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 div(n, m):
    i = m+1
    while i*i < n:
        if(n%i == 0):
            return(i, n // i)
        i += 1

    return(-1, -1)

t = int(input())

for _ in range(t):
    n = int(input())
    a = 0
    i = 2
    while i * i < n:
        if (n % i == 0):
            a = i
            break
        i += 1
        
    if(a == 0):
        print("NO")
    else:
        b, c = div(n//a, a)
        if(b == -1):
            print("NO")
        else:
            print("YES\n",a," ",b," ",c)