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.
test_cases = int(input())
primeNumbers = set()
##notPrime = set()
maxTried = [1]

def is_prime(n):
    if n<maxTried[0]:
        if n in primeNumbers:
            return True
        else:
            return False
    for i in range(3, int(n**0.5)+1,2):
        if n%i==0:
            return False
    primeNumbers.add(n)
    return True
##    for i in range(maxTried[0]+2, int(n**0.5)+1,2):
##        is_prime(i)
##    maxTried[0] = n
##    for p in primeNumbers:
##        if n%p==0:
####            notPrime.add(n)
####            print(n)
##            return False
##    primeNumbers.add(n)
####    print(n)
##    return True

for _ in range(test_cases):
    n = int(input())
    output = ["FastestFinger","Ashishgup"]
    if n==1:
        print(output[0])
    elif n%2==1:
        print(output[1])
    elif n==2:
        print(output[1])
    elif n==4:
        print(output[0])
    elif n%4==0:
        k = n
        while k%2==0:
            k//=2
        if k==1:
            print(output[0])
        else:
            print(output[1])
    else:
        k = n//2
        prime = is_prime(k)
        if prime:
            print(output[0])
        else:
            print(output[1])
##        prime = True
##        k = n//2
##        if k in primeNumbers:
##            print(output[0])
##        elif k in notPrime:
##            print(output[1])
##        else:
##            for i in range(3,k//2+1,2):
##                if k%i==0:
##                    prime = False
##                    break
##            if prime:
##                print(output[0])
##            else:
##                print(output[1])
