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.
# Contest No.: 651
# Problem No.: C
# Solver:      JEMINI
# Date:        20200620

import sys
import heapq

def main():
    tempList = [True] * (10 ** 5 + 1)
    tempList[0] = False
    tempList[1] = False
    for i in range(10 ** 5 + 1):
        if tempList[i]:
            cnt = i * 2
            while cnt < 10 ** 5 + 1:
                tempList[cnt] = False
                cnt += i
    prime = []
    for i in range(10 ** 5 + 1):
        if tempList[i]:
            prime.append(i)

    t = int(input())
    for _ in range(t):
        n = int(input())
        if n == 2:
            print("Ashishgup")
            continue
        if n == 1:
            print("FastestFinger")
            continue
        if n % 2:
            print("Ashishgup")
            continue
        
        twoCnt = 0
        oddCnt = 0
        tempN = n
        for p in prime:
            if tempN < p:
                break
            while tempN % p == 0:
                tempN = tempN // p
                if p == 2:
                    twoCnt += 1
                else:
                    oddCnt += 1
        if tempN != 1:
            oddCnt += 1
        
        if oddCnt == 0:
            print("FastestFinger")
            continue
        
        elif twoCnt == 1:
            if oddCnt == 1:
                print("FastestFinger")
                continue
            else:
                print("Ashishgup")
                continue
        else:
            print("Ashishgup")
            continue
        
        
        
    return

if __name__ == "__main__":
    main()