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:
t = int(input())

for i in range(t):
	n = int(input())
	
	dvdrs = []
	passs = True
	if n < 24:
		print("NO")
		continue
		
	for k in range(2,n):
		if k*k*k > n:
			passs = False
			break
		if n%k == 0:
			dvdrs += [k]
			n = int(n/k)
			break
		
	if passs:
		for k in range(dvdrs[0]+1, n):
			if k*k > n:
				passs = False
				break
			if n%k == 0:
				dvdrs += [k]
				n = int(n/k)
				break
	
	if passs and n != dvdrs[0] and n != dvdrs[1]:
		print("YES")
		print(str(dvdrs[0]) + " " + str(dvdrs[1]) + " " + str(n))
	else:
		print("NO")