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.

# Problem 3: Number game

import sys

def solve(n):
    """
    Ashishgup
    FastestFinger
    """
    pow2 = []
    for i in range(1, 30):
        pow2.append(1 << i)
        
    if n == 1:
        return "FastestFinger"
        
    elif n == 2:
        return "Ashishgup"
        
    elif n % 2 == 0:
        if n in pow2:
            return "FastestFinger"
            
        elif (n // 2) % 2 == 1:
            oddFactors = 0
            n //= 2
            for i in range(3, int(n ** 0.5) + 2, 2):
                if n % i == 0:
                    oddFactors += 1
                    
            if oddFactors >= 1:
                return "Ashishgup"
                
            else:
                return "FastestFinger"
            
    return "Ashishgup"
    
caseCount = int(next(sys.stdin))

ans = ""

for i in range(caseCount):
    ans += solve(int(next(sys.stdin))) + "\n"
    
print(ans)