From Zero to Infinity

#include <bits/stdc++.h>
using namespace std;
struct R{double tot=0,in=0;};
bool vowel(char c){
    return c=='a'||c=='e'||c=='i'||c=='o'||c=='u';
}
bool ForAlice(string s){
    for (int i=0; i<s.size(); i++){
        int vw=0,cn=0;
        vowel(s[i]) ? vw++:cn++;
        for (int j=i+1; j<s.size(); j++){
            vowel(s[j]) ? vw++:cn++;
            if (cn>vw) return false;
        }
    }
    return true;
}
int main(){
    int t,n;
    cin>>t;
    while (cin>>n){
        vector<string> alice,bob;
        string s;
        while (n--){
            cin>>s;
            if (ForAlice(s)) alice.push_back(s);
            else bob.push_back(s);
        }

        R cntA[200], cntB[200];
        for (auto it:alice){
            //cout<<it<<" ";puts("");
            int fl[200]={0};
            for (auto jt:it){
                cntA[jt].tot++;
                if (!fl[jt]) cntA[jt].in++;
                fl[jt]=1;
            }
        }
        for (auto it:bob){
            //cout<<it<<" ";puts("");
            int fl[200]={0};
            for (auto jt:it){
                cntB[jt].tot++;
                if (!fl[jt]) cntB[jt].in++;
                fl[jt]=1;
            }
        }

        double scoreA=1,scoreB=1,sa=alice.size(),sb=bob.size(),f=1;
        //printf("%f %f\n",sa,sb);
        for (int i='a'; i<='z' && f; i++){
            if (cntA[i].in){
                scoreA*=cntA[i].in/
                    pow(cntA[i].tot,sa);
                //printf("Alice=%c=%.0f/%.0f\n",i,cntA[i].in,cntA[i].tot);
            }

            if (cntB[i].in){
                scoreB*=cntB[i].in/
                    pow(cntB[i].tot,sb);
                //printf("Bob=%c=%.0f/%.0f\n",i,cntB[i].in,cntB[i].tot);
            }
            //if (scoreA>1e7 || scoreB>1e7) f=0;
        }
        double ans=scoreA/scoreB;
        if (ans>1e7) puts("Infinity");
        else printf("%.7f\n",ans);
    }
}