human
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.
Using python3 can you solve the prior task?
assistant
#Here is Python program to determine the winner of the game if both of them play optimally.

# @author 

import sys

class CNumberGame:
    def solve(self, tc=0):

        def solve1(n, p):
            if n in dp:
                return dp[n]

            if n == 1:
                dp[n] = 1 # I lose
                return dp[n]

            if n & 1:
                dp[n] = 0
                return dp[n]
            # print(n)
            for pd in range(2, int(n ** .5) + 1):
                if n % pd != 0:
                    continue
                for d in [pd, n // pd]:
                    if d % 2 == 1:
                        him = solve1(n // d, 1 - p)
                        if him == 1:
                            dp[n] = 0
                            return dp[n]

            dp[n] = 1 - solve1(n - 1, 1 - p)
            return dp[n]

        for _ in range(int(input())):
            players = ["Ashishgup", "FastestFinger"]
            n = int(input())

            dp = {}
            solve1(n, 0)
            # print(dp)
            print(players[dp[n]])

solver = CNumberGame()
input = sys.stdin.readline

solver.solve()