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 math import sqrt

t = int(input())

for i in range(t):
	n = int(input())
	l = []
	temp = n
	for j in range(2,int(sqrt(n))+1):
		if temp%j == 0:
			l.append(j)
			temp = temp//j
		if len(l) == 2:
			break
	if len(l) < 2:
		print("NO")
		continue
	l.append(n//(l[0]*l[1]))
	# print(l)
	l.sort()
	a,b,c = l[0],l[1],l[2]
	if a*b*c != n or a == b or b == c or c == a or a == 1 or b == 1 or c == 1:
		print("NO")
	else:
		print("YES")
		print(a,b,c)