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;
void print(long long int a[], long long int n) {
  for (long long int i = 0; i < n; i++) {
    cout << a[i] << " ";
  }
  cout << "\n";
}
long long int power(long long int x) {
  long long int u = 0;
  while (x % 2 == 0) {
    u++;
    x = x / 2;
  }
  return u;
}
long long int powM(long long int x, long long int y, long long int m) {
  long long int ans = 1, r = 1;
  x %= m;
  while (r > 0 && r <= y) {
    if (r & y) {
      ans *= x;
      ans %= m;
    }
    r <<= 1;
    x *= x;
    x %= m;
  }
  return ans;
}
int powm(long long int a, long long int b) {
  long long int res = 1;
  while (b) {
    if (b & 1) res = (res * a);
    a = (a * a);
    b >>= 1;
  }
  return res;
}
long long int gcd(long long int a, long long int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
bool isPrime(int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t1 = 1;
  cin >> t1;
  long long int M = 1e9 + 7;
  while (t1--) {
    long long int n;
    cin >> n;
    long long int u = power(n);
    if (u == 1) {
      if (n == 2) {
        cout << "Ashishgup\n";
      } else {
        n = n / 2;
        if (isPrime(n)) {
          cout << "FastestFinger\n";
        } else {
          cout << "Ashishgup\n";
        }
      }
    } else {
      if (powm(2, u) == n) {
        cout << "FastestFinger\n";
      } else {
        cout << "Ashishgup\n";
      }
    }
  }
  return 0;
}
