<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> representing the score of students in an exam. The teacher would like to form one <strong>non-empty</strong> group of students with maximal <strong>strength</strong>, where the strength of a group of students of indices <code>i<sub>0</sub></code>, <code>i<sub>1</sub></code>, <code>i<sub>2</sub></code>, ... , <code>i<sub>k</sub></code> is defined as <code>nums[i<sub>0</sub>] * nums[i<sub>1</sub>] * nums[i<sub>2</sub>] * ... * nums[i<sub>k</sub>​]</code>.</p>

<p>Return <em>the maximum strength of a group the teacher can create</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,-1,-5,2,5,-9]
<strong>Output:</strong> 1350
<strong>Explanation:</strong> One way to form a group of maximal strength is to group the students at indices [0,2,3,4,5]. Their strength is 3 * (-5) * 2 * 5 * (-9) = 1350, which we can show is optimal.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [-4,-5,-4]
<strong>Output:</strong> 20
<strong>Explanation:</strong> Group the students at indices [0, 1] . Then, we&rsquo;ll have a resulting strength of 20. We cannot achieve greater strength.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 13</code></li>
	<li><code>-9 &lt;= nums[i] &lt;= 9</code></li>
</ul>

class Solution:
    def __init__(self):
        self.ans = -99999999
    def maxStrength(self, nums: List[int]) -> int:
        subset = []
        def backtrack(start, end):
            if math.prod(subset) > self.ans and len(subset)>0:
                self.ans = math.prod(subset)
            for i in range(start, end):
                subset.append(nums[i])
                backtrack(i+1, end)
                subset.pop()
        backtrack(0, len(nums))
        return self.ans
        
515