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 java.util.*;
import java.io.*;
import java.math.*;

public class C651 {

    public static void main(String args[]) {
        FastReader sc = new FastReader();
        StringBuilder sb = new StringBuilder();
        int t, i, n;
        t = sc.nextInt();
        while (t-- > 0) {
            n = sc.nextInt();
            if (n == 1) {
                sb.append("FastestFinger\n");
                continue;
            }
            if (n == 2 || n % 2 == 1) {
                sb.append("Ashishgup\n");
                continue;
            }
            if (n > 2 && (n & (n - 1)) == 0) {
                sb.append("FastestFinger\n");
                continue;
            }
            int count = 0;
            while (n % 2 == 0) {
                n /= 2;
                count++;
            }
            if (count == 1) {
                count = 0;
                for (i = 3; i <= (int) Math.sqrt(n); i += 2) {
                    while (n % i == 0) {
                        n /= i;
                        count++;
                    }
                }
                if (n > 1)
                    count++;
                if (count != 1)
                    sb.append("Ashishgup\n");
                else
                    sb.append("FastestFinger\n");
                continue;
            }
            sb.append("Ashishgup\n");
        }
        sb.deleteCharAt(sb.length() - 1);
        out.println(sb);
    }

    static PrintWriter out;

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out, true);
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static boolean isPrime(int n) {
        if (n < 2)
            return false;
        for (int i = 2; i <= (int) Math.sqrt(n); i++) {
            if (n % i == 0)
                return false;
        }
        return true;
    }

    public static void print(int a[], int l, int r) {
        int i;
        for (i = l; i <= r; i++)
            out.print(a[i] + " ");
        out.println();
    }

    public static long fastexpo(long x, long y, long p) {
        long res = 1;
        while (y > 0) {
            if ((y & 1) == 1)
                res = ((res % p) * (x % p)) % p;
            y = y >> 1;
            x = ((x % p) * (x % p)) % p;
        }
        return res;
    }

    public static boolean[] sieve(int n) {
        boolean primes[] = new boolean[n + 1];
        Arrays.fill(primes, true);
        primes[0] = primes[1] = false;
        for (int i = 2; i * i <= n; i++) {
            if (primes[i]) {
                for (int j = i * i; j <= n; j += i)
                    primes[j] = false;
            }
        }
        return primes;
    }

    public static long gcd(long a, long b) {
        return (BigInteger.valueOf(a).gcd(BigInteger.valueOf(b))).longValue();
    }

    public static void merge(long a[], int l, int m, int r) {
        int n1, n2, i, j, k;
        n1 = m - l + 1;
        n2 = r - m;

        long L[] = new long[n1];
        long R[] = new long[n2];

        for (i = 0; i < n1; i++)
            L[i] = a[l + i];
        for (j = 0; j < n2; j++)
            R[j] = a[m + 1 + j];

        i = 0;
        j = 0;

        k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                a[k] = L[i];
                i++;
            } else {
                a[k] = R[j];
                j++;
            }
            k++;
        }

        while (i < n1) {
            a[k] = L[i];
            i++;
            k++;
        }
        while (j < n2) {
            a[k] = R[j];
            j++;
            k++;
        }
    }

    public static void sort(long a[], int l, int r) {
        int m;
        if (l < r) {
            m = (l + r) / 2;
            sort(a, l, m);
            sort(a, m + 1, r);
            merge(a, l, m, r);
        }
    }
}