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 prime(n):
    d = {}
    if n%2 == 0:
        d[2]=0
        while n%2 == 0:
            d[2] += 1
            n = n//2
    for i in range(3,int(sqrt(n))+1,2):
        if n % i == 0:
            d[i] = 0
            while n % i == 0:
                d[i] += 1
                n = n//i
    if n>2:
        d[n]=1
    return d


t = int(input())
for jack in range(t):
    n = int(input())
    if n == 1:
        f = 'f'
    elif n==2:
        f = 'a'
    elif n%2 !=0:
        f = 'a'
    else:
        x = n
        r = prime(x)
        p2 = r[2]
        podd = sum(r.values())-p2
        # print(p2,podd)
        if p2>=2:
            if podd>0:
                f='a'
            else:
                f='f'
        else:
            if podd == 1:
                f='f'
            else:
                f='a'

    if f=='a':
        print("Ashishgup")
    else:
        print("FastestFinger")

