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 sys
import math
from functools import reduce


def getN():
    return int(input())


def getNM():
    return map(int, input().split())


def getList():
    return list(map(int, input().split()))


def getArray(intn):
    return [int(input()) for i in range(intn)]


def input():
    return sys.stdin.readline().rstrip()


def factorize(n):
    factors = []
    for i in range(2, int(math.sqrt(n) + 1)):
        while n % i == 0:
            factors.append(i)
            n //= i
    if n != 1:
        factors.append(n)
    return factors


for _ in range(int(input())):
    n = getN()
    factors = factorize(n)

    if len(factors) < 3:
        print("NO")
        continue

    if factors[0] == factors[1]:
        factors[1] = factors[1] * factors[2]
        factors.pop(2)

    if len(factors) < 3:
        print("NO")
        continue
    factors[2] = reduce((lambda x, y: x * y), factors[2:])

    if len(set(factors)) < 3:
        print("NO")
        continue
    print("YES")
    print(*factors[:3])