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
from collections import Counter
t = int(input())
for _ in range(t):
    n = int(input())
    divisors = Counter()
    for p in range(2, int(math.sqrt(n))+1):
        while n % p == 0:
            divisors[p] += 1
            n //= p
    if n > 1:
        divisors[n] += 1

    ans = [1, 1, 1, 1]
    i = 1
    for k, v in divisors.items():
        for j in range(v):
            ans[i] *= k
            if all(ans[i] != ans[j] for j in range(i)) and i < 3:
                i += 1

    if len(set(ans)) == 4:
        print('YES')
        print(*ans[1:])
    else:
        print('NO')