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:
N = int(input())

from math import *

for _ in range(N):
	n = int(input())

	sn = int(sqrt(n))+1
	cnt = 0
	ans = []
	for i in range(2, sn):
		if n % i == 0:
			ans.append(i)
			n //= i
			cnt += 1
			if cnt == 2:
				cnt = i
				break

	if n not in ans and len(ans) == 2:
		print("YES")
		print(' '.join(map(str, ans)), n)
	else:
		print("NO")

"""
TEST 1:
5
64
32
97
2
12345
===
YES
2 4 8 
NO
NO
NO
YES
3 5 823
///

TEST 2:
2
98
196
===
NO
///
"""