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


def check(count,n):
    a = int(math.sqrt(n))
    for i in range(count, a+1):
        if n % i == 0:
            return i
    return 0


for i in range(int(input())):
    n = int(input())
    a,b,c  = 0, 0 , 0
    while(n != 0):
        if (check(2,n) == 0):
            c = n
            n = 0
            break
        elif (check(2,n) != 0 ):
            a = check(2,n)
            b = check(a+1,n /a)
            if (b == 0):
                break
            c = n / (a*b)
            break
    if (c <= 1 or a <=1 or b <=1 or a == b or b == c or c == a ) :
        print("NO")
        continue
    print("YES")
    print(a,' ',b,' ',int(c))