<p>You are given a positive integer <code>n</code> representing <code>n</code> cities numbered from <code>1</code> to <code>n</code>. You are also given a <strong>2D</strong> array <code>roads</code> where <code>roads[i] = [a<sub>i</sub>, b<sub>i</sub>, distance<sub>i</sub>]</code> indicates that there is a <strong>bidirectional </strong>road between cities <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> with a distance equal to <code>distance<sub>i</sub></code>. The cities graph is not necessarily connected.</p>

<p>The <strong>score</strong> of a path between two cities is defined as the <strong>minimum </strong>distance of a road in this path.</p>

<p>Return <em>the <strong>minimum </strong>possible score of a path between cities </em><code>1</code><em> and </em><code>n</code>.</p>

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

<ul>
	<li>A path is a sequence of roads between two cities.</li>
	<li>It is allowed for a path to contain the same road <strong>multiple</strong> times, and you can visit cities <code>1</code> and <code>n</code> multiple times along the path.</li>
	<li>The test cases are generated such that there is <strong>at least</strong> one path between <code>1</code> and <code>n</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/12/graph11.png" style="width: 190px; height: 231px;" />
<pre>
<strong>Input:</strong> n = 4, roads = [[1,2,9],[2,3,6],[2,4,5],[1,4,7]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> The path from city 1 to 4 with the minimum score is: 1 -&gt; 2 -&gt; 4. The score of this path is min(9,5) = 5.
It can be shown that no other path has less score.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/12/graph22.png" style="width: 190px; height: 231px;" />
<pre>
<strong>Input:</strong> n = 4, roads = [[1,2,2],[1,3,4],[3,4,7]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The path from city 1 to 4 with the minimum score is: 1 -&gt; 2 -&gt; 1 -&gt; 3 -&gt; 4. The score of this path is min(2,2,4,7) = 2.
</pre>

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

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= roads.length &lt;= 10<sup>5</sup></code></li>
	<li><code>roads[i].length == 3</code></li>
	<li><code>1 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li><code>1 &lt;= distance<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
	<li>There are no repeated edges.</li>
	<li>There is at least one path between <code>1</code> and <code>n</code>.</li>
</ul>

import heapq

class Solution:
    def minScore(self, n: int, roads: List[List[int]]) -> int:
        graph = {}

        for city in range(1, n+1):
            graph[city] = []
        for a, b, distance in roads:
            graph[a].append((distance, b))
            graph[b].append((distance, a))
        
        min_heap = [(float("inf"), 1)]
        visited = set()
        min_score = float("inf")
        while min_heap:
            score, city = heapq.heappop(min_heap)
            min_score = min(min_score, score)
            if city in visited:
                continue
            
            visited.add(city)
            for distance, neighbour_city in graph[city]:
                heapq.heappush(min_heap, (min(score, distance), neighbour_city))
        return min_score
1773