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
class Read:
    @staticmethod
    def int():
        return int(input())
 
    @staticmethod
    def list(sep=' '):
        return input().split(sep)
 
    @staticmethod
    def list_int(sep=' '):
        return list(map(int, input().split(sep)))
 
 
def main():
    n = Read.int()
    status = False
    for a in range(2, int(math.sqrt(n) + 1)):
        if n % a == 0:
            k = n / a
            for b in range(a+1, int(math.sqrt(k) +1)):
                if k % b == 0:
                    c = int(k / b)
                    if b != c and c > 2:
                        print('YES')
                        print('{} {} {}'.format(a, b, c))
                        status = True
                        break;
        if status:
            break;
    if status == False:
        print('NO')

query_count = Read.int()
while query_count:
    query_count -= 1
    main()