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;
long long int e = 0, o = 0;
void primeFactors(long long int n) {
  while (n % 2 == 0) {
    e++;
    n = n / 2;
  }
  for (long long int i = 3; i <= sqrt(n); i = i + 2) {
    while (n % i == 0) {
      if (i % 2 == 0) {
        e++;
      } else {
        o++;
      }
      n = n / i;
    }
  }
  if (n > 2) {
    if (n % 2 == 0) {
      e++;
    } else {
      o++;
    }
  }
}
void solve() {
  long long int i, j, k, l, n, m, a, b, c, d, x, y;
  cin >> n;
  if (n == 1) {
    cout << "FastestFinger" << endl;
    return;
  }
  e = 0;
  o = 0;
  primeFactors(n);
  if (o == 0) {
    if (e > 1) {
      cout << "FastestFinger" << endl;
    } else {
      cout << "Ashishgup" << endl;
    }
  } else {
    if (e == 0) {
      cout << "Ashishgup" << endl;
    } else if (e == 1) {
      if (o == 1) {
        cout << "FastestFinger" << endl;
      } else {
        cout << "Ashishgup" << endl;
      }
    } else {
      if (o == 0) {
        cout << "FastestFinger" << endl;
      } else {
        cout << "Ashishgup" << endl;
      }
    }
  }
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}
