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 
import math


def fun(s):
    for i in range(2, int(math.sqrt(s)) + 1):
        if s % i == 0:
            w = s // i
            for j in range(i + 1, int(math.sqrt(w) + 1)):
                d = w // j
                if w % j == 0 and d != j and d != i:
                    return i, j, d
    return -1


for t in range(int(input())):
    n = int(input())
    q = fun(n)
    if q != -1:
        print('YES')
        print(q[0], q[1], q[2])
    else:
        print('NO')
