<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:
        import math
        if n <= 2: return 0
        if n == 3: return 1
        flag = [1] * n  # assume all primes
        flag[0] = flag[1] = 0  # non prime
        upper = math.ceil(math.sqrt(n))
        for i in range(2, upper):
            if flag[i] == 0: continue # non prime
            else:
                # n = 10, i = 2 requires -1 below because 10 doesn't count 
                m = (n - i - 1) // i  # every step with i size, how may steps
                # if 2 * i < n:  # don't need this check
                flag[2*i::i] = [0] * m
        return sum(flag)
104793