Gregor is learning about RSA cryptography, and although he doesn't understand how RSA works, he is now fascinated with prime numbers and factoring them.

Gregor's favorite prime number is P. Gregor wants to find two bases of P. Formally, Gregor is looking for two integers a and b which satisfy both of the following properties.

  * P mod a = P mod b, where x mod y denotes the remainder when x is divided by y, and 
  * 2 ≤ a < b ≤ P. 



Help Gregor find two bases of his favorite prime number!

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 1000).

Each subsequent line contains the integer P (5 ≤ P ≤ {10}^9), with P guaranteed to be prime.

Output

Your output should consist of t lines. Each line should consist of two integers a and b (2 ≤ a < b ≤ P). If there are multiple possible solutions, print any.

Example

Input


2
17
5


Output


3 5
2 4

Note

The first query is P=17. a=3 and b=5 are valid bases in this case, because 17 mod 3 = 17 mod 5 = 2. There are other pairs which work as well.

In the second query, with P=5, the only solution is a=2 and b=4.
2
17
5
 1
55439
 5
5
7
11
13
19

2 16
2 4
 2 55438
 2 4
2 6
2 10
2 12
2 18

import java.io.*;
import java.lang.*;
import java.util.*;

//* --> number of prime numbers less then or equal to x are  -->  x/ln(x)
//* --> String concatenation using the + operator within a loop should be avoided. Since the String object is immutable, each call for concatenation will
// result in a new String object being created.
// THE SIEVE USED HERE WILL RETURN A LIST CONTAINING ALL THE PRIME NUMBERS TILL N
public class e {
    static FastScanner sc;
    static PrintWriter pw;

    static class FastScanner {
        InputStreamReader is;
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            is = new InputStreamReader(System.in);
            br = new BufferedReader(is);
        }

        String next() throws Exception {
            while (st == null || !st.hasMoreElements())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        int[] readArray(int num) throws Exception {
            int arr[] = new int[num];
            for (int i = 0; i < num; i++)
                arr[i] = nextInt();
            return arr;
        }

        String nextLine() throws Exception {
            return br.readLine();
        }
    }

    public static boolean power_of_two(int a) {
        if ((a & (a - 1)) == 0) {
            return true;
        }
        return false;
    }

    static boolean PS(double x) {
        if (x >= 0) {
            double i = Math.sqrt(x);
            if (i % 1 != 0) {
                return false;
            }
            return ((i * i) == x);
        }
        return false;
    }

    public static int[] ia(int n) {
        int ar[] = new int[n];
        return ar;
    }

    public static long[] la(int n) {
        long ar[] = new long[n];
        return ar;
    }

    public static void print(int ans, int t) {
        System.out.println("Case" + " " + "#" + t + ":" + " " + ans);
    }

    static long mod = 1000000007;
    static int max = Integer.MIN_VALUE;
    static int min = Integer.MAX_VALUE;

    public static void sort(long[] arr) {// because Arrays.sort() uses quicksort which is dumb
        // Collections.sort() uses merge sort
        ArrayList<Long> ls = new ArrayList<Long>();
        for (long x : arr)
            ls.add(x);
        Collections.sort(ls);
        for (int i = 0; i < arr.length; i++)
            arr[i] = ls.get(i);
    }

    public static long fciel(long a, long b) {
        if (a == 0)
            return 0;
        return (a - 1) / b + 1;
    }

    static boolean[] is_prime = new boolean[1000001];
    static ArrayList<Integer> list = new ArrayList<>();
    static long n = 1000000;

    public static void sieve() {
        Arrays.fill(is_prime, true);
        is_prime[0] = is_prime[1] = false;
        for (int i = 2; i * i <= n; i++) {
            if (is_prime[i]) {
                for (int j = i * i; j <= n; j += i)
                    is_prime[j] = false;
            }
        }
        for (int i = 2; i <= n; i++) {
            if (is_prime[i]) {
                list.add(i);
            }
        }
    }

    public static void main(String args[]) throws java.lang.Exception {
        sc = new FastScanner();
        pw = new PrintWriter(System.out);
        StringBuilder s = new StringBuilder();
        int t = sc.nextInt();
        while (t-- > 0) {
            long p = sc.nextLong();
            long b = p - 1;
            long a = b / 2;
            s.append(a + " " + b);
            if (t > 0) {
                s.append("\n");
            }
        }
        pw.print(s);
        pw.close();
    }
}