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 math
def getFactors(n):
    factors = []
    while n%2==0:
        factors.append(2)
        n = n//2
    k=3
    
    while k <= math.sqrt(n):
        if n%k==0:
            n= n//k
            factors.append(k)
        else:
            k+=2
    
    if n>1:
        factors.append(n)
    return factors

t = int(input())
numbers = [ int(input()) for _ in range(t) ]
for n in numbers:
    factors = getFactors(n)
    distinct = set()
    i=0
    num = 1
    while i < len(factors):
        num *= factors[i]
        if len(distinct)==2:
            pass
        elif num not in distinct:
            distinct.add(num)
            num=1
        else:
            pass
        i+=1

    if num!=1: distinct.add(num)
    if len(distinct)==3:
        print('YES')
        print(" ".join(map(str,sorted(list(distinct)))))
    else:
        print('NO')