601      10601
' formula'                14806      14806
' and'                      323        323
' sum'                     2629       2629
' these'                   1493       1493
' values'                  2750       2750
' to'                       311        311
' get'                      633        633
' the'                      279        279
' total'                   2790       2790
' number'                  1372       1372
' of'                       315        315
' attacking'              22818      22818
' pairs'                  13530      13530
'.\n\n'                     382        382
'This'                     1986       1986
' approach'                5486       5486
' efficiently'            29720      29720
' groups'                  5203       5203
' bishops'                65623      65623
' by'                       553        553
' their'                    862        862
' diagon'                 84018      84018
'als'                      1127       1127
' and'                      323        323
' calculates'             47417      47417
' the'                      279        279
' attacking'              22818      22818
' pairs'                  13530      13530
' in'                       304        304
' linear'                 13482      13482
' time'                     882        882
','                          11         11
' making'                  3259       3259
' it'                       432        432
' suitable'               14452      14452
' for'                      369        369
' large'                   3460       3460
' input'                   1946       1946
' sizes'                  12282      12282
' up'                       705        705
' to'                       311        311
' '                         220        220
'2'                          17         17
'0'                          15         15
'0'                          15         15
','                          11         11
'0'                          15         15
'0'                          15         15
'0'                          15         15
' bishops'                65623      65623
'.\n\n'                     382        382
'<'                          27         27
'|'                          91         91
'end'                       408        408
'_of'                      3575       3575
'_solution'               50274      50274
'|'                          91         91
'>'                          29         29
'<|im_end|>'             151645     151645
'\n'                        198        198
````