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 collections import Counter

def primes(n):
    primfac = []
    d = 2
    while d*d <= n:
        while (n % d) == 0:
            primfac.append(d)  
            n //= d
        d += 1
    if n > 1:
       primfac.append(n)
    return primfac

for _ in range(int(input())):
	n = int(input())
	a = primes(n)
	if(len(a) < 3):
		print("NO")
	else:
		c = Counter(a)
		y = list(c.keys())			
		if(len(c) >= 3):
			print("YES")
			x = 1
			for i in a[2:]:
				x *= i
			print(y[0], y[1], n//(y[0]*y[1]))
		else:
			# print(c, list(c.keys())[0])
			if(len(c) == 1):
				if(c[y[0]] > 5):
					print("YES")
					print(a[0], a[0]*a[1], n//(a[0]*a[0]*a[0]))
				else:
					print("NO")
			else:
				if(c[y[0]] + c[y[1]] >= 4):
					print("YES")
					print(y[0], y[1], n//(y[0]* y[1]))
				else:
					print("NO")