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 collections import Counter
import string
import math
import sys
def array_int():
    return [int(i) for i in sys.stdin.readline().split()]
def vary(number_of_variables):
    if number_of_variables==1:
        return int(sys.stdin.readline())
    if number_of_variables>=2:
        return map(int,sys.stdin.readline().split()) 
def makedict(var):
    return dict(Counter(var))
mod=100000007
# sys.stdin=open('input.txt','r')
# sys.stdout=open('output.txt','w')
def isPrime(n) : 
  
    # Corner cases 
    if (n <= 1) : 
        return False
    if (n <= 3) : 
        return True
  
    # This is checked so that we can skip  
    # middle five numbers in below loop 
    if (n % 2 == 0 or n % 3 == 0) : 
        return False
  
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
  
    return True
powers=[int(2**i) for i in range(1,32)]
st=set(powers)
for _ in range(vary(1)):
    n=vary(1)
    if n==1:
        print('FastestFinger')
        continue
    if n==2:
        print('Ashishgup')
        continue
    if n in st:
        print('FastestFinger')
        continue
    if n%2!=0:
        print('Ashishgup')     
    else:
        if n%4==0:
            print('Ashishgup')
        else:
            if isPrime(n//2):
                print('FastestFinger')
            else:
                print('Ashishgup')

""" n=vary(1)
num=array_int()
dp=[[0 for i in range(3)] for j in range(102)]
# print(dp)
for i in range(1,n+1):
    if num[i-1]==0:
        dp[i][0]=dp[i-1][0]+1
        dp[i][1]=float('inf')
        dp[i][2]=float('inf')
    if num[i-1]==1:
        dp[i][2]=float('inf')
        dp[i][0]=min(dp[i-1][0],dp[i-1][1],dp[i-1][2])+1
        dp[i][1]=min(dp[i-1][2],dp[i-1][0])+1
    if num[i-1]==2:
        dp[i][1]=float('inf')
        dp[i][0]=min(dp[i-1][0],dp[i-1][1],dp[i-1][2])
        dp[i][2]=min(dp[i-1][1],dp[i-1][0])
    if num[i-1]==3:
        dp[i][1]=float('inf')
        dp[i][0]=min(dp[i-1][0],dp[i-1][1],dp[i-1][2])
        dp[i][2]=min(dp[i-1][1],dp[i-1][0])
print(min(dp[n][0],dp[n][1],dp[n][2])) """

    

        


        



    


    


    



