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
t = int(input())
for tt in range(t):
    n = int(input())
    f = 0
    for i in range(2, int(math.sqrt(n)) + 1):
        if n % i == 0:
            a = i
            c = 1
            b = 1
            for j in range(2, int(math.sqrt(n / a)) + 1):
                if (n / a) % j == 0 and j != a:
                    b = j
                    c = int(n / (a * j))
                    break

            if a != c and b != c and c != 1:
                print("YES")
                print("%s %s %s" % (a, b, c))
                f = 1
            else:
                print ("NO")
                f = 1
            break
    if f == 0:
        print ("NO")