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 math
# N, M = map(int, input().split())
# A = list(map(int, input().split()))
T = int(input())
def primeFactors(n):
	c = 1
	for i in range(2,int(math.sqrt(n))+1,1):  
		while n % i== 0: 
			c = c*i
			if c not in L and c > 1 and len(L) < 2:
				L.append(c)
				c = 1
			n = n // i 
			  
	# Condition if n is a prime 
	# number greater than 2 
	if n > 2: 
		c *= n
	if c > 1 and c not in L:
		L.append(c) 
for t in range(T):
	N = int(input())
	L = []
	primeFactors(N)
	if len(L) == 3:
		print("YES")
		# print(L)
		print(L[0], L[1], L[2])
	else:
		print("NO")