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:
"""
author : dokueki
"""
import math


def divisor(x):
    i = 1
    div = []
    while i <= math.sqrt(x):
        if x%i == 0:
            if x//i == i:
                div.append(i)
            else:
                div.extend([i,x//i])
        i += 1
    div.remove(max(div))
    div.remove(min(div))
    return div


for _ in range(int(input())):
    n = int(input())
    div1 = divisor(n)
    if len(div1) == 0:
        a = False
    else:
        a = min(div1)
    if a:
        div2 = sorted(divisor(n // a))
        if len(div2) == 0:
            b = False
        else:
            for i in div2:
                if i > a:
                    b = i
                    break
    else:
        b = False
    #print(div2)

    if a and b:
        c = n//(a*b)
        if c > a and c > b :
            pass
        else:
            c = False
    else:
        c = False
    #print((a,b,c))
    if a and b and c:
        print("YES")
        print(a,b,c)
    else:
        print("NO")