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:
t = int(input())

def isnotprime(n):
    for i in range(1, int(n**0.5)+1):
        if n%i == 0:
            return True

    return False


for _ in range(t):
    n = int(input())

    if n<8:
        print('NO')
        continue
    
    found = list()
    foundmul = 1
    done = False
    for i in range(2, int(((n//2)+1)**0.5)+1):

        if n%i == 0:
            found.append(i)
            foundmul *= i
            n //= i

        if len(found) >= 2:
            if n >= 2 and (n not in found):
                print('YES')
                print(found[0], found[1], n)
                done = True
                break

            else:
                done = True
                print('NO')
                break

        if n <= 1:
            done = True
            print("NO")
            break


    if not done:
        print('NO')