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 isPrime(n):
    for i in range(2,n):
        if n % i:
            return False
    return True
t = int(input())
for _ in range(t):
    n = int(input())
    if isPrime(n):
        print("NO")
    else:
        ip = False
        i = 0
        for i in range(2,int(math.sqrt(n)) + 1):
            if n % i == 0:
                if not isPrime(n // i):
                    ip = True
                    break
        if ip:
            ip = False
            for j in range(i+1,int(math.sqrt(n//i)) + 1):
                if (n // i) % j == 0:
                    ip = True
                    a = i
                    b = j
                    c = (n//i)//j
                    break
            if ip and (a !=b and b !=c and a != c):
                print("YES")
                print(a,b,c)
            else:
                print("NO")
        else:
            print("NO")