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 
def main():
    n = int(input())
    a = 2
    while a * a * a < n:
        if n % a == 0:
            b = a + 1
            while b * b < n // a:
                if (n // a) % b == 0:
                    c = n // a // b
                    if a != c and b != c:
                        print("YES")
                        print(a, b, n // a // b)
                        return 0
                b += 1
        a += 1
    print("NO")
p = int(input())
for i in range(p):
        main()