<p>Given two arrays <code>nums1</code>&nbsp;and <code><font face="monospace">nums2</font></code><font face="monospace">.</font></p>

<p>Return the maximum dot product&nbsp;between&nbsp;<strong>non-empty</strong> subsequences of nums1 and nums2 with the same length.</p>

<p>A subsequence of a array is a new array which is formed from the original array by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie,&nbsp;<code>[2,3,5]</code>&nbsp;is a subsequence of&nbsp;<code>[1,2,3,4,5]</code>&nbsp;while <code>[1,5,3]</code>&nbsp;is not).</p>

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

<pre>
<strong>Input:</strong> nums1 = [2,1,-2,5], nums2 = [3,0,-6]
<strong>Output:</strong> 18
<strong>Explanation:</strong> Take subsequence [2,-2] from nums1 and subsequence [3,-6] from nums2.
Their dot product is (2*3 + (-2)*(-6)) = 18.</pre>

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

<pre>
<strong>Input:</strong> nums1 = [3,-2], nums2 = [2,-6,7]
<strong>Output:</strong> 21
<strong>Explanation:</strong> Take subsequence [3] from nums1 and subsequence [7] from nums2.
Their dot product is (3*7) = 21.</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [-1,-1], nums2 = [1,1]
<strong>Output:</strong> -1
<strong>Explanation: </strong>Take subsequence [-1] from nums1 and subsequence [1] from nums2.
Their dot product is -1.</pre>

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

<ul>
	<li><code>1 &lt;= nums1.length, nums2.length &lt;= 500</code></li>
	<li><code>-1000 &lt;= nums1[i], nums2[i] &lt;= 1000</code></li>
</ul>

class Solution:
    def maxDotProduct(self, nums1: List[int], nums2: List[int]) -> int:
        if max(nums1) < 0 and min(nums2) > 0:
            return max(nums1) * min(nums2)
        if max(nums2) < 0 and min(nums1) > 0:
            return max(nums2) * min(nums1)
        n1 = len(nums1)
        n2 = len(nums2)
        dp = [[0] * (n2+1) for _ in range(n1+1)]
        ans = float('-inf')
        for i in range(n1-1, -1, -1):
            for j in range(n2-1, -1, -1):
                # # print(i-1, ":", dp[i-1], i, j, dp[i][j], (nums1[i-1] * nums2[j-1]), dp[i-1][j-1])
                # if j == n2-1 and i == n1-1:
                #     dp[i][j] = (nums1[i] * nums2[j])
                # elif j == n2-1:
                #     dp[i][j] = max(dp[i+1][j], (nums1[i] * nums2[j]))
                # elif i == n1-1:
                #     dp[i][j] = max(dp[i][j+1], (nums1[i] * nums2[j]))
                # else:
                temp = (nums1[i] * nums2[j]) + (dp[i+1][j+1] if dp[i+1][j+1] > 0 else 0)
                dp[i][j] = max(max(dp[i+1][j], dp[i][j+1]), temp)
                # ans = max(ans, dp[i][j])
                # print(dp[i])
                # print(dp[i-1])
                # print("--")
        print(dp)
        return dp[0][0]

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