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

t = int(input())
for i in range(t):
    n = int(input())
    ans = []
    if n < 24:
        print('NO')
    else:
        for i in range(2, ceil(n**(1/3))+1):
            if n % i == 0:
                ans.append(i)
                break
        if len(ans)==0:
            print('NO')
        else:
            n1 = n//ans[0]
            for j in range(ans[0]+1, ceil(n**(1/2))+1):
                if n1 % j == 0:
                    ans.append(j)
                    break

            if len(ans) != 2:
                print('NO')

            else:
                n2 = n1 //ans[1]
                if n2 <= ans[1]:
                    print('NO')
                else:
                    print('YES')
                    print(f'{ans[0]} {ans[1]} {n2}')