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 sys import stdin
import math
inp = stdin.readline

def divisors(n) : 
    divis = []
    i = 1
    while i <= math.sqrt(n): 
        if (n % i == 0) : 
            if (n / i == i) : 
                if i%2 and i!= 1:
                    divis.append(i)
            else : 
                if i != 1 and i%2:
                    divis.append(i)
                if (n//i)%2 and (n//i)!=1: 
                    divis.append(n//i) 
        i = i + 1
    return divis
 
t = int(inp())

def best(n,counter):
    if False:
        pass
    else:
        div = divisors(n)
        for i in div:
            ans = best(n//i,counter + 1)
            if ans == 'Ashishgup' and not counter%2:
                return 'Ashishgup'
            elif ans == 'FastestFinger' and counter%2:
                return 'FastestFinger'
        if n > 1 and not div:
            return best(n-1,counter + 1)
        else:
            if counter %2:
                return 'Ashishgup'
            else:
                return 'FastestFinger'
for _ in range(t):
    n = int(inp())
    counter = 0
    if n == 1:
        print('FastestFinger')
        continue
    elif n % 2:
        print('Ashishgup')
        continue
    else:
        print(best(n,0))