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 math
def p(n):
    j = []
    i = 1
    while i <= math.sqrt(n):

        if (n % i == 0):
            if (n / i == i):
                if i%2 != 0 and i > 1:
                    j.append(i)
            else:
                if i%2 != 0 and i > 1:
                    j.append(i)
                if (n/i)%2 != 0 and i > 1:
                    j.append(n / i)
        i = i + 1
    return j


a = int(input())
for x in range(a):
    b = int(input())
    c = "Ashishgup"
    if b == 1:
        print("FastestFinger")
    elif b == 2:
        print(c)
    elif b % 2 != 0:
        print(c)
    else:
        j = p(b)
        t = len(j)
        if t == 0:
            print("FastestFinger")
        else:
            if (b//j[t-1])%2 != 0 or (b//j[t-1]) == 2:
                print("FastestFinger")
            else:
                print(c)
