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 isPrime(n : int):
    if n == 1:
        return False
    if n == 2:
        return True
    else:
        for i in range(2, n // 2):
            if n % i == 0:
                return False
        return True
t = int(input())
for i in range(t):
    n = int(input())
    y = n
    res = []
    k = 2
    for k in range(2, int(y ** 0.5) + 1):
        if n % k == 0:
            res.append(k)
            n = n // k
        k += 1
        if len(res) == 2:
            break
    if len(res) == 2 and res[-1] < n:
        print("YES")
        print(*res, n)
    else:
        print("NO")