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 gcd(long long int a, long long int b) {
  return b ? gcd(b, a % b) : a;
}
long long int lcm(long long int a, long long int b) {
  return a * b / gcd(a, b);
}
long long int po(long long int a, long long int b, long long int m) {
  a %= m;
  long long int res = 1;
  while (b > 0) {
    if (b & 1) res = (res * a) % m;
    a = (a * a) % m;
    b >>= 1;
  }
  return res;
}
vector<int> pri;
bool pr[1000001] = {0};
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    if (n == 1)
      cout << "FastestFinger\n";
    else if (n == 2)
      cout << "Ashishgup\n";
    else if (n & 1) {
      cout << "Ashishgup\n";
    } else {
      int e2 = 0, ee = 0, i, l = n;
      while (n % 2 == 0) {
        e2++;
        n /= 2;
      }
      for (i = 3; i * i <= n; i += 2) {
        if (n % i == 0) {
          int k = n;
          while (n % i == 0) {
            ee++;
            n /= i;
          }
        }
      }
      if (n > 2) ee++;
      if (ee == 0)
        cout << "FastestFinger\n";
      else if (e2 == 1) {
        if (ee > 1)
          cout << "Ashishgup\n";
        else
          cout << "FastestFinger\n";
      } else
        cout << "Ashishgup\n";
    }
  }
  return 0;
}
