Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class CF1294C extends PrintWriter {
	CF1294C() { super(System.out); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF1294C o = new CF1294C(); o.main(); o.flush();
	}

	void main() {
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int u = 1, ku = 0, v = 1, kv = 0, w = n;
			for (int p = 2; p <= w / p; p++)
				if (w % p == 0) {
					int k = 0;
					while (w % p == 0) {
						k++;
						w /= p;
					}
					if (u == 1) {
						u = p; ku = k;
					} else {
						v = p; kv = k;
						break;
					}
				}
			if (w != 1) {
				if (u == 1) {
					u = w; ku = 1;
					w = 1;
				} else if (v == 1) {
					v = w; kv = 1;
					w = 1;
				}
			}
			int a = -1, b = -1, c = -1;
			if (u != 1 && v != 1 && w != 1 || u != 1 && v != 1 && ku + kv >= 4) {
				a = u;
				b = v;
				c = n / a / b;
			} else if (ku >= 6) {
				a = u;
				b = u * u;
				c = n / a / b;
			}
			if (c == -1)
				println("NO");
			else {
				println("YES");
				println(a + " " + b + " " + c);
			}
		}
	}
}