<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 histogram(vector<int> v){
        int n=v.size();
        stack<int> st;
        int ans=0;
        for(int i=0;i<n;i++){
                while(!st.empty() and v[st.top()]>v[i]){
                    int ht=v[st.top()];
                    st.pop();
                    int width=(st.empty())? i: i-st.top()-1;
                    ans=max(ans,ht*width);
                }
                st.push(i);
        }
        while(!st.empty()){
            int ht=v[st.top()];
            st.pop();
            int width=(st.empty())? n: n-st.top()-1;
            ans=max(ans,ht*width);
        }        
        return ans;
    }
    int maximalRectangle(vector<vector<char>>& matrix) {
        int n=matrix.size();
        if(n==0) return 0;
        int m=matrix[0].size();
        vector<int> base(m,0);
        int answer=0;
        for(int row=0;row<n;row++){
            for(int col=0;col<m;col++){
                if(matrix[row][col]=='1'){
                    base[col]++;
                }
                else{
                    base[col]=0;
                }
            }
            answer=max(answer,histogram(base));
        }        
        return answer;
    }
};
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