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:
t = int(input())

for i in range(t):
    n = int(input())

    divisorarr = []

    for divisor in range(2, int(n ** 0.5) + 2):
        if n % divisor == 0:
            while n % divisor == 0:
                n = n // divisor
                divisorarr.append(divisor)
    if n != 1:            
        divisorarr.append(n)
    if len(divisorarr) < 3:
        print('NO')
    else:
        a = divisorarr[0]
        b = divisorarr[1]
        index = 2
        while b == a and index < len(divisorarr) - 1:
            b *= divisorarr[index]
            index += 1
        c = 1
        for divisor in range(index, len(divisorarr)):
            c *= divisorarr[divisor]
        if not a != b != c != a:
            print('NO')
        else:
            print('YES')
            print(a, b, c)