<p>Given a <code>rows x cols</code>&nbsp;binary <code>matrix</code> filled with <code>0</code>&#39;s and <code>1</code>&#39;s, find the largest rectangle containing only <code>1</code>&#39;s and return <em>its area</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/14/maximal.jpg" style="width: 402px; height: 322px;" />
<pre>
<strong>Input:</strong> matrix = [[&quot;1&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;],[&quot;1&quot;,&quot;0&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;],[&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;],[&quot;1&quot;,&quot;0&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The maximal rectangle is shown in the above picture.
</pre>

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

<pre>
<strong>Input:</strong> matrix = [[&quot;0&quot;]]
<strong>Output:</strong> 0
</pre>

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

<pre>
<strong>Input:</strong> matrix = [[&quot;1&quot;]]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>rows == matrix.length</code></li>
	<li><code>cols == matrix[i].length</code></li>
	<li><code>1 &lt;= row, cols &lt;= 200</code></li>
	<li><code>matrix[i][j]</code> is <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
</ul>

class Solution {
    private:
    int solve(vector<int>&heights){
      stack<int>st,st1;
      int n=heights.size();
      vector<int>pre,suff;
      for(int i=n-1;i>=0;i--){
        while(!st.empty() && heights[st.top()]>=heights[i]){
          st.pop();
        }
        if(st.empty()){
           pre.push_back(n);
        }
        else{
          pre.push_back(st.top());
        }
        st.push(i);
      }
      for(int i=0;i<n;i++){
        while(!st1.empty() && heights[st1.top()]>=heights[i]){
          st1.pop();
        }
        if(st1.empty()){
          suff.push_back(-1);
        }
        else{
          suff.push_back(st1.top());
        }
        st1.push(i);
      }
      int ans=0;
      reverse(pre.begin(),pre.end());
      for(int i=0;i<n;i++){
         int temp=heights[i]*(pre[i]-suff[i]-1);
         ans=max(ans,temp);
      }
      return ans;
    }
public:
    int maximalRectangle(vector<vector<char>>& matrix) {
       vector<int>prev(matrix[0].size());
       for(int i=0;i<matrix[0].size();i++){
        prev[i]=matrix[0][i]-'0';
       }
       cout<<endl;
        int ans=solve(prev);
        for(int i=1;i<matrix.size();i++){
            vector<int>res(matrix[i].size(),0);
            for(int j=0;j<prev.size();j++){
                if(matrix[i][j]=='0'){
                    res[j]=0;
                }
                else{
                    res[j]=matrix[i][j]-'0'+prev[j];
                }
            }
            ans=max(ans,solve(res));
            prev=res;
        }
        return ans;
    }
};
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