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:

from math import sqrt

def solve(R:list):
    n = int(input())

    m = n
    for i in range(2,int(sqrt(m))):
        if i >= n :
            return
        if n % i == 0:
            R.append(i)
            n //= i
        if len(R) == 2:
            break

    if len(R) == 2:
        if n > R[-1]:
            R.append(n)


t = int(input())

for cnt in range(t):
    R = []
    solve(R)
    # print("CASE : " + str(cnt+1))
    if len(R) == 3:
        print("YES")
        print(" ".join(map(str,R)))
    else:
        print("NO")