<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 minPathSum(self, grid: List[List[int]]) -> int:
        
        m = len(grid)
        n = len(grid[0])
        answer_split = [[[grid[j][t] for t in range(n)] for j in range(m)] for z in range(2)]
        answer = [[grid[j][t] for t in range(n)] for j in range(m)]
        for i in range(m):
            for j in range(n):
                row = m - i - 1
                col = n - j - 1
                move_left = col > 0
                move_up = row > 0
                move_right = col < n -1
                move_down = row < m-1
                if(move_right and move_down): 
                    answer[row][col] = min(answer_split[0][row][col], answer_split[1][row][col])
                elif(move_right):
                    answer[row][col] = answer_split[0][row][col]
                elif(move_down):
                    answer[row][col] = answer_split[1][row][col]  
                if(move_left):
                    answer_split[0][row][col-1] += answer[row][col]
                if(move_up):
                    answer_split[1][row - 1][col] += answer[row][col]

        return answer[0][0]               






        
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