<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>

vector<bool> prime;
vector<int> cnt;

class Solution {
public:

    int sieve(int n){
        prime.assign(n+1,true);
        cnt.assign(n+1,0);
        prime[0]=false;
        prime[1]=false;
        for(int i=2;i*i<=n;i++){
            if(!prime[i]) continue;
            for(int j=i*i;j<=n;j+=i){
                prime[j]=false;
            }
        }  
        for(int i=1;i<=n;i++){
            cnt[i]=cnt[i-1];
            if(prime[i])cnt[i]++;
        }
        if(n==0) return 0;
        return cnt[n-1];
    }

    int countPrimes(int n) {
        return sieve(n);
    }
};
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