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.
T = int(input())


def getPow(n,d):
    count = 0
    while n%d==0:
        n = n/d
        count+=1
    return count

def getOddFacs(n):
    count = 0
    d = 1
    while n >1:
        
        p=getPow(n,d)

        n = int(n/d**p)
        if d % 2 == 1:
            count+=p
        d+=2   
    return count

def hasOddFacs(n):
    count = 0
    d = 3

    while count<2 and d<=int(pow(n,0.5)):

        
        p=getPow(n,d)
        n = int(n/d**p)
            
        count+=p
        d+=2
    return count
# i need to check if a in 2*a is a prime number>2!

def isPrime(n):
    #assume that n is odd
    for i in range (3,int(pow(n,0.5))+1):
        if n%i==0:
            return False

    return True 



while T>0:

    n = int(input())
    """
    if n==1:
        print('FastestFinger')
    elif n%2 == 1:
        print('Ashishgup')
    elif n%2 == 0:
        count = getOddFacs(n)
        if n == 2:
            
             print('Ashishgup')
        elif count%2 == 1:
             if n%4==0:
                print('Ashishgup')
             else:
                print('FastestFinger')

        elif count%2 == 0:
              if n%4==0:
                print('FastestFinger')
              else:
                print('Ashishgup')
    """

    #count = hasOddFacs(n)
    if n==1:
        print('FastestFinger')
    elif n%2 == 1:
        print('Ashishgup')
    elif n%2 == 0:
        p = getPow(n,2)
        m = int(n/2**p)
        pFlag = isPrime(m) 
     
        if n == 2:
            print('Ashishgup')
        elif n%4!=0:
            if pFlag:
                print('FastestFinger')
            elif pFlag == False:
                #the fist removes all odds except one fron the product
                # the only even factor is 2
                print('Ashishgup')

        elif n%4==0:
               if m!=1:
                    print('Ashishgup')          
               else:
                    print('FastestFinger')

            
                

            

    T-=1
