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
def solve(n):
	A=[]
	for i in range(2,int(math.sqrt(n))+1):
		if(n%i==0):
			A.append(i)
			break
	if(len(A)==0):
		print("NO")
		return
	n=n//A[0]
	for i in range(A[0]+1,int(math.sqrt(n))+1):
		if(n%i==0):
			A.append(i)
			A.append(int(n/(i)))
			break
	if(len(A)!=3):
		print("NO")
		return
	if(A[0]<A[1] and A[1]<A[2]):
		print("YES")
		print(A[0],A[1],A[2])
	else:
		print("NO")
t=int(input())
for _ in range(t):
	n=int(input())
	solve(n)