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 sys
I=sys.stdin.readline
ans=""
for _ in range(int(I())):
	n=int(input())
	fac=[]
	for i in range(2,int(n**.5)):
		if n%i==0:
			fac.append((i,n//i))
			break

	if len(fac)!=0:
		x=fac[0][1]
		for i in range(2,int(x**.5)+1):
			if x%i==0 and i!=fac[0][0] and i!=x//i:
				ans+="YES\n"
				ans+="{} {} {}\n".format(fac[0][0],i,x//i)
				break
		else:
			ans+="NO\n"
	else:
		ans+="NO\n"
print(ans)