<p>Given a <code>m x n</code> <code>grid</code> filled with non-negative numbers, find a path from top left to bottom right, which minimizes the sum of all numbers along its path.</p>

<p><strong>Note:</strong> You can only move either down or right at any point in time.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/05/minpath.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> grid = [[1,3,1],[1,5,1],[4,2,1]]
<strong>Output:</strong> 7
<strong>Explanation:</strong> Because the path 1 &rarr; 3 &rarr; 1 &rarr; 1 &rarr; 1 minimizes the sum.
</pre>

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

<pre>
<strong>Input:</strong> grid = [[1,2,3],[4,5,6]]
<strong>Output:</strong> 12
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 200</code></li>
</ul>

class Solution:
    def __init__(self):
        self.memo = {}
    def caminhar(self, obstacle, x, y):
        height = len(obstacle)
        width = len(obstacle[0])
        key = str((x, y))
        if key in self.memo:
            return self.memo[key]
        if x >= width or y >= height:
            return 99999999
        if x == width - 1 and y == height - 1:
            return obstacle[y][x]
        # print(x, y, obstacle[y][x])
        ans = obstacle[y][x] + min([self.caminhar(obstacle, x + 1, y), self.caminhar(obstacle, x , y+1)])
        self.memo[key] = ans
        return ans
    def minPathSum(self, grid: List[List[int]]) -> int:
        return self.caminhar(grid, 0, 0)
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