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

def minp():
	return sys.stdin.readline().strip()

def mint():
	return int(minp())

def mints():
	return map(int, minp().split())

def solve():
	n = mint()
	a = []
	nn = n
	for i in range(2,n+1):
		if i*i > n:
			break
		if n % i == 0:
			c = 0
			while n % i == 0:
				n //= i
				if len(a) == 2:
					break
				c += 1
			a.append((i, c))
	if n != 1:
		a.append((n, 1))
	if len(a) == 1:
		if a[0][1] < 6:
			print('NO')
		else:
			print('YES')
			print(a[0][0],a[0][0]**2,nn // (a[0][0]**3))
	elif len(a) == 2:
		if a[0][1] > 1 and a[1][1] > 1:
			print('YES')
			print(a[0][0],a[1][0],nn // (a[0][0]*a[1][0]))
		elif a[0][1] > 2:
			print('YES')
			print(a[0][0],a[0][0]**2,nn // (a[0][0]**3))
		elif a[1][1] > 2:
			print('YES')
			print(a[1][0],a[1][0]**2,nn // (a[1][0]**3))
		else:
			print('NO')
	else:
		print('YES')
		print(a[0][0],a[1][0],nn // (a[0][0]*a[1][0]))

for i in range(mint()):
	solve()