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.
import logging, sys
from math import sqrt
logging.basicConfig(level=logging.INFO)

def main():
    test = int(sys.stdin.readline())
    while(test > 0):
        test -= 1
        n = int(sys.stdin.readline())
        S = int(sqrt(n))
        kt = int(0)
        if(n % 2 == 1 and n > 1):
            kt = 1
            print('Ashishgup')
            continue
        if(n == 2):
            kt = 1
            print('Ashishgup')
            continue
        le = 0
        for k in range(2, S + 1, 1):
            if(n % k == 0):
                if(k % 2 == 1):
                    le += 1
                if((n / k) % 2 == 1):
                    le += 1
        if(le > 1):
            print('Ashishgup')
        else:
            if(le == 0):
                print('FastestFinger')
            else:
                if((n / 2) % 2 == 1):
                    print('FastestFinger')
                else:
                    print('Ashishgup')

if __name__ == "__main__":
    try:
        sys.stdin = open('input.txt', 'r')
        sys.stdout = open('output.txt', 'w')
    except:
        pass
    main()