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 main():
    t = int(input())
    out_lst = []
    if t <=100 and t >= 1:
        for i in range(t):
            n = int(input())
            div_n = n
            lst = []
            n_rang = int(math.sqrt(n))
            for j in range(2,n_rang):
                if div_n % j == 0:
                    div_n = div_n / j
                    lst.append(j)
                    if len(lst) == 2:
                        if(int(div_n) not in lst):
                            lst.append(int(div_n))
                        break
            if len(lst) == 3 and 1 not in lst:
                out_lst.append("YES")
                out_lst.append("{} {} {}".format(lst[0], lst[1], lst[2]))
            else:
                out_lst.append("NO")
        for k in out_lst:
            print(k)
    else:
        return False


main()