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 sys
input = sys.stdin.readline

t=int(input())

import math

def f(x):
    
    xr=math.ceil(math.sqrt(x))

    LIST=[]
    for i in range(1,xr+1):
        if x%i==0:
            LIST.append(i)
            LIST.append(x//i)

    return sorted(set(LIST))[1:]


for test in range(t):
    n=int(input())
    L=f(n)

    A=L[0]

    for i in f(n):
        if i!=A and i*A<n and n%(i*A)==0 and n//(i*A)!=i and n//(i*A)!=A and n//(i*A)!=1:
            print("YES")
            print(A,i,n//(i*A))
            break

    else:
        print("NO")