<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 maxArea(vector<int>&v){
        stack<int>st;
        int ans = 0;
        int n = v.size();
        for(int i = 0; i<=n; i++){
            while(!st.empty() && (i == n || v[st.top()] >= v[i])){
                int height = v[st.top()];
                st.pop();
                int width;
                if(st.empty()){
                    width = i;
                }
                else{
                    width = i - st.top()-1;
                }
                ans = max(ans, width*height);
            }
            st.push(i);
        }
        return ans;
    }
    int maximalRectangle(vector<vector<char>>& matrix) {
        int ans = 0;
        vector<int>height(matrix[0].size(), 0);
        for(int i = 0; i<matrix.size(); i++){
            for(int j = 0; j<matrix[0].size(); j++){
                if(matrix[i][j] == '1'){
                    height[j]++;
                }
                else{
                    height[j] = 0;
                }
            }
            int area = maxArea(height);
            ans = max(ans, area);
        }
        return ans;
    }
};
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