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 product_of_3_numbers(n):
    for i in range(2, int(n ** (1 / 2)) + 1):
        if n % i == 0:
            d = n // i
            for j in range(i + 1, int(d ** (1 / 2)) + 1):
                if d % j == 0 and j != d // j:
                    print("YES")
                    print(i, j, d // j)
                    return
    print("NO")


t = int(input())
for _ in range(t):
    n = int(input())
    product_of_3_numbers(n)