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:
'use strict'

const problem = (n) => {
    for (let i = 2; i < Math.cbrt(n); i++) {
        if (n % i === 0) {
            n /= i;
            for (let j = i + 1; j < Math.sqrt(n); j++) {
                if (n % j === 0) return `YES\n${i} ${j} ${n/j}`;
            }
        }
    }
    return 'NO';
}

let t = +readline();
while(t--) print(problem(+readline()));