// Graph Gift // Solution by Jacob Plachta #define DEBUG 0 #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define LL long long #define LD long double #define PR pair #define Fox(i,n) for (i=0; 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 T Abs(T x) { return(x<0 ? -x : x); } template T Sqr(T x) { return(x*x); } string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } const int INF = (int)1e9; const LD EPS = 1e-12; const LD PI = acos(-1.0); #if DEBUG #define GETCHAR getchar #else #define GETCHAR getchar_unlocked #endif 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 30003 int NA,NB; LL A[LIM],B[LIM]; LL SB[LIM]; LL mem3[LIM]; // cost for cross-pairing B values such that ny = n-y LL Comp3(int ny) { if (mem3[ny]) return(mem3[ny]); int i; LL ans=0; Fox(i,(ny-1)/2) ans+=B[NB-i-2]*B[NB-ny+i]; return(mem3[ny]=ans); } // min. cost for connecting last B values LL Comp2(int n) { if (!n) return(0); if ((n==1) && (NB>=2)) return(B[NB-1]*B[NB-2]); int y; LL cur,ans=(LL)6e18; // pair first y values with the last value Fox1(y,n-1) { if ((n-y-1)%2) continue; cur=B[NB-1]*(SB[NB-n+y]-SB[NB-n]); // cross-pair the remaining n-y-1 values cur+=Comp3(n-y); Min(ans,cur); } return(ans); } // min. cost with last x A values paired with different B values LL Comp1(int x) { int i; LL ans=0; Fox(i,NA-x) ans-=B[0]*A[i]; Fox(i,x) ans-=B[i+1]*A[NA-x+i]; ans+=Comp2(NB-x-1); return(ans); } int main() { if (DEBUG) freopen("in.txt","r",stdin); // vars int T,t; int N; int i,x; LL ans,v; // testcase loop Read(T); Fox1(t,T) { // input Read(N); NA=NB=0; while (N--) { Read(x); if (x>0) A[NA++]=x; else B[NB++]=-x; } // sort each list in non-increasing order sort(A,A+NA); sort(B,B+NB); reverse(A,A+NA); reverse(B,B+NB); // precompute prefix sums Fox(i,NB) SB[i+1]=SB[i]+B[i]; // special case: all positive/negative? Fill(mem3,0); if ((!NA) || (!NB)) { if (!NB) { NB=NA; memcpy(B,A,sizeof(A)); Fox(i,NB) SB[i+1]=SB[i]+B[i]; } ans=Comp2(NB); } else { // try all parameters ans=(LL)6e18; Fox(x,min(NA,NB)) Min(ans,Comp1(x)); } // output printf("Case #%d: %lld\n",t,ans); } return(0); }