<p>Given an <code>n x n</code> integer matrix <code>grid</code>, return <em>the minimum sum of a <strong>falling path with non-zero shifts</strong></em>.</p>

<p>A <strong>falling path with non-zero shifts</strong> is a choice of exactly one element from each row of <code>grid</code> such that no two elements chosen in adjacent rows are in the same column.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/falling-grid.jpg" style="width: 244px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [[1,2,3],[4,5,6],[7,8,9]]
<strong>Output:</strong> 13
<strong>Explanation:</strong> 
The possible falling paths are:
[1,5,9], [1,5,7], [1,6,7], [1,6,8],
[2,4,8], [2,4,9], [2,6,7], [2,6,8],
[3,4,8], [3,4,9], [3,5,7], [3,5,9]
The falling path with the smallest sum is&nbsp;[1,5,7], so the answer is&nbsp;13.
</pre>

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

<pre>
<strong>Input:</strong> grid = [[7]]
<strong>Output:</strong> 7
</pre>

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

<ul>
	<li><code>n == grid.length == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 200</code></li>
	<li><code>-99 &lt;= grid[i][j] &lt;= 99</code></li>
</ul>

class Solution {
public:
 
long long int solve(int i, int j,vector<vector<int>>& grid,vector<vector<long long int>> &dp){
    if(i>=grid.size() ||j>=grid.size()){
        return 0;
    }
    
    long long int ans= INT_MAX;
   if(dp[i][j]!= -1) return dp[i][j];
    for(int k=0; k<grid[0].size(); k++){
        if(k!= j) {
          ans= min(ans, solve(i+1,k,grid,dp)+ grid[i][k]);
        }
    }
    return dp[i][j]= ans;
}
    int minFallingPathSum(vector<vector<int>>& grid) {
     long long  int ans = INT_MAX;
     vector<vector<long long int>> dp(grid.size(),vector<long long int>(grid[0].size(),-1));
      for(int i=0; i<grid[0].size(); i++){
        ans= min(ans, solve(1,i,grid, dp)+ grid[0][i]);
      }  

      return ans;
    }
};
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