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
def factors(n):
    l = []
    for i in range(2, int(math.sqrt(n))+1):
        if n%i == 0:
            l.append(i)
            l.append(n//i)
    return l


for _ in range(int(input())):
    n = int(input())
    l = factors(n)
    nn = len(l)
    flag = 0
    for i in range(nn):
        for j in range(nn):
            for k in range(nn):
                if l[i] * l[j] * l[k] == n:
                    if not (i == j or j == k or k == i):
                        print("YES")
                        print(l[i], l[j], l[k])
                        flag = 1
                        break
            if flag == 1:
                break
        if flag == 1:
            break
    if flag == 0:
        print("NO")