In Omkar's last class of math, he learned about the least common multiple, or LCM. LCM(a, b) is the smallest positive integer x which is divisible by both a and b.

Omkar, having a laudably curious mind, immediately thought of a problem involving the LCM operation: given an integer n, find positive integers a and b such that a + b = n and LCM(a, b) is the minimum value possible.

Can you help Omkar solve his ludicrously challenging math problem?

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10). Description of the test cases follows.

Each test case consists of a single integer n (2 ≤ n ≤ 10^{9}).

Output

For each test case, output two positive integers a and b, such that a + b = n and LCM(a, b) is the minimum possible.

Example

Input


3
4
6
9


Output


2 2
3 3
3 6

Note

For the first test case, the numbers we can choose are 1, 3 or 2, 2. LCM(1, 3) = 3 and LCM(2, 2) = 2, so we output 2 \ 2.

For the second test case, the numbers we can choose are 1, 5, 2, 4, or 3, 3. LCM(1, 5) = 5, LCM(2, 4) = 4, and LCM(3, 3) = 3, so we output 3 \ 3.

For the third test case, LCM(3, 6) = 6. It can be shown that there are no other pairs of numbers which sum to 9 that have a lower LCM.
import java.io.*;
import java.util.*;

public class MainB {

    public static void main(String[] args) {
        var sc = new FastScanner(System.in);
        var pw = new PrintWriter(System.out);
        var T = sc.nextInt();
        for (int t = 0; t < T; t++) {
            var N = sc.nextInt();
            solve(N, pw);
        }
        pw.flush();
    }

    private static void solve(int N, PrintWriter pw) {
        int[] facs = enumPrimeFactors(N);
        int youngPrime = facs[0];

        // 1 : youngPrime-1
        int d = N/youngPrime;
        pw.println(d + " " + (youngPrime-1)*d);
    }

    static int[] enumPrimeFactors(int n) {
        List<Integer> factors = new ArrayList<>();
        for (int i = 2; i <= Math.sqrt(n); i++) {
            int cnt = 0;
            while( n % i == 0 ) {
                n/=i;
                cnt++;
            }
            if( cnt > 0 ) {
                factors.add(i);
            }
        }
        if( n != 1 ) {
            factors.add(n);
        }
        int[] ret = new int[factors.size()];
        for (int i = 0; i < factors.size(); i++) {
            ret[i] = factors.get(i);
        }
        return ret;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

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

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

        int[] nextIntArray(int n) {
            var a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            var a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            var a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }
    }

    static void writeLines(int[] as) {
        var pw = new PrintWriter(System.out);
        for (var a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        var pw = new PrintWriter(System.out);
        for (var a : as) pw.println(a);
        pw.flush();
    }

    static void writeSingleLine(int[] as) {
        var pw = new PrintWriter(System.out);
        for (var i = 0; i < as.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(as[i]);
        }
        pw.println();
        pw.flush();
    }

    static void debug(Object... args) {
        var j = new StringJoiner(" ");
        for (var arg : args) {
            if (arg == null) j.add("null");
            else if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }
}
