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 PYTHON3):

Solution:
import os,sys,math,random

def dep(a):
    a0 = a
    res = []
    for b in range(2, int(a**(1/3))+1):
        if a % b == 0:
            res.append(b)
            break
    if len(res) == 0:
        return "NO"

    a /= res[0]
    for b in range(2, int(a**(1/2))+1):
        if a % b == 0 and b != res[0]:
            res.append(b)
            break
    if len(res) == 1:
        return "NO"

    c = int(a0 / res[0] / res[1])
    if c == 1 or c == res[0] or c == res[1]:
        return "NO"
    
    res.append(c)

    return "YES\n" + " ".join(map(str, res))

T = int(input())
for _ in range(T):
    a = int(input())
    print(dep(a))