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
input = sys.stdin.readline

def factors(n):
	ret = set()
	for i in range(2, int(n**.5) + 1):
		if n%i == 0:
			ret.add(i)
			ret.add(n//i)
	return ret

def solve(n):
	for i in range(2, int(n**.5)+1):
		if n%i == 0 and i != n//i:
			a, b = i, n//i
			fa, fb = factors(a), factors(b)
			# option 1
			if len(fa) > 0:
				for fac in fa:
					if len(set([fac, a//fac, b])) == 3:
						return [fac, a//fac, b]
			# option 2
			if len(fb) > 0:
				for fac in fb:
					if len(set([fac, b//fac, a])) == 3:
						return [fac, b//fac, a]
	return 'NO'


for _ in range(int(input())):
	n = int(input())
	ans = solve(n)
	if ans == 'NO':
		print('NO')
	else:
		print('YES')
		print(*sorted(ans))