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 ceil


def factorize(n):
    ans = []
    sq = ceil(n ** 0.5)
    while n > 1 and len(ans) < 2:
        prime = True
        for i in range(2, sq + 1):
            if n % i == 0:
                if i not in ans:
                    ans.append(i)
                    n //= i
                    prime = False
                    break
        if prime:
            if n != 1 and n not in ans:
                ans.append(n)
                n = 1
            else:
                break
    if n != 1 and n not in ans:
        ans.append(n)
    return ans


#print(factorize(2 * 2 * 2 * 2 * 2 * 69 * 228 * 1337))
t = int(input())
for i in range(t):
    n = int(input())
    #print(factorize(n))
    if len(factorize(n)) == 3:
        print('YES')
        print(*factorize(n))
    else:
        print('NO')