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 *

for ct in range(int(input())):
    n = int(input())

    flag = False
    for i in range(2, int(sqrt(n))):
        if flag:
            break
        if n % i == 0:
            par = n//i
            for j in range(2, int(sqrt(par))+1):
                if par % j == 0:
                    k = par // j
                    if i != j and j != k and i != k:
                        print("YES")
                        print(i, j, k)
                        flag = True
                        break
            else:
                for j in range(2, int(sqrt(i))+1):
                    if i % j == 0:
                        k = i // j
                        if par != j and j != k and par != k:
                            print("YES")
                            print(par, j, k)
                            flag = True
                            break
    else:
        print("NO")