<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) {
        map<int, vector<int>> bucket;
        for(auto &i: properties){
            bucket[i[0]].push_back(i[1]);
        }
        int maxdef = 0;
        int ret = 0;
        for(auto i = bucket.rbegin(); i != bucket.rend(); i++){
            if(i == bucket.rbegin()){
                for(auto &j: i->second){
                    maxdef = max(maxdef, j);
                }
            }else{
                int tmpdef = 0;
                for(auto &j: i->second){
                    if(j < maxdef)
                        ret++;
                    tmpdef = max(tmpdef, j);
                }
                maxdef = max(tmpdef, maxdef);
            }
        }
        return ret;
    }
};
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