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 is_prime(n):
    if n == 1:
        return False
    i = 2
    while i*i <= n:
        if n % i == 0:
            return False
        i += 1
    return True

for _ in range(int(input())):
    n = int(input())
    a = []
    z = int(math.sqrt(n))
    if is_prime(n) == True:
        print("NO")
    else:
        for i in range(2, z):
            if n%i==0:
                a.append(i)
                n = n//i
            if len(a)==2:
                break
        if n<2:
            print("NO")
        elif len(a)==2:
            if n==a[0] or n==a[1]:
                print("NO")
            else:
                print("YES")
                for i in a:
                    print(i, end=' ')
                print(n)
        else:
            print("NO")