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
from collections import defaultdict,deque

input = sys.stdin.readline
def inar():
    return [int(el) for el in input().split()]
def toogle(char):
    if char=="b":
        return "w"
    else:
        return "b"
def take(lis):
    l=-10**9+7
    ans=-10**9+7
    for i in range(len(lis)):
        l=max(lis[i],lis[i]+l)
        ans=max(ans,l)
    return ans
def main():
    for _ in range(int(input())):
        n=int(input())
        odd=[]
        for i in range(2,int(n**0.5)+1):
            if n % i==0:
                if i%2!=0:
                    odd.append(i)
                if (n//i)%2!=0:
                    odd.append(n//i)
        # print(odd)
        if n==1:
            print("FastestFinger")
        elif n==2:
            print("Ashishgup")
        elif n % 2!=0 or  len(odd)>=2:
            print("Ashishgup")
        elif len(odd)==1:
            if (n//odd[0])==2:
                print("FastestFinger")
            else:
                print("Ashishgup")
        else:
            print("FastestFinger")







if __name__ == '__main__':
    main()



