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:
from collections import deque
import sys

def inp():
    return sys.stdin.readline().strip()
for _ in range(int(inp())):
    n=int(inp())
    i=2
    fac=set()
    while i*i<=n:
        if n%i==0:
            x=n//i
            fac.add(i)
            fac.add(x)
        i+=1 
    fac=sorted(fac)
    if len(fac)<3:
        print('NO')
        continue
    f=False
    for i in range(len(fac)):
        for j in range(i+1,len(fac)):
            x=fac[i]
            y=fac[j]
            z=n//(x*y) 
            if x!=y and y!=z and z>=2 and x!=z and x*y*z==n:
                f=True
                break
        if f:
            break
    if f:
        print('YES')
        print(x,y,z)
    else:
        print('NO')