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 sys import stdin,stdout 
from bisect import bisect,bisect_left,bisect_right
def gt(): return map(int, stdin.readline().split())
def gi(): return int(stdin.readline())
def gl(): return list(map(int, stdin.readline().split())) 
def gs(): return stdin.readline() 
t=gi()
for _ in range(t):
    n=gi()
    tn=n
    count=0 
    if n==1:
        print("FastestFinger")
    elif n==2:
        print("Ashishgup")
    elif (n%2)!=0:
        print("Ashishgup")
    else:
        tc=0
        while((n%2)==0):
            n=n//2
            tc+=1
        count=0
        i=3
        # print(n)
        while(i*i<=n):
            while((n%i)==0):
                n=n//i
                count+=1 
            i+=1
        if(n>1):
            count+=1 
        # print(count)
        # print(tc,count)
        if count>1:
            print("Ashishgup")
        elif count==0:
            if tc==1:
                print("Ashishgup")
            else:
                print("FastestFinger")
        else:
            if tc==1:
                print("FastestFinger")
            else:
                print("Ashishgup")
    
        