<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:
    def countPrimes(self, n: int) -> int:
        # create an array of 0 - n
        # if n <= 2, then the primes are 0
        if n <= 2:
            return 0
        primes = [False, False] + [True] * (n - 2)

        def is_prime(n):
            for i in range(2,int(n**0.5)+1):
                if n%i==0:
                    return False
            return True

        # [0, 0, 1, 0] => 1
        # [0, 0, 1, 1] = > 2
        # [0, 0, 1, 1, 0, 1, 0, 1, 0, 0]
        for i in range(2, (int(sqrt(n))) + 1):
            if primes[i]:
                for j in range(i * i, n, i):
                    primes[j] = False
        return sum(primes)
        

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