<p>Given an <code>m x n</code> grid. Each cell of the grid has a sign pointing to the next cell you should visit if you are currently in this cell. The sign of <code>grid[i][j]</code> can be:</p>

<ul>
	<li><code>1</code> which means go to the cell to the right. (i.e go from <code>grid[i][j]</code> to <code>grid[i][j + 1]</code>)</li>
	<li><code>2</code> which means go to the cell to the left. (i.e go from <code>grid[i][j]</code> to <code>grid[i][j - 1]</code>)</li>
	<li><code>3</code> which means go to the lower cell. (i.e go from <code>grid[i][j]</code> to <code>grid[i + 1][j]</code>)</li>
	<li><code>4</code> which means go to the upper cell. (i.e go from <code>grid[i][j]</code> to <code>grid[i - 1][j]</code>)</li>
</ul>

<p>Notice that there could be some signs on the cells of the grid that point outside the grid.</p>

<p>You will initially start at the upper left cell <code>(0, 0)</code>. A valid path in the grid is a path that starts from the upper left cell <code>(0, 0)</code> and ends at the bottom-right cell <code>(m - 1, n - 1)</code> following the signs on the grid. The valid path does not have to be the shortest.</p>

<p>You can modify the sign on a cell with <code>cost = 1</code>. You can modify the sign on a cell <strong>one time only</strong>.</p>

<p>Return <em>the minimum cost to make the grid have at least one valid path</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/02/13/grid1.png" style="width: 400px; height: 390px;" />
<pre>
<strong>Input:</strong> grid = [[1,1,1,1],[2,2,2,2],[1,1,1,1],[2,2,2,2]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> You will start at point (0, 0).
The path to (3, 3) is as follows. (0, 0) --&gt; (0, 1) --&gt; (0, 2) --&gt; (0, 3) change the arrow to down with cost = 1 --&gt; (1, 3) --&gt; (1, 2) --&gt; (1, 1) --&gt; (1, 0) change the arrow to down with cost = 1 --&gt; (2, 0) --&gt; (2, 1) --&gt; (2, 2) --&gt; (2, 3) change the arrow to down with cost = 1 --&gt; (3, 3)
The total cost = 3.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/02/13/grid2.png" style="width: 350px; height: 341px;" />
<pre>
<strong>Input:</strong> grid = [[1,1,3],[3,2,2],[1,1,4]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> You can follow the path from (0, 0) to (2, 2).
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/02/13/grid3.png" style="width: 200px; height: 192px;" />
<pre>
<strong>Input:</strong> grid = [[1,2],[4,3]]
<strong>Output:</strong> 1
</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;= 100</code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 4</code></li>
</ul>

class Solution {
    int solve(int i,int j, vector<vector<int>>& grid){
        if(i==grid.size()-1 && j==grid[0].size()-1) return 0;
        if(i<0 || j<0 || i>=grid.size() || j>=grid[0].size()) return 1e5;
        if(grid[i][j]==5) return 1e5;
        int l1=1,l2=1,l3=1,l4=1;
        if(grid[i][j]==1) l1=0;
        if(grid[i][j]==2) l2=0;
        if(grid[i][j]==3) l3=0;
        if(grid[i][j]==4) l4=0;
        int org=grid[i][j];
        grid[i][j]=5;
        int ans=1e5;
        ans=min(ans, l1+ solve(i,j+1,grid));
        ans=min(ans, l2+solve(i,j-1,grid));
        ans=min(ans,l3+ solve(i+1,j,grid));
        ans=min(ans, l4+solve(i-1,j,grid));

        grid[i][j]=org;
        return ans;


    }
public:
    int minCost(vector<vector<int>>& grid) {
        int n=grid.size(), m=grid[0].size();
        vector<vector<int>> vis(n, vector<int>(m,0));
        set<pair<int,pair<int,int>>> st;
        st.insert({0,{0,0}});

        while(!st.empty()){
            auto node=*st.begin();
            int c=node.first;
            int i=node.second.first;
            int j=node.second.second;
            cout<<"i:"<<i<<" j:"<<j<<endl;
            if(i==n-1 && j==m-1) return c;
            st.erase(st.begin());

            if(i<0 || j<0 ||i>=n || j>=m) continue;


            if(vis[i][j]) continue;
            vis[i][j]=1;

        int l1=1,l2=1,l3=1,l4=1;
        if(grid[i][j]==1) l1=0;
        if(grid[i][j]==2) l2=0;
        if(grid[i][j]==3) l3=0;
        if(grid[i][j]==4) l4=0;
        if(j+1<m) st.insert({c+l1,{i,j+1}});
        if(j-1>=0) st.insert({c+l2,{i,j-1}});
        if(i+1<n) st.insert({c+l3,{i+1,j}});
        if(i-1>=0) st.insert({c+l4,{i-1,j}});
          
        }
        return -1;
        }
};
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