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 cf1372_Div2_B {
	public static long gcd(long a, long b) {
		if (b == 0) return a;
		return gcd(b,a % b);
	}
	
	public static long lcm(long a, long b) {
		return a / gcd(a, b) * b;
	}
	
	public static void main(String[] args) throws IOException {
		FastScanner in = new FastScanner();
		int t = in.nextInt();
		for ( ; t > 0; --t) {
			long n = in.nextInt();
			long ans = 1;
			long lcm = n - 1;
			long other1 = -1;
			long other = -1;
			for (int i = 2; i * i <= n; i++) {
				if (n % i == 0) {
					other1 = lcm(n / i, (i - 1) * n / i); 
					other = lcm(i, (n / i - 1) * i);
					if (other < lcm) { ans = i; lcm = other;}
					if (other1 < lcm) { ans = n / i; lcm = other1;}
				}
			}
			// System.out.println(ans);
			System.out.println(ans + " " + (n / ans - 1) * ans);
		}
	}  
	
    public static void shuffle(int[] arr) {
    	Random rgen = new Random();
    	
    	for (int i = 0; i < arr.length; i++) {
    		int rPos = rgen.nextInt(arr.length);
    		int temp = arr[i];
    		arr[i] = arr[rPos];
    		arr[rPos]=temp;
    	}
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

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

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        String next() {
    		while (st == null || !st.hasMoreElements()) {
    			try {
    				st = new StringTokenizer(br.readLine());
    			} catch (IOException e) {
    				e.printStackTrace();
    			}
    		}
    		return st.nextToken();
    	}

        String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return null;
        }

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

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

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}

