// Integers as a Service // 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 2000 int N; char O[LIM]; int V[LIM],R[LIM]; map minE,maxE,Fv,Fr; map::iterator I; map Fact(int v) { map F; int p,e; for (p=2; p*p<=v; p++) { e=0; while (v%p==0) v/=p,e++; if (e) F[p]=e; } if (v>1) F[v]=1; return(F); } void SetMin(int p,int e) { Max(minE[p],e); } void SetMax(int p,int e) { if (maxE.count(p)) Min(maxE[p],e); else maxE[p]=e; } int main() { if (DEBUG) freopen("in.txt","r",stdin); // vars int T,t; int i,p,e,ev,er; LL ans; bool hasAP; set AP; set::iterator J,K; // testcase loop Read(T); Fox1(t,T) { // init printf("Case #%d: ",t); minE.clear(),maxE.clear(); hasAP=0; // input Read(N); Fox(i,N) scanf("%c%d%d\n",&O[i],&V[i],&R[i]); // assemble prime exponent requirements based on original requirements Fox(i,N) { Fv=Fact(V[i]),Fr=Fact(R[i]); if (O[i]=='G') { if (V[i]%R[i]) goto Imp; Foxen(I,Fv) { p=I->x,ev=I->y; er=Fr[p]; SetMin(p,er); if (ev>er) SetMax(p,er); } } else { if (R[i]%V[i]) goto Imp; Foxen(I,Fr) { p=I->x,er=I->y; ev=Fv[p]; SetMax(p,er); if (evx); } else for (J=AP.begin(); J!=AP.end();) { K=J,J++; if (!Fr.count(*K)) AP.erase(K); } } } // construct min. valid value of X ans=1; Foxen(I,minE) { p=I->x,e=I->y; if ((e) && (hasAP) && (!AP.count(p))) goto Imp; if ((maxE.count(p)) && (maxE[p]INF) goto Imp; } } // output printf("%lld\n",ans); continue; Imp:; printf("-1\n"); } return(0); }