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 main():
    T = int(input())
    for t in range(T):
        m = int(input())
        n = m
        dic = {}
        i = 2
        while i * i <= n:
            while n % i == 0:
                dic[i] = dic.get(i, 0) + 1
                n //= i
            i += 1
        if m % n == 0 and n != 1:
            dic[n] = dic.get(n, 0) + 1
        keys = list(dic.keys())
        # print("*" + str(len(dic)))
        if len(dic) == 0:
            print("NO")
        elif len(dic) == 1:
            x = keys[0]
            y = dic[x]
            if y < 6:
                print("NO")
            else:
                print("YES")
                print(str(x) + ' ' + str(x**2) + ' ' + str(x**(y-3)))
        elif len(dic) == 2:
            x1, x2 = keys[0], keys[1]
            y1, y2 = dic[x1], dic[x2]
            if y1 + y2 <= 3:
                print("NO")
            else:
                print("YES")
                print(str(x1) + ' ' + str(x2) + ' ' + str((x1**(y1-1)) * (x2**(y2-1))))
        else:
            x1, x2 = keys[0], keys[1]
            y1, y2 = dic[x1], dic[x2]
            print("YES")
            print(str(x1**y1) + ' ' + str(x2**y2) + ' ' + str(m // (x1**y1) // (x2**y2)))



if __name__ == "__main__":
    main()