Ashishgup and FastestFinger play a game. 

They start with a number n and play in turns. In each turn, a player can make any one of the following moves:

  * Divide n by any of its odd divisors greater than 1. 
  * Subtract 1 from n if n is greater than 1. 



Divisors of a number include the number itself.

The player who is unable to make a move loses the game.

Ashishgup moves first. Determine the winner of the game if both of them play optimally.

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.

The only line of each test case contains a single integer — n (1 ≤ n ≤ 10^9).

Output

For each test case, print "Ashishgup" if he wins, and "FastestFinger" otherwise (without quotes).

Example

Input


7
1
2
3
4
5
6
12


Output


FastestFinger
Ashishgup
Ashishgup
FastestFinger
Ashishgup
FastestFinger
Ashishgup

Note

In the first test case, n = 1, Ashishgup cannot make a move. He loses.

In the second test case, n = 2, Ashishgup subtracts 1 on the first move. Now n = 1, FastestFinger cannot make a move, so he loses.

In the third test case, n = 3, Ashishgup divides by 3 on the first move. Now n = 1, FastestFinger cannot make a move, so he loses.

In the last test case, n = 12, Ashishgup divides it by 3. Now n = 4, FastestFinger is forced to subtract 1, and Ashishgup gets 3, so he wins by dividing it by 3.
#include <bits/stdc++.h>
using namespace std;
vector<bool> prime(200002, true);
void seive(long long mx) {
  prime[0] = prime[1] = false;
  for (long long i = 2; i * i <= mx; i++) {
    if (prime[i]) {
      for (long long j = i * i; j <= mx; j += i) {
        prime[j] = false;
      }
    }
  }
}
const long long M = 1e9 + 7;
const long long Mxn = 3e5;
long long power(long long i, long long p) {
  long long ans = 1;
  while (p) {
    if (p & 1) ans = (ans * i) % M;
    i = (i * i) % M;
    p /= 2;
  }
  return ans % M;
}
int main() {
  int t = 1;
  cin >> t;
  while (t--) {
    long long n;
    cin >> n;
    if (n == 1) {
      cout << "FastestFinger" << endl;
    } else if (n == 2) {
      cout << "Ashishgup" << endl;
    } else if (n & 1)
      cout << "Ashishgup" << endl;
    else {
      long long cnt = 0;
      while (n % 2 == 0) {
        cnt++;
        n /= 2;
      }
      if (cnt > 1 && n != 1) {
        cout << "Ashishgup" << endl;
      } else if (n == 1) {
        cout << "FastestFinger" << endl;
      } else {
        long long cnti = 0;
        vector<long long> v;
        v.push_back(n);
        for (long long i = 3; i * i <= n; i++) {
          if (n % i == 0) {
            v.push_back(i);
            if (i * i != n) v.push_back(n / i);
          }
        }
        sort(v.begin(), v.end());
        for (long long i = 0; i < v.size(); i++) {
          while (n % v[i] == 0) {
            n /= v[i];
            cnti++;
          }
        }
        if (cnti > 1)
          cout << "Ashishgup" << endl;
        else
          cout << "FastestFinger" << endl;
      }
    }
  }
  return 0;
}
