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 math

def isPrimes2(n):
    if n > 1:
        if n == 2:
            return True
        if n % 2 == 0:
            return False
        for x in range(3, int(math.sqrt(n) + 1), 2):
            if n % x == 0:
                return False
        return True
    return False

def isok(n):
    while n!=1:
        if n%2==1:
            return False
        n/=2
    return True

def main():
    # t = int(input())
    # list1 = list(map(int, input().split()))
    # ans1 = 0
    # ans2 = 0
    # for i in range(len(list1)):
    #     ans1 += list1[i]**2
    # for i in range(len(list1)):
    #
    # for t in range(int(input())):
    t = int(input())
    for i in range(t):
        n = int(input())
        if n == 1:
            print("FastestFinger")
        elif n == 2:
            print("Ashishgup")
        elif n % 2 == 1:
            print("Ashishgup")
        else:
            k = n / 2
            if isok(k) or (k%2 == 1 and isPrimes2(k)):
                print("FastestFinger")
            else:
                print("Ashishgup")
            # if cnt2 == 0:
            #     print("FastestFinger")
            # elif cnt2 == 1 and cnt1 == 1:
            #     print("FastestFinger")
            # elif cnt2 == 1 and cnt1 > 1:
            #     print("Ashishgup")
            # elif cnt2 > 1:
            #     print("Ashishgup")

if __name__ == '__main__':
    main()