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

public class Main {

    static long startTime = System.currentTimeMillis();

    // for global initializations and methods starts here

    // global initialisations and methods end here

    static void run() {
        boolean tc = true;
        AdityaFastIO r = new AdityaFastIO();
        //FastReader r = new FastReader();

        try (OutputStream out = new BufferedOutputStream(System.out)) {

            //long startTime = System.currentTimeMillis();

            int testcases = tc ? r.ni() : 1;
            int tcCounter = 1;
            // Hold Here Sparky------------------->>>
            // Solution Starts Here

            start:
            while (testcases-- > 0) {

                int P = r.ni();

                out.write(((2 + " " + (--P)) + " ").getBytes());
                out.write(("\n").getBytes());

            }
            // Solution Ends Here
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    static class AdityaFastIO {
        final private int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;
        public BufferedReader br;
        public StringTokenizer st;

        public AdityaFastIO() {
            br = new BufferedReader(new InputStreamReader(System.in));
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public AdityaFastIO(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

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

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

        public String readLine() throws IOException {
            byte[] buf = new byte[100000001]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int ni() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public long nl() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public double nd() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (c == '.') while ((c = read()) >= '0' && c <= '9') ret += (c - '0') / (div *= 10);
            if (neg) return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null) return;
            din.close();
        }
    }

    public static void main(String[] args) throws Exception {
        run();
    }

    static long mod = 998244353;

    static long modInv(long base, long e) {
        long result = 1;
        base %= mod;
        while (e > 0) {
            if ((e & 1) > 0) result = result * base % mod;
            base = base * base % mod;
            e >>= 1;
        }
        return result;
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

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

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

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

        int ni() {
            return Integer.parseInt(word());
        }

        long nl() {
            return Long.parseLong(word());
        }

        double nd() {
            return Double.parseDouble(word());
        }
    }

    static int MOD = (int) (1e9 + 7);

    static long powerLL(long x, long n) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1) result = result * x % MOD;
            n = n / 2;
            x = x * x % MOD;
        }
        return result;
    }

    static long powerStrings(int i1, int i2) {
        String sa = String.valueOf(i1);
        String sb = String.valueOf(i2);
        long a = 0, b = 0;
        for (int i = 0; i < sa.length(); i++) a = (a * 10 + (sa.charAt(i) - '0')) % MOD;
        for (int i = 0; i < sb.length(); i++) b = (b * 10 + (sb.charAt(i) - '0')) % (MOD - 1);
        return powerLL(a, b);
    }

    static long gcd(long a, long b) {
        if (a == 0) return b;
        else return gcd(b % a, a);
    }

    static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    static long lower_bound(List<Long> list, long k) {
        int s = 0;
        int e = list.size();
        while (s != e) {
            int mid = (s + e) >> 1;
            if (list.get(mid) < k) s = mid + 1;
            else e = mid;
        }
        if (s == list.size()) return -1;
        return s;
    }

    static int upper_bound(List<Long> list, long k) {
        int s = 0;
        int e = list.size();
        while (s != e) {
            int mid = (s + e) >> 1;
            if (list.get(mid) <= k) s = mid + 1;
            else e = mid;
        }
        if (s == list.size()) return -1;
        return s;
    }

    static void addEdge(ArrayList<ArrayList<Integer>> graph, int edge1, int edge2) {
        graph.get(edge1).add(edge2);
        graph.get(edge2).add(edge1);
    }

    public static class Pair implements Comparable<Pair> {
        int first;
        int second;

        public Pair(int first, int second) {
            this.first = first;
            this.second = second;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(Pair o) {
            // TODO Auto-generated method stub
            if (this.first != o.first)
                return (int) (this.first - o.first);
            else return (int) (this.second - o.second);
        }
    }

    public static class PairC<X, Y> implements Comparable<PairC> {
        X first;
        Y second;

        public PairC(X first, Y second) {
            this.first = first;
            this.second = second;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(PairC o) {
            // TODO Auto-generated method stub
            return o.compareTo((PairC) first);
        }
    }

    static boolean isCollectionsSorted(List<Long> list) {
        if (list.size() == 0 || list.size() == 1) return true;
        for (int i = 1; i < list.size(); i++) if (list.get(i) <= list.get(i - 1)) return false;
        return true;
    }

    static boolean isCollectionsSortedReverseOrder(List<Long> list) {
        if (list.size() == 0 || list.size() == 1) return true;
        for (int i = 1; i < list.size(); i++) if (list.get(i) >= list.get(i - 1)) return false;
        return true;
    }

}