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

t = sys.stdin.readline().rstrip()
t = int(t)
for i in range(t):
    n = sys.stdin.readline().rstrip()
    n = int(n)
    norg = n
    k = 0
    while(n%2==0):
        n = n//2
        k+=1
    a = []
    x = 3
    while(n>1 and x<=norg**0.5):
        if(n%x==0):
            a.append(x)
            n = n//x
        else:
            x+=2
    if(n>1):
        a.append(n)
    p = len(a)
    #print(norg)
    #print(str(k)+" "+str(p))
    if(k==0 and p==0):
        print("FastestFinger")
    elif k==0:
        print("Ashishgup")
    elif k==1:
        if(p==1):
            print("FastestFinger")
        else:
            print("Ashishgup")
    else:
        if p==0:
            print("FastestFinger")
        else: print("Ashishgup")
