<p>You are playing a game that contains multiple characters, and each of the characters has <strong>two</strong> main properties: <strong>attack</strong> and <strong>defense</strong>. You are given a 2D integer array <code>properties</code> where <code>properties[i] = [attack<sub>i</sub>, defense<sub>i</sub>]</code> represents the properties of the <code>i<sup>th</sup></code> character in the game.</p>

<p>A character is said to be <strong>weak</strong> if any other character has <strong>both</strong> attack and defense levels <strong>strictly greater</strong> than this character&#39;s attack and defense levels. More formally, a character <code>i</code> is said to be <strong>weak</strong> if there exists another character <code>j</code> where <code>attack<sub>j</sub> &gt; attack<sub>i</sub></code> and <code>defense<sub>j</sub> &gt; defense<sub>i</sub></code>.</p>

<p>Return <em>the number of <strong>weak</strong> characters</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> properties = [[5,5],[6,3],[3,6]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> No character has strictly greater attack and defense than the other.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> properties = [[2,2],[3,3]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The first character is weak because the second character has a strictly greater attack and defense.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> properties = [[1,5],[10,4],[4,3]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The third character is weak because the second character has a strictly greater attack and defense.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= properties.length &lt;= 10<sup>5</sup></code></li>
	<li><code>properties[i].length == 2</code></li>
	<li><code>1 &lt;= attack<sub>i</sub>, defense<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution 
{
public:
    int numberOfWeakCharacters(vector<vector<int>>& properties) 
    {
        int n = properties.size();
        sort(properties.begin(), properties.end());
        vector<int> max_defence(n, 0);
        max_defence[n-1] = properties[n-1][1];

        for(int i=n-2;i>=0;i--) max_defence[i] = max(max_defence[i+1], properties[i][1]);

        int ans = 0;
        for(int i=0;i<n;i++)
        {
            // cout<<i<<" ";
            // get upper index
            int low = i+1, high = n-1, upper = n;
            while(low <= high)
            {
                int mid = low + (high - low)/2;
                if(properties[mid][0] > properties[i][0])
                {
                    upper = mid;
                    high = mid - 1;
                }
                else    low = mid + 1;
            }

            if(upper == n)  break;
            // cout<<i<<" "<<upper<<endl;
            
            if(properties[i][1] < max_defence[upper]) ans++;

        }

        // for(int i=0;i<properties.size();i++)    cout<<properties[i][0]<<" "<<properties[i][1]<<endl;
        // for(int i=0;i<properties.size();i++)    cout<<max_defence[i]<<" ";

        return ans;

    }
};
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