2019/round3/integers_as_service.cpp

// Integers as a Service
// Solution by Jacob Plachta

#define DEBUG 0

#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); }
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<int,int> minE,maxE,Fv,Fr;
map<int,int>::iterator I;

map<int,int> Fact(int v)
{
	map<int,int> 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<int> AP;
	set<int>::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 (ev<er)
										SetMin(p,er);
							}
							if (!hasAP)
							{
								hasAP=1,AP.clear();
									Foxen(I,Fr)
										AP.insert(I->x);
							}
							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]<e))
							goto Imp;
						while (e--)
						{
							ans*=p;
								if (ans>INF)
									goto Imp;
						}
				}
			// output
			printf("%lld\n",ans);
			continue;
Imp:;
			printf("-1\n");
		}
	return(0);
}