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 
# Function to calculate all the prime  
# factors and count of every prime factor 
def factorize(n): 
    count = 0; 
    l=[]
    # count the number of  
    # times 2 divides  
    while ((n % 2 > 0) == False):  
          
        # equivalent to n = n / 2; 
        n >>= 1;  
        count += 1; 
  
    # if 2 divides it 
    if (count > 0): 
        l.append([2, count]); 
  
    # check for all the possible 
    # numbers that can divide it 
    for i in range(3, int(math.sqrt(n)) + 1): 
        count = 0; 
        while (n % i == 0):  
            count += 1; 
            n = int(n / i); 
        if (count > 0): 
            l.append([i, count]); 
        i += 2; 
    # if n at the end is a prime number. 
    if (n > 2): 
        l.append([n, 1]);
    return l
t=int(input())
for i in range(t):
    n=int(input())
    if n%2 or n==2:
        if n!=1:
            print('Ashishgup')
        else:
            print('FastestFinger')
    else:
        l=factorize(n)
        l.sort()
        if len(l)>1:
            if l[0][1]>1:
                print('Ashishgup')
            else:
                c=0
                for i in range(1,len(l)):
                    c+=l[i][1]
                    if c>1:
                        break
                if c>1:
                    print('Ashishgup')
                else:
                    print('FastestFinger')
        else:
            print('FastestFinger')
            
