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.*;

public class Main {
    static String a="Ashishgup",b="FastestFinger";
    public static void main(String[] args) throws Exception {
        InputReader sc = new InputReader(System.in);
        StringBuilder sb=new StringBuilder();
        int t=sc.nextInt();
        while(t-->0){
            int n=sc.nextInt();
            solve(n);
        }
    }
    static void solve(int n){
        int N=n;
        if(N==1){
            System.out.println(b);
            return;
        }
        if (N==2){
            System.out.println(a);
            return;
        }
        if (N%2==1){
            System.out.println(a);
        }else {
            LinkedList<Integer> p= fac(N);
            boolean z[]=new boolean[2];
            for (int PP:p){
                if (PP%2==0 && PP!=2)z[0]=true;
                if (PP%2==1)z[1]=true;
            }
            if (z[0] && z[1])System.out.println(a);
            else System.out.println(b);
        }
    }
    static LinkedList<Integer> fac(int n){
        LinkedList<Integer> ll=new LinkedList<>();
        for (int i=2;i*i<=n;i++){
            if (n%i==0){
                ll.add(i);
                if (i!=n/i){
                    ll.add(n/i);
                }
            }
        }
        return ll;
    }
}
/*******************************************************************
 --------------------------(SOLUTION END)---------------------------
 *******************************************************************/
class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
    private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    public InputReader(InputStream stream) {
        this.stream = stream;
    }
    public int read() {
        if (numChars==-1) throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try { numChars = stream.read(buf); }
            catch (IOException e) { throw new InputMismatchException(); }
            if(numChars <= 0) return -1;
        }
        return buf[curChar++];
    }
    public String nextLine() {
        String str = "";
        try { str = br.readLine(); }
        catch (IOException e) { e.printStackTrace(); }
        return str;
    }
    public int nextInt() {
        int c = read();
        while(isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if(c<'0'||c>'9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        while (!isSpaceChar(c));
        return res * sgn;
    }
    public long nextLong() {
        int c = read();
        while (isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        while (!isSpaceChar(c));
        return res * sgn;
    }
    public double nextDouble() {
        int c = read();
        while (isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E') return res * Math.pow(10, nextInt());
            if (c < '0' || c > '9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E') return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9') throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }
    public String readString() {
        int c = read();
        while (isSpaceChar(c)) c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        }
        while (!isSpaceChar(c));
        return res.toString();
    }
    public boolean isSpaceChar(int c) {
        if (filter != null) return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
    public String next() { return readString();}
    public interface SpaceCharFilter { public boolean isSpaceChar(int ch);}
}