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 sys
import math
input = sys.stdin.readline
 
t = int(input())

'''
FastestFinger
Ashishgup
primes = [3]

for i in range(4, int((10**9) ** 0.5) + 3):
    ok = 1
    for j in range(int(i**0.5) + 2):
        if i % j == 0 and i!=j:
            ok = 0
    if ok == 1 and i%2==1:
        primes.append(i)
        
print(primes)
'''

for i in range(t):
    a = int(input())
    
    if a==1:
        print('FastestFinger')
    elif a==2:
        print('Ashishgup')
    elif a%2==1:
        print('Ashishgup')
    elif a%2==0:
        ok = 0
        for j in range(3, int(a**0.5) + 1, 2):
            #print(j)
            if a % j == 0:
                if a//j > 2 and (a//j) % 2 == 0:
                    ok = 1
                    break
                
                x = a//j
                if x%2==1:
                    if a//x > 2 and (a//x) % 2 == 0:
                        ok = 1
                        break
                    
        if ok == 0:
            if a%4 == 0:
                while a%2==0:
                    a = a//2
                if a>2:
                    ok = 1
                    
        if ok == 1:
            print('Ashishgup')
        else:
            print('FastestFinger')