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;
const int mod = 1000000007;
const double long pi = std::acos(-1);
int gcd(int a, int b) {
  if (!b) {
    return a;
  }
  return gcd(b, a % b);
}
int gcdE(int a, int b, int* x, int* y) {
  if (!a) {
    *x = 0;
    *y = 1;
    return b;
  }
  int x1, y1;
  int _gcd = gcdE(b % a, a, &x1, &y1);
  *x = y1 - (b / a) * x1;
  *y = x1;
  return _gcd;
}
long long int power(long long int x, long long int y) {
  long long int res = 1;
  while (y) {
    if (y & 1) {
      res = (res * x) % mod;
    }
    y >>= 1;
    x = (x * x) % mod;
  }
  return res;
}
long long int inverse(long long int x) { return power(x, mod - 2); }
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  while (t--) {
    long long n;
    cin >> n;
    if (n == 1) {
      cout << "FastestFinger"
           << "\n";
      continue;
    }
    if (n == 2) {
      cout << "Ashishgup"
           << "\n";
      continue;
    }
    if (n % 2) {
      cout << "Ashishgup"
           << "\n";
      continue;
    }
    long long counter = 0;
    long long counter2 = 0;
    long long k = n;
    while (n % 2 == 0) {
      counter2 += 1;
      n = n / 2;
    }
    for (long long i = 3; i <= sqrt(n); i += 2) {
      while (n % i == 0) {
        counter += 1;
        n = n / i;
      }
    }
    if (n != 1) {
      counter += 1;
    }
    if (counter == 0) {
      cout << "FastestFinger"
           << "\n";
      continue;
    }
    if (counter2 == 1) {
      if (counter == 1) {
        cout << "FastestFinger"
             << "\n";
        continue;
      } else {
        cout << "Ashishgup"
             << "\n";
        continue;
      }
    } else {
      cout << "Ashishgup"
           << "\n";
      continue;
    }
  }
}
