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.
from bisect import bisect_left as lower_bound, bisect_right as upper_bound
from sys import stdin, stdout
from collections import defaultdict

def solve(n):
    i = 2
    cnt = 0

    while i*i <= n:
        if n%i == 0: cnt += 2
        i += 1

    if cnt == 0: cnt += 1
    return cnt

def main():
    t = int(input())

    for _ in range(t):
        n = int(input())
        
        if n == 1:
            print("FastestFinger")
            continue

        if (n&1) or (n == 2):
            print("Ashishgup")
            continue

        if n&(n-1) == 0:
            print("FastestFinger")
            continue

        cnt = 0

        while n%2 == 0:
            n //= 2
            cnt += 1

        if cnt > 1: print("Ashishgup")

        else:
            ret = solve(n)

            if ret&1: print("FastestFinger")
            else: print("Ashishgup")


if __name__ == "__main__": main()
