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

input = sys.stdin.readline

t = int(input())
tt = []
p = 10 ** 9
cnt = 2
while cnt <= p:
    cnt *= 2
    tt.append(cnt)

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n ** 0.5 // 1)) + 1):
        if temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append([i, cnt])

    if temp != 1:
        arr.append([temp, 1])

    if arr == []:
        arr.append([n, 1])

    return arr


for _ in range(t):
    n = int(input())
    cnt = 0
    while True:
        cnt += 1
        if cnt % 2 == 1 and n == 1:
            print("FastestFinger")
            break
        elif cnt % 2 == 0 and n == 1:
            print("Ashishgup")
            break
        if n % 2 == 1:
            n = 1
        elif n == 2:
            n = 1
        elif n in tt:
            n -= 1
        else:
            f = factorization(n)
            if f[0][0] == 2 and f[0][1] >= 2:
                n = f[0][0] ** f[0][1]
            else:
                if len(f) == 2 and f[1][1] == 1:
                    n = f[0][0] ** f[0][1]
                else:
                    n = f[0][0] ** f[0][1] * f[1][0]

