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.
#include <bits/stdc++.h>
using namespace std;
long long sign(long long x) { return (x > 0) - (x < 0); }
void Sieve(long long n) {
  bool prime[n + 1];
  memset(prime, true, sizeof(prime));
  for (long long p = 2; p * p <= n; p++)
    if (prime[p] == true)
      for (long long i = p * p; i <= n; i += p) prime[i] = false;
}
long long MIN(long long x, long long y) { return x > y ? y : x; }
long long MAX(long long x, long long y) { return x > y ? x : y; }
void swap(long long *x, long long *y) {
  long long temp = *x;
  *x = *y;
  *y = temp;
}
bool isPrime(long long n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  long long p = sqrt(n);
  for (long long i = 5; i <= p; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
long long gcdExtended(long long a, long long b, long long *x, long long *y) {
  if (a == 0) {
    *x = 0, *y = 1;
    return b;
  }
  long long x1, y1;
  long long gcd = gcdExtended(b % a, a, &x1, &y1);
  *x = y1 - (b / a) * x1;
  *y = x1;
  return gcd;
}
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
const long long MOD = 1e9 + 7, N = 2e5 + 5, bit = 64, Big = 1e18;
long long mod_pow(long long a, long long b, long long M = MOD) {
  long long res = 1;
  while (b) {
    if (b & 1) res = (res * a) % M;
    a = (a * a) % M;
    b >>= 1;
  }
  return res;
}
long long fact(long long n) {
  long long j = 0;
  for (long long i = 3; i <= n; i += 2)
    if (!(n % i)) j = MAX(j, i);
  return j;
}
bool solve(long long n) {
  long long cnt = 0;
  if (n == 1) return n == 1;
  if (n & 1 || n == 2) return false;
  while (n % 2 == 0) {
    cnt++;
    n /= 2;
  }
  if (n == 1) return true;
  return ((isPrime(n)) && (cnt == 1));
}
void start() {
  long long n;
  cin >> n;
  if (solve(n))
    cout << "FastestFinger" << endl;
  else
    cout << "Ashishgup" << endl;
}
signed main() {
  long long test = 1;
  cin >> test;
  while (test--) start();
}
