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.
pri={}
def Sieve():
    n=100000
    prime = [True for i in range(n + 1)] 
    p = 2
    while (p * p <= n): 
        if (prime[p] == True): 
            for i in range(p * 2, n + 1, p): 
                prime[i] = False
        p += 1
    prime[0]= False
    prime[1]= False
    for p in range(n + 1): 
        if prime[p]: 
            pri[p]=1
Sieve()
def chk_prime(n):
    if(n==2):
        return False
    for i in range(2,int(n**(1/2))+1):
        if(n%i==0):
            return False
    return True
def cal(n):
    a=0;li=[]
    for i in sorted(pri.keys()):
        while(n%i==0):
            n//=i
            a+=1
            #print(n,a)
            li.append(i)
        if(n==1):
            break
    #print(li)
    if(n!=1):
        a+=1
    return a
for _ in range(int(input())):
    p1="Ashishgup";p2="FastestFinger"
    n=int(input())
    if(n==1):
        print(p2)
        continue
    if(n%2==1):
        #print(n-1,chk_prime(n-1))
        print(p1)
        continue
    chance=1;temp=n
    while(n%2==0):
        n//=2
    x=cal(n)
    #print(n,x)
    if(x==0):
        ans=p1 if(temp//n==2) else p2
    elif(x==1):
        ans=p1 if(temp//n!=2) else p2
    else:
        ans=p1
    print(ans)
