<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 n, m;

    /// from problem 84. Largest Rectangle in Histogram
	int largestRectangleArea(vector<int>& heights) {
		stack<int> st;
		int ans = 0;
		heights.push_back(0);
		for (int i = 0; i < heights.size(); i++) {
			while (!st.empty() && heights[st.top()] > heights[i]) {
				int top = heights[st.top()];
				st.pop();
				int ran = st.empty() ? -1 : st.top();
				ans = max(ans, top * (i - ran - 1));
			}
			st.push(i);
		}
		return ans;
	}
	int maximalRectangle(vector<vector<char>>& inMatrix) {
		n = inMatrix.size();
		m = inMatrix[0].size();
		vector<vector<int>> arr(n, vector<int>(m));
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				arr[i][j] = inMatrix[i][j] - '0';
			}
		}	
		for (int j = 0; j < m; j++)
		{
			for (int i = 0; i < n; i++)
			{
				if (i > 0 && arr[i][j])
				{
					arr[i][j] += arr[i - 1][j];
				}
			}
		}

		int res=0;
		for (int i = 0; i < n; i++)
		{
			res = max(res, largestRectangleArea(arr[i]));
		}
		return res;
	}
};
19975