C. Number Game

#include <bits/stdc++.h>
using namespace std;
typedef pair<int,int> ii;

const int MaxN = 1e9 + 2e2;
const int N = (int)sqrt(MaxN) + 1;
map<ii ,int> Memo;
vector<int> Div;
int n;

int calc(int n ,bool T) {
    //  T = Ashishgup
    // !T = FastestFinger

    int &Re = Memo[ {n,T} ];

    if(Re != 0) return Re;
    if( n % 2 &&  T ) return Re = +1;
    if( n % 2 && !T ) return Re = -1;

    int Res = -1;
    for(auto i : Div){
        if( i <= n && n % i == 0) {
            if( (n / i) % 2 == 0 ){
                Res = calc(n / i ,!T);
                if( Res == 1 )
                    break;
            }
        }
    }
    if( Res == -1 ) Res = calc(n-1 ,!T);
    return Re = Res;
}

void Solve(){
    scanf("%d" ,&n);

    for(int i=2 ; i <= (int)sqrt(n) + 1 ; i ++){
        if(n % i == 0) {
            if( i & 1 )
                Div.push_back(i);
            if( (n / i) & 1 && (n / i) > 1 )
                Div.push_back(n/i);
        }
    }

    bool Ashishgup     = true;
    bool FastestFinger = false;

    Memo[ {1 ,Ashishgup} ]     = -1;
    Memo[ {1 ,FastestFinger} ] = +1;
    int Ans = calc(n ,1);

    puts( (Ans > 0) ? "Ashishgup" : "FastestFinger" );
    Div.clear();
}

int main() {
    int Tc; scanf("%d" ,&Tc);
    while( Tc-- ) Solve();
    return 0;
}