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.util.*;


public class gregor {
    static FastScanner sc = new FastScanner();
    static PrintWriter out = new PrintWriter(System.out);
    
    public static void main(String[] args) {
        int t=sc.nextInt();
        while(t-- > 0) {
            int p=sc.nextInt();
            int a=2,b=0;
            if(p%2==0)
            System.out.println(a+" "+p);
            else{p--;
                b=p;
            System.out.println(a+" "+b);}  
        }
       
        out.close();
    }
    
    static class FastScanner {
        private int BS = 1 << 16;
        private char NC = (char) 0;
        private byte[] buf = new byte[BS];
        private int bId = 0, size = 0;
        private char c = NC;
        private double cnt = 1;
        private BufferedInputStream in;
    
        public FastScanner() {
            in = new BufferedInputStream(System.in, BS);
        }
    
        public FastScanner(String s) {
            try {
                in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
            } catch (Exception e) {
                in = new BufferedInputStream(System.in, BS);
            }
        }
    
        char getChar() {
            while (bId == size) {
                try {
                    size = in.read(buf);
                } catch (Exception e) {
                    return NC;
                }
                if (size == -1) return NC;
                bId = 0;
            }
            return (char) buf[bId++];
        }
    
        int nextInt() {
            return (int) nextLong();
        }
    
        long nextLong() {
            cnt = 1;
            boolean neg = false;
            if (c == NC) c = getChar();
            for (; (c < '0' || c > '9'); c = getChar()) {
                if (c == '-') neg = true;
            }
            long res = 0;
            for (; c >= '0' && c <= '9'; c = getChar()) {
                res = (res << 3) + (res << 1) + c - '0';
                cnt *= 10;
            }
            return neg ? -res : res;
        }
    
        double nextDouble() {
            boolean neg = false;
            if (c == NC) c = getChar();
            for (; (c < '0' || c > '9'); c = getChar()) {
                if (c == '-') neg = true;
            }
            double cur = nextLong();
            if (c != '.') {
                return neg ? -cur : cur;
            } else {
                double frac = nextLong() / cnt;
                return neg ? -cur - frac : cur + frac;
            }
        }
    
        String next() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c > 32) {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }
    
        String nextLine() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c != '\n') {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }
    
        boolean hasNext() {
            if (c > 32) return true;
            while (true) {
                c = getChar();
                if (c == NC) return false;
                else if (c > 32) return true;
            }
        }
    }
    
    static void ASSERT(boolean assertion, String message) {
        if (!assertion) throw new AssertionError(message);
    }
    
    static void ASSERT(boolean assertion) {
        if (!assertion) throw new AssertionError();
    }
}