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.
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Jun 20 22:04:11 2020

@author: shailesh
"""
#def make_sieve(upper_limit):
#    l = [0 for i in range(upper_limit+1)] #1 indicates composite
#    for i in range(4,upper_limit+1,2):
#        l[i] = 1
#    curr_divisor = 3
#    while(curr_divisor  < int(math.sqrt(upper_limit))+1):
#        while(l[curr_divisor] == 1):
#            curr_divisor += 2
#        loop_val = 2*curr_divisor
#        while(loop_val <= upper_limit):
##            print(loop_val)
#            l[loop_val] = 1
#            loop_val += curr_divisor
#        curr_divisor += 2
#        
##    prime_list = [i for i in range(upper_limit) if l[i]== 0]
#    return l
import math

def check_prime(x):
    if x == 1:
        return 1
    root = int(math.sqrt(x))
    if x%2 == 0:
        return 0
    for i in range(3,root+1):
        if x%i == 0:
            return 0
    return 1

#import math
def check_int(x):
    return math.floor(x) == x
T = int(input())
#prime_list = make_sieve(10**9 + 1)
for t in range(T):
    n = int(input())
#    x = math.log2(n)
    count = 0
    if n%2 == 1:
        if n==1:
            print("FastestFinger")
        else:
            print("Ashishgup")
    else:
        if n == 2:
            print("Ashishgup")
        else:
            while(n%2 ==0):
                n//=2
                count +=1
            if count != 1:
                if n == 1:
                    print("FastestFinger")
                else:
                    print("Ashishgup")
            else:
                if not check_prime(n):
                    #prime
                    print("Ashishgup")
                else:
                    print("FastestFinger")
                
            
            
                