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
from math import sqrt
input=sys.stdin.readline
f=lambda :list(map(int, input().split()))
for _ in range(int(input())):
	n=int(input())
	a=0
	for i in range(2, int(sqrt(n))+1):
		if n%i==0:
			a=i
			break
	b=0
	if a:
		for i in range(a+1, int(sqrt(n//a))+1):
			if (n//a)%i==0:
				b=i
				break
	c=0
	if b and n%(a*b)==0:
		c=n//(a*b)
	if c and c!=1 and c!=a and c!=b:
		print('YES\n', a, b, c)
	else:
		print('NO')