<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:
    vector<int> findNSE(vector<int>& nums) {
        int n = nums.size();
        vector<int> nse(n);
        stack<int> st;
        for (int i = n - 1; i >= 0; i--) {
            while (!st.empty() && nums[st.top()] >= nums[i])
                st.pop();
            nse[i] = st.empty() ? n : st.top();
            st.push(i);
        }
        return nse;
    }

    vector<int> findPSEE(vector<int>& nums) {
        int n = nums.size();
        vector<int> psee(n);
        stack<int> st;
        for (int i = 0; i < n; i++) {
            while (!st.empty() && nums[st.top()] > nums[i])
                st.pop();
            psee[i] = st.empty() ? -1 : st.top();
            st.push(i);
        }
        return psee;
    }

    int lra(vector<int>& heights) {
        vector<int> nse = findNSE(heights);
        vector<int> psee = findPSEE(heights);
        int maxi = 0;
        
        for (int i = 0; i < heights.size(); i++) {
            int width = nse[i] - psee[i] - 1;
            int area = heights[i] * width;
            maxi = max(maxi, area);
        }
        
        return maxi;
    }
    int maximalRectangle(vector<vector<char>>& matrix) {
        int n = matrix.size();
        int m = matrix[0].size();
        int maxiarea = 0;
        vector<vector<int>> presum(n, vector<int>(m, 0));

        for (int j = 0; j < m; j++) {
            int sum = 0;
            for (int i = 0; i < n; i++) {
                if (matrix[i][j] == '1') {
                    sum += 1;
                } else {
                    sum = 0;
                }
                presum[i][j] = sum;
            }
        }

        for (int i = 0; i < n; i++) {
            if(lra(presum[i])>maxiarea){
                maxiarea=lra(presum[i]);
            }
        }

        return maxiarea;
    }

 
};
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