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 numofodd( n ):
    res = 1
    while(n % 2 == 0):
        n = n // 2
    ttcnt = 0
    for i in range(3, int(math.sqrt(n) + 1)):
        count = 0
        sumi = 0
        term = 3
        while n % i == 0:
            count+=1
            n = n // i
            term *= i
            sumi += i
        res *=  sumi
        ttcnt += count
    if n >= 2:
        res *= (1 + n)
        ttcnt += 1
    return(ttcnt)

t = int(input())
for _ in range(t):
    n = int(input())
    if(n==1):
        print('FastestFinger')
    elif(n==2):
        print('Ashishgup')
    elif(n%2!=0):
        print('Ashishgup')
    else:
        cnt = 0
        power = (n and (not(n & (n - 1))))
        # print(power)
        if(power):
            print('FastestFinger')
        else:
            if(n%4!=0):
                if(numofodd(n)>1):
                    print('Ashishgup')
                else:  
                    print('FastestFinger')
            else:
                print('Ashishgup')