// Hacker Cup 2017 // Final Round // Fox Moles // Jacob Plachta #include <algorithm> #include <functional> #include <numeric> #include <iostream> #include <iomanip> #include <cstdio> #include <cmath> #include <complex> #include <cstdlib> #include <ctime> #include <cstring> #include <cassert> #include <string> #include <vector> #include <list> #include <map> #include <set> #include <deque> #include <queue> #include <stack> #include <bitset> #include <sstream> using namespace std; #define LL long long #define LD long double #define PR pair<int,int> #define Fox(i,n) for (i=0; i<n; i++) #define Fox1(i,n) for (i=1; i<=n; i++) #define FoxI(i,a,b) for (i=a; i<=b; i++) #define FoxR(i,n) for (i=(n)-1; i>=0; i--) #define FoxR1(i,n) for (i=n; i>0; i--) #define FoxRI(i,a,b) for (i=b; i>=a; i--) #define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) #define Min(a,b) a=min(a,b) #define Max(a,b) a=max(a,b) #define Sz(s) int((s).size()) #define All(s) (s).begin(),(s).end() #define Fill(s,v) memset(s,v,sizeof(s)) #define pb push_back #define mp make_pair #define x first #define y second template<typename T> T Abs(T x) { return(x<0 ? -x : x); } template<typename T> T Sqr(T x) { return(x*x); } const int INF = (int)1e9; const LD EPS = 1e-12; const LD PI = acos(-1.0); bool Read(int &x) { char c,r=0,n=0; x=0; for(;;) { c=getchar(); if ((c<0) && (!r)) return(0); if ((c=='-') && (!r)) n=1; else if ((c>='0') && (c<='9')) x=x*10+c-'0',r=1; else if (r) break; } if (n) x=-x; return(1); } #define LIM 900009 int K,A,B; map<int,int> M; vector<int> con[LIM],con2[LIM]; bool col0[LIM]; int col[LIM],ind[LIM],P1[LIM],P2[LIM],dist[LIM]; int Make(int i) { if (M.count(i)) return(M[i]); return(M[i]=K++); } bool DFS(int i,int c) { // conflict? if ((col0[i]) && (c) || (col[i]>=0) && (c!=col[i])) return(0); // already coloured? if (col[i]>=0) return(1); // colour node and its neighbours col[i]=c; int j; Fox(j,Sz(con[i])) if (!DFS(con[i][j],1-c)) return(0); return(1); } bool MatchBFS() { int i,a,b,a2; queue<int> Q; Fill(dist,60); Fox(a,A) if (P1[a]<0) dist[a]=0,Q.push(a); while (!Q.empty()) { a=Q.front(),Q.pop(); if (dist[a]<dist[A]) Fox(i,Sz(con2[a])) { b=con2[a][i]; a2=P2[b]; if (dist[a2]>=INF) dist[a2]=dist[a]+1,Q.push(a2); } } return(dist[A]<INF); } bool MatchDFS(int a) { if (a==A) return(1); int i,b,a2; Fox(i,Sz(con2[a])) { b=con2[a][i]; a2=P2[b]; if ((dist[a2]==dist[a]+1) && (MatchDFS(a2))) { P1[a]=b; P2[b]=a; return(1); } } dist[a]=INF; return(0); } int MaxMatching() { int a,b,m=0; Fill(P1,-1); Fox(b,B) P2[b]=A; while (MatchBFS()) { Fox(a,A) if ((P1[a]<0) && (MatchDFS(a))) m++; } return(m); } int main() { // vars int T,t; int N=0; int i,j,a,b,p,r,z,ans; // testcase loop Read(T); Fox1(t,T) { // init Fox(i,K) con[i].clear(); Fox(i,A) con2[i].clear(); K=0; M.clear(); Fill(col0,0); Fill(col,-1); Fill(ind,-1); Fill(P1,-1); Fill(P2,-1); // input Read(N); while (N--) { Read(p),Read(r); i=Make(p),a=Make(p-r),b=Make(p+r); col0[i]=1; con[a].pb(b); con[b].pb(a); } // attempt to 2-color the graph (initially just from forced nodes) Fox(z,2) Fox(i,K) if (col[i]<0) { if ((!z) && (!col0[i])) continue; if (!DFS(i,0)) { ans=-1; goto Done; } } // construct the bipartite graph, ignoring forced nodes A=B=0; Fox(i,K) if (!col0[i]) { Fox(j,Sz(con[i])) if (col0[con[i][j]]) goto Skip; if (!col[i]) ind[i]=A++; else ind[i]=B++; Skip:; } Fox(i,K) if ((ind[i]>=0) && (!col[i])) { a=ind[i]; Fox(j,Sz(con[i])) { b=ind[con[i][j]]; if (b>=0) con2[a].pb(b); } } ans=A+B-MaxMatching()+1; // output Done:; printf("Case #%d: %d\n",t,ans); } return(0); }