<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 {
public:
    int hist(vector<int>v,int n){
        vector<int>pse(n,-1),nse(n,n);
        stack<int>st;
        int prod=0,maxProd=0;
        for(int i=0; i<n; i++){
            while(!st.empty() && v[st.top()] >= v[i]){
                st.pop();
            }
            if(!st.empty())pse[i] = st.top();
            st.push(i);
        }
        while(!st.empty())st.pop();
        for(int i=n-1; i>=0; i--){
            while(!st.empty() && v[st.top()] >= v[i]){
                st.pop();
            }
            if(!st.empty())nse[i] = st.top();
            st.push(i);
        }
        for(int i=0; i<n; i++){
            prod = (nse[i] - pse[i] -1 )*v[i];
            maxProd = max(prod,maxProd);
        }
        return maxProd;
    }
    int maximalRectangle(vector<vector<char>>& matrix) {
        int n = matrix.size(),m = matrix[0].size();
        int maxArea = 0;
        vector<vector<int>>pSum(n,vector<int>(m,0));
        for(int j=0; j<m; j++){
            for(int i=0; i<n; i++){
                if(matrix[i][j]-'0' == 0){
                    pSum[i][j] = 0;
                }else{
                    pSum[i][j] = (i == 0) ? matrix[i][j]-'0' :(matrix[i][j]-'0' + pSum[i-1][j]);
                }
            }
        }
        for(int i=0; i<n; i++){
            maxArea = max(maxArea, hist(pSum[i],m));
        }
        return maxArea;
    }
};
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