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.
from math import sqrt

def countfact(n):
    count=0
    for i in range(3,int(sqrt(n))+1,2):
        while n%i==0:
            count+=1
            n=n//i
            if count>1:
                break
        if count>1:
            break

    if n>2:
        count+=1
    return count

for _ in range(int(input())):
    n = int(input())
    if n%2==1 and n>1:
        print('Ashishgup')
        continue
    if n==1:
        print('FastestFinger')
        continue
    if n==2:
        print('Ashishgup')
        continue
    if n%2==0 and n>2:
        count_2 = 0
        while n%2==0:
            count_2+=1
            n=n//2
        if n>1:
            if count_2==1:
                count=countfact(n)
                if count==1:
                    print('FastestFinger')
                    continue
                else:
                    print('Ashishgup')
                    continue
            else:
                print('Ashishgup')
                continue

        else:
            print('FastestFinger')
            continue
