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:
n = int(input())
def f(a):
        q = a
        x = 0
        y = 0
        z = 0
        for i in range(2, a):
            if i * i > a:
                break
            if a % i == 0:
                x = i
                break
        if x == 0:
            return 'NO'
        else:
            a = a // x
        for i in range(2, a):
            if i * i > a:
                break
            if i != x and a % i == 0:
                y = i
                break
        if y == 0:
            return 'NO'
        else:
            z = a//y
        if z != y and z != x and y != x and x * y * z == q:
            return 'YES' + '\n' + str(x) + ' ' + str(y) + ' ' + str(z)
        return 'NO'
for i in range(n):
    a = int(input())
    print(f(a))