<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:

    void fillSieve(vector<int>& sieve) {
        for(int i = 0; i < sieve.size(); i++) {
            if(sieve[i] == 0) continue;
            
            int v = i + 2, k = 2;
            while(v * k <= 1 + sieve.size()) {
                sieve[v * k - 2] = 0;
                k++;
            }
        }
    }

    int countPrimes(int n) {
        if(n <= 2) return 0;
        vector<int> sieve(n - 2, 1);
        fillSieve(sieve);

        int cnt = 0;
        for(int i : sieve) cnt += i;
        return cnt;
    }
};
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