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:
def three_nums(n):
    ret = []
    i_max = int(n ** 0.5 + 0.5)
    remainder = n
    cnt = 0
    for i in range(2, i_max + 1):
        if remainder % i == 0:
            ret.append(i)
            remainder //= i
            i_max = int(remainder ** 0.5 + 0.5)
            cnt += 1
            if cnt == 2:
                ret.append(remainder)
                break
    if len(ret) != 3 or ret[1] >= ret[2]:
        return None
    return ret


if __name__ == "__main__":
    t = int(input())
    for _ in range(t):
        n = int(input())
        xs = three_nums(n)
        if xs is not None:
            print("YES")
            print(*xs)
        else:
            print("NO")