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
inp = sys.stdin.readline
for i in range(int(inp())):
	n = int(inp())
	arr = ""
	c = 0
	flag = 0
	for i in range(2, round(sqrt(n))+1):
		if n % i == 0:
			c += 1
			arr += str(i)+" "
			n = n//i
			if c == 2 and n > i:
				flag = 1
				arr += str(n)
				break
	if flag:
		print("YES\n" + arr)
	else:
		print("NO")