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:
''' بِسْمِ اللَّهِ الرَّحْمَٰنِ الرَّحِيمِ '''
#codeforces
gi = lambda : list(map(int,input().split()))
t, = gi()
for k in range(t):
	n, = gi()
	div = 1
	sq = int(n ** .5)
	for j in range(2, sq + 1):
		if n % j == 0:
			div = j
			break
	x = n // div
	sq = int(x ** .5)
	div2 = 1
	for j in range(2, sq + 1):
		if x % j == 0:
			if len({div, j, x // j}) == 3:
				div2 = j
				break;
	if div == 1 or div2 == 1:
		print("NO")
	else:
		print("YES")
		print(div, div2, x // div2)