<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>

using ll = long long;
class Solution {
public:
    int maximalRectangle(vector<vector<char>>& matrix) {
        ll n = matrix.size(),m = matrix[0].size();

        auto a = matrix;
        for(auto x:a) { for(auto ch:x) cout << ch<<' '; cout <<endl;}
        vector<vector<int>> pos(n,vector<int>(m,n));
        for(int j = 0;j<m;j++){
            stack<int> st;
            for(int i =n-1;i>=0;i--){
                while(not empty(st) and a[st.top()][j]>=a[i][j]) st.pop();
                if(not empty(st)) pos[i][j] = st.top();
                st.emplace(i);
            }
        }
        // for(int i = 0;i<m;i++) cout << pos[0][i] <<' ';cout <<endl;
        ll ans = 0;
        auto cur = [&](int i,int j){return pos[i][j] - i;};
        for(int i = 0;i<n;i++){
            vector<int> av(m,m);
            stack<int> st;
            for(int j = m-1;j>=0;j--){
                if(a[i][j]=='0') pos[i][j] = -1e9;
                while(not empty(st) and cur(i,st.top()) >= cur(i,j) ) st.pop();
                if(not empty(st)) av[j] = st.top();
                st.emplace(j); 
            }
            for(int j = 0;j<m;j++) cout << av[j] <<' ';cout <<endl;
            st = stack<int>();
            for(int j = 0;j<m;j++){
                while(not empty(st) and cur(i,st.top())>=cur(i,j) ) st.pop();
                ll x = empty(st) ? -1:st.top();
                ans = max(ans,cur(i,j) * (av[j] - x -1));
                st.emplace(j);
            }
        }
        return int(ans);
    }
};
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