<p>Given a 2D integer array <code>circles</code> where <code>circles[i] = [x<sub>i</sub>, y<sub>i</sub>, r<sub>i</sub>]</code> represents the center <code>(x<sub>i</sub>, y<sub>i</sub>)</code> and radius <code>r<sub>i</sub></code> of the <code>i<sup>th</sup></code> circle drawn on a grid, return <em>the <strong>number of lattice points</strong> </em><em>that are present inside <strong>at least one</strong> circle</em>.</p>

<p><strong>Note:</strong></p>

<ul>
	<li>A <strong>lattice point</strong> is a point with integer coordinates.</li>
	<li>Points that lie <strong>on the circumference of a circle</strong> are also considered to be inside it.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/02/exa-11.png" style="width: 300px; height: 300px;" />
<pre>
<strong>Input:</strong> circles = [[2,2,1]]
<strong>Output:</strong> 5
<strong>Explanation:</strong>
The figure above shows the given circle.
The lattice points present inside the circle are (1, 2), (2, 1), (2, 2), (2, 3), and (3, 2) and are shown in green.
Other points such as (1, 1) and (1, 3), which are shown in red, are not considered inside the circle.
Hence, the number of lattice points present inside at least one circle is 5.</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/02/exa-22.png" style="width: 300px; height: 300px;" />
<pre>
<strong>Input:</strong> circles = [[2,2,2],[3,4,1]]
<strong>Output:</strong> 16
<strong>Explanation:</strong>
The figure above shows the given circles.
There are exactly 16 lattice points which are present inside at least one circle. 
Some of them are (0, 2), (2, 0), (2, 4), (3, 2), and (4, 4).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= circles.length &lt;= 200</code></li>
	<li><code>circles[i].length == 3</code></li>
	<li><code>1 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 100</code></li>
	<li><code>1 &lt;= r<sub>i</sub> &lt;= min(x<sub>i</sub>, y<sub>i</sub>)</code></li>
</ul>

import math
from typing import List

class Solution:
    def countLatticePoints(self, circles: List[List[int]]) -> int:
        total_lattice = set()  # Use a set to avoid counting duplicate points

        for center_x, center_y, radius in circles:
            # Check all y values from center_y - radius to center_y + radius
            for y in range(center_y - radius, center_y + radius + 1):
                # Calculate the maximum horizontal distance from the center for this y
                horizontal_distance = int(math.sqrt(radius**2 - (y - center_y)**2))
                
                # Add all lattice points on this horizontal line
                for x in range(center_x - horizontal_distance, center_x + horizontal_distance + 1):
                    total_lattice.add((x, y))  # Add the lattice point to the set

        return len(total_lattice)

# Example usage:
s = Solution()
print(s.countLatticePoints([[2, 2, 2], [3, 4, 1]]))  # Example output

446