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 mx = -1e18;
long long mn = 1e18;
long long M = 1e9 + 7;
long long mod(long long x) { return ((x % M + M) % M); }
bool prime(long long n) {
  if (n < 2)
    return false;
  else if (n == 2)
    return true;
  else if (n % 2 == 0)
    return false;
  else {
    for (long long i = 3; i <= sqrt(n); i = i + 2) {
      if (n % i == 0) return false;
    }
  }
  return true;
}
void solve() {
  long long n;
  cin >> n;
  if (n % 2 == 1) {
    if (n == 1)
      cout << "FastestFinger" << endl;
    else
      cout << "Ashishgup" << endl;
    return;
  }
  if (n == 2) {
    cout << "Ashishgup" << endl;
    return;
  }
  long long x = 0;
  while (n > 1) {
    if (n % 2 == 0) {
      x++;
      n /= 2;
    } else {
      if (prime(n) == true) {
        if (x > 1)
          cout << "Ashishgup" << endl;
        else
          cout << "FastestFinger" << endl;
        return;
      }
      cout << "Ashishgup" << endl;
      return;
    }
  }
  cout << "FastestFinger" << endl;
  return;
}
int main() {
  long long t;
  cin >> t;
  while (t--) {
    solve();
  }
}
