<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 max_rectangle(vector<int> arr){
        int maxi = 0;
        arr.push_back(0);
        stack<int> stk;
        int i=0,n=arr.size();
        while(i<n){
            while(!stk.empty() && arr[stk.top()]>arr[i]){
                int temp = stk.top();
                stk.pop();
                int pse = stk.empty()?-1:stk.top();
                int nse = i;
                maxi = max(maxi,(nse-pse-1)*arr[temp]);
            }
            stk.push(i);
            i++;
        }
        return maxi;
    }
    int maximalRectangle(vector<vector<char>>& matrix) {
        int n=matrix.size(),m=matrix[0].size();
        vector<vector<int>> prefix_sum;
        for(int i=0;i<n;i++){
            vector<int> temp;
            for(int j=0;j<m;j++){
                if(i==0){
                    temp.push_back(matrix[i][j]-48);
                }
                else if(matrix[i][j]-48 == 0){
                    temp.push_back(0);
                }
                else{
                    temp.push_back(prefix_sum[i-1][j]+1);
                }
            }
            prefix_sum.push_back(temp);
        }
        int result = 0;
        for(int i=0;i<n;i++){
            result = max(result,max_rectangle(prefix_sum[i]));
        }
        return result;
    }
};
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