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, sqrt

n = int(input())
for i in range(n):
    num = int(input())
    ans = []
    for mult in range(2, ceil(sqrt(num))):
        #print('Try ', mult,' for ', num)
        if num < mult:
            break
        if num % mult == 0:
            ans.append(mult)
            num = num / mult
            if (len(ans) == 2) and (ans[0] != num) and (ans[1] != num) and (num != 1):
                ans.append(int(num))
                break
    if len(ans) == 3:
        print('YES')
        print(' '.join([str(x) for x in ans]))
    else:
        print('NO')