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 PYTHON):

Solution:
from math import ceil, sqrt
def main():
	t = int(input())
	while t:
		n = int(input())
		findProd(n)
		t -= 1
def findProd(n):
	a = 2
	found = 0
	temp = n
	while a <= ceil(sqrt(n)):
		if n%a == 0:
			n = n // a
			b = a + 1
			while b <= ceil(sqrt(n)):
				c = n//b
				if n%b == 0 and c > 1 and c != b and c != a :
					found = 1
					print("YES")
					print(a),
					print(b),
					print(c)
					break
				else:
					b += 1
			if found:
				break
				
		else:
			a += 1
	if not found:
		print("NO")
main()