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:
from sys import stdin

inp = (s.rstrip() for s in stdin).__next__


def mpint():
	return map(int, inp().split())

# sieve
N = int(1e5)
is_prime = [True] * (N + 1)  # have 0
is_prime[0] = is_prime[1] = False
prime = []
for n in range(2, N + 1):
	if is_prime[n]:
		prime.append(n)
	for p in prime:
		if n * p > N:  # Index out of range
			break
		is_prime[p * n] = False
		# print("%d*%d = %d" % (p, n, p*n))
		if n % p == 0:
			break
# print(prime)

def f():
	global n
	if len(ans) == 2:
		return

	for p in prime:
		if p*p > n:
			return

		if n % p == 0:
			n //= p
			ans.append(p)
			return f()

for case in range(int(inp())):
	n = int(inp())
	ans = []
	f()
	if len(ans) <= 1:
		print("NO")
		continue

	if ans[0] == ans[1]:
		for p in range(2, int(n**0.5)+1):
			if n % p == 0:
				n //= p
				ans[1] *= p
				break

	if len(set(ans + [n])) == 3:
		print("YES")
		print(*ans, n)
	else:
		print("NO")