<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 {
private:
    int nums = 0;
    int prime[500000] = {};
    bool not_prime[5000005];
    void prime_sieve(int n) {
        not_prime[0] = not_prime[1] = true;
        for(int i = 2; i < n; i++) {
            if (!not_prime[i] && (long long) i*i <= n) {
                for (int j = i*i; j <= n; j += i) {
                    not_prime[j] = true;
                }
            }
            if(!not_prime[i]) prime[nums++] = i;
        }
    }
public:
    int countPrimes(int n) {
        prime_sieve(n);
        return nums;
    }
};
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