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 sys
RI = lambda : [int(x) for x in sys.stdin.readline().strip().split()]
from collections import defaultdict as df
import copy
p1 = "Ashishgup"
p2 = "FastestFinger"

primes = []
sieve = [0]*40000
for i in range(2,40000):
    if(sieve[i]==0):
        primes.append(i)
        for j in range(i*i,40000,i):
            sieve[j]=1
#print(primes)
t = int(input().strip())
for _ in range(t):
    n =  int(input().strip())
    
    if(n==1):
        print(p2)
    elif(n>1 and n%2==1):
        print(p1)
    elif(n==2):
        print(p1)
    else:
        even = 0
        odd = 0
        i = 0
        l = len(primes)

        while(i<l):
            if(n%primes[i]==0):
                while(n%primes[i]==0):
                    #print(n,primes[i])
                    n//=primes[i]
                    if(primes[i]%2==0):
                        even+=1
                    else:
                        odd+=1
            i+=1
        #print(odd,even)
        if(n>1):
            if(n%2==0):
                even+=1
            else:
                odd+=1
        
        #print(odd,even)
        if(odd==0):
            print(p2)
        elif(odd==1 and even==1):
            print(p2)
        elif(odd==1 and even>1):
            print(p1)        
        elif(odd>1 and even==1):
            print(p1)
        else:
            print(p1)
