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
 
for _ in range(int(input())):
    n = int(input())
 
    flag = False
 
    if n < 24:
        print('NO')
    elif n == 24:
        print('YES')
        print(2, 3, 4)
    else:
 
        for a in range(2, int(math.sqrt(n)) + 1):
            if n % a == 0:
                tn = int(n / a)
                for b in range(a + 1, int(math.sqrt(tn)) + 1):
                    if tn % b == 0:
                        c = int(tn / b)
                        if c != b and a != c:
                            print('YES')
                            print(a, b, c)
                            flag = True
                            break
            if flag is True:
                break
 
        if flag is False:
            print('NO')