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:
nn = int(input())
import math 
def isprime(n):
    if n <= 7:
        return False, 1 
    sqrt = int( math.sqrt(n) ) + 1 
    for i in range(2, sqrt):
        if n % i == 0:
            return True, i 
    
    return False, 1

def isprime2(n):
    if n <= 3:
        return False, 1 
    sqrt = int( math.sqrt(n) ) + 1 
    for i in range(2, sqrt):
        if n % i == 0:
            return True, i 
    
    return False, 1


for dfdfdi in range(nn):
    v = int(input())
    if v <= 7:
        print("NO")
        continue
    firstTrue, firstPrime = isprime(v)
    if not firstTrue:
        print("NO")
        continue
    v = v // firstPrime
    secondTrue, secondPrime = isprime2(v)
    if not secondTrue:
        print("NO")
        continue
    final = v // secondPrime
    if firstPrime == secondPrime or secondPrime == final:
        
        thirdTrue, thirdPrime = isprime2(final)
        if not thirdTrue:
            print("NO")
        else:
            secondPrime *= thirdPrime
            final = final // thirdPrime
            #if secondPrime == final:
            if secondPrime == final or secondPrime == firstPrime or final == firstPrime:
                print("NO")
                continue
            else:
                print("YES")
                print(str(firstPrime) + " " + str(secondPrime) + " " + str(final))
    else:    
        print("YES")
        print(str(firstPrime) + " " + str(secondPrime) + " " + str(final))