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

num = int(input())

nums = []
for i in range(num):
    nums.append(int(input()))

def isPrime(num):
    for i in range(2, int(math.sqrt(num)) + 1):
        if num % i == 0:
            return False
    return True

def getDel(num, left):
    for i in range(left, int(math.sqrt(num)) + 1):
        if num % i == 0:
            return [i, num // i]
    return [-1]

def thirdNum(f, s, num):
    if num != f and num != s:
        return num
    elif isPrime(num):
        return -1
    else:
        for i in range(s + 1, num):
            if num % i == 0:
                return i
    return -1

for i in nums:
    if isPrime(i) == True:
        print("NO")
    else:
        f = getDel(i, 2)
        if f[0] > 0:
            s = getDel(f[1], f[0] + 1)
            if s[0] > 0:
                t = thirdNum(f[0], s[0], s[1])
                if t > 0:
                    print("YES")
                    print(' '.join(map(str, [f[0],s[0],t])))
                else:
                    print("NO")
            else:
                print("NO")
        else:
            print("NO")