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())


def check(n,p):
    ans = -1
    for i in range(p+1, int(math.sqrt(n)) + 1):
        if n % i == 0:
            ans = i
            break
    return ans


for i in range(T):
    l = []
    n = int(input())
    ans = 'YES'
    hello = 1
    for i in range(3):
        hello = check(n,hello)
        if hello == -1 and n < 2:
            ans = 'NO'
            break
        else:
            if hello == -1 or i==2:
                hello = n
                if len(l) > 0 and l[-1] == hello:
                    ans = 'NO'
                    break
            n = n // hello
            l.append(hello)
    print(ans)
    if ans == 'YES':
        print(str(l[0]) + ' ' + str(l[1]) + ' ' + str(l[2]))