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


t = int(input())
for _ in range(t):
    n = int(input())
    d = []
    temp = n
    while n % 2 == 0:
        d.append(2)
        n //= 2
    for i in range(3, (int(math.sqrt(n)) + 1), 2):
        while n % i == 0:
            d.append(i)
            n //= i
    if n > 2:
        d.append(n)
    if len(d) < 3:
        print('NO')
    elif len(d) == 3 and (d[0] == d[1] or d[1] == d[2]):
        print('NO')
    else:
        # print(d)
        a = d[0]
        if d[1] == d[0]:
            b = d[1] * d[2]
            c = int(temp / (a * b))
        else:
            b = d[1]
            c = int(temp / (a * b))
        if a == b or a == c or b == c:
            print('NO')
        else:
            print('YES')
            print(a, b, c)