<p>Given an integer <code>n</code>, return <em>the number of prime numbers that are strictly less than</em> <code>n</code>.</p>

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

<pre>
<strong>Input:</strong> n = 10
<strong>Output:</strong> 4
<strong>Explanation:</strong> There are 4 prime numbers less than 10, they are 2, 3, 5, 7.
</pre>

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

<pre>
<strong>Input:</strong> n = 0
<strong>Output:</strong> 0
</pre>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>0 &lt;= n &lt;= 5 * 10<sup>6</sup></code></li>
</ul>

class Solution {
public:
    int countPrimes(int n) {
        if (n <= 2) return 0;
        vector<int> v((n-1)/2, 1);
        for (int i=3; i*i<=n; i+=2){
            if (v[(i-3)/2]){
                for (int j=i*i; j<=n; j+=2*i){
                    v[(j-3)/2] = 0;
                }
            }
        }
        int ans = 1;
        for (int i=0; i<v.size()-(n&1); ++i){
            if (v[i]) ans+=1;
        }
        return ans;
    }
};
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