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, ceil

for _ in range(int(input())):
    n = int(input())

    ans = "YES"
    out = [0, 0, 0]
    for i in range(2, int(ceil(sqrt(n)))):
        if n % i == 0:
            n //= i
            out[0] = i
            break
    else:
        ans = "NO"
    
    if ans == "YES":
        for j in range(2, int(ceil(sqrt(n)))):
            if j == out[0]: continue
            if n % j == 0:
                n //= j
                if n == out[0]: continue
                out[1], out[2] = j, n
                break
        else:
            ans = "NO"
    
    if ans == "NO":
        print(ans)
    else:
        print(ans)
        print(*out)