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

public class LastMathClassMath {
	public static void main(String[] args) {
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		int T = sc.nextInt();
		outer:
		while (T-- > 0) {
			int N = sc.nextInt();
			
			for (int k = 2; k <= Math.sqrt(N); k++) {
				if (N % k == 0) {
					System.out.println(N / k + " " + (N - N / k));
					continue outer;
				}
			}
			
			System.out.println(1 + " " + (N - 1));
		}
	}
}

/*

8
527
622
63
423
147
791
838
903

31 496
311 311
21 42
141 282
49 98
113 678
419 419
301 602

6
861605021
68328580
877214985
692261986
3399371
684035729

1 861605021
34164290 34164290
292404995 584809990
346130993 346130993
199963 3199408
52618133 631417596

*/