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:
t = int(input())
for _ in range(t):
    n = int(input())
    if n < 2*3*4:
        print("NO")
    else:
        r = []
        i = 2
        j = 3
        while j > 1:
            l = len(r)
            for k in range(i, int(n**(1/j) + 2)):
                if n % k == 0:
                    r.append(k)
                    n //= k
                    i = k + 1
                    j -= 1
                    break
            if len(r) == l or len(r) == 2:
                break
        if len(r) == 2 and n > int(r[-1]):
            r.append(n)
            print('YES')
            print(' '.join(map(str, r)))
        else:
            print('NO')