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 functools import reduce
t = int(input())
for cas in range(t):
    n = int(input())
    ans = []
    m = n
    sqrt_n = int(math.sqrt(m))
    for i in range(2, sqrt_n):
        cal = 0
        if n == 1:
            break
        while n % i == 0 and n > 1:
            n //= i
            ans.append(i)
    if n > 1:
        ans.append(n)
    if len(ans) < 3:
        print("NO")
    elif len(ans) == 3:
        if len(set(ans)) < 3:
            print("NO")
        else:
            print("YES")
            print(ans[0], ans[1], ans[2])
    elif len(ans) == 4:
        if len(set(ans)) == 1:
            print("NO")
        else:
            print("YES")
            print(ans[0], ans[1] * ans[2], ans[3])
    elif len(ans) == 5:
        if len(set(ans)) == 1:
            print("NO")
        else:
            print("YES")
            print(ans[0], ans[1] * ans[2] * ans[3], ans[4])
    else:
        print("YES")
        print(ans[0], ans[1] * ans[2], m//(ans[0]*ans[1]*ans[2]))
        #reduce(lambda x, y: x * y, ans[3:])