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 my_def(x):
    a, b, c = 1, 1, 1
    for j in range(2, int(x ** 0.5) + 2):
        while x % j == 0:
            if a == 1:
                a = j
            elif b == 1 or b == a:
                b *= j
            else:
                return (a, b, x)
            x //= j
    return (a, b, x)


n = int(input())

for i in range(n):
    x = int(input())
    a, b, c = my_def(x)
    if a != b and b != c and a != c and a != 1 and b != 1 and c != 1:
        print("YES")
        print(a, b, c)
    else:
        print("NO")