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 as m
t=int(input())

for i in range(t):
    n=int(input())
    a=0
    b=0
    c=0

    for j in range(2,int(m.sqrt(n))+1):
        if n%j==0:
            a=j
            n=n/j
            break
    for k in range(a+1,int(m.sqrt(n))+1):
        if n%k==0:
            b=k
            c=n/k
            break

    if a>1 and b>1 and c>1 and  ( a!=b and a!=c and b!=c) :
        print("YES")
        print(int(a),int(b),int(c))
    else:
        print("NO")