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 printDivisors(n) : 
	i = 2
	c = []
	while i <= math.sqrt(n): 
		if (n % i == 0) : 
			if (n / i == i) : 
				c.append(n//i)
			else : 
				c.extend([i,n//i])
		i = i + 1
	return c

def countTriplets(arr, n, m):
    count = 0
    arr.sort()
    for end in range(n - 1, 1, -1):
        start = 0
        mid = end - 1
        while (start < mid):
            prod = (arr[end]*arr[start]*arr[mid])
            if (prod > m):
                mid -= 1
            elif (prod < m):
                start += 1
            elif (prod == m):
                print("YES")
                print(arr[end],arr[start],arr[mid])
                count += 1
                mid -= 1
                start += 1
                return count
    return count
for _ in range(int(input())):
    n = int(input())
    a = printDivisors(n)
    #print(len(a),a)
    if countTriplets(a,len(a),n) == 0:
        print("NO")