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 
player = ["Ashishgup", "FastestFinger"]

def isPrime (m): 
    if m <2: 
        return False
    i=2
    while i*i <= m: 
        if m%i == 0: 
            return False
        i += 1 

    return True

T = int(input()) 
for _ in range (T): 
    n = int(input()) 
    if n == 1: 
        print (player[1]) 
        continue 

    if n%2 == 1: 
        print (player[0]) 
        continue

    if n ==2 :
        print (player[0]) 
        continue

    if math.floor(math.log2(n)) == math.ceil(math.log2(n)): 
        print (player[1]) 
        continue
    
    if n%4 == 0: 
        print (player[0]) 
        continue

    m = n//2 
    if isPrime (m): 
        print (player[1]) 
    else: 
        print (player[0]) 