<p>You are given an array <code>routes</code> representing bus routes where <code>routes[i]</code> is a bus route that the <code>i<sup>th</sup></code> bus repeats forever.</p>

<ul>
	<li>For example, if <code>routes[0] = [1, 5, 7]</code>, this means that the <code>0<sup>th</sup></code> bus travels in the sequence <code>1 -&gt; 5 -&gt; 7 -&gt; 1 -&gt; 5 -&gt; 7 -&gt; 1 -&gt; ...</code> forever.</li>
</ul>

<p>You will start at the bus stop <code>source</code> (You are not on any bus initially), and you want to go to the bus stop <code>target</code>. You can travel between bus stops by buses only.</p>

<p>Return <em>the least number of buses you must take to travel from </em><code>source</code><em> to </em><code>target</code>. Return <code>-1</code> if it is not possible.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> routes = [[1,2,7],[3,6,7]], source = 1, target = 6
<strong>Output:</strong> 2
<strong>Explanation:</strong> The best strategy is take the first bus to the bus stop 7, then take the second bus to the bus stop 6.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> routes = [[7,12],[4,5,15],[6],[15,19],[9,12,13]], source = 15, target = 12
<strong>Output:</strong> -1
</pre>

<p>&nbsp;</p>

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

<ul>
	<li><code>1 &lt;= routes.length &lt;= 500</code>.</li>
	<li><code>1 &lt;= routes[i].length &lt;= 10<sup>5</sup></code></li>
	<li>All the values of <code>routes[i]</code> are <strong>unique</strong>.</li>
	<li><code>sum(routes[i].length) &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= routes[i][j] &lt; 10<sup>6</sup></code></li>
	<li><code>0 &lt;= source, target &lt; 10<sup>6</sup></code></li>
</ul>

class Solution:
    def numBusesToDestination(self, routes: List[List[int]], source: int, target: int) -> int:
        if source == target:
            return 0
        if len(routes) == 1:
            if (source in routes[0]) and (target in routes[0]):
                return 1
            else:
                return -1
        crossroads = [{} for i in range(len(routes))]
        routes_in_dict = [{} for i in range(len(routes))]
        for j in range(len(routes)):
            for elem in routes[j]:
                routes_in_dict[j][elem] = 1
        for j in range(len(routes)):
            for stop in routes_in_dict[j]:
                for i in range(len(routes)):
                    if i != j:
                        if i not in crossroads[j]:
                            if stop in routes_in_dict[i]:
                                crossroads[j][i] = 1
        lines_to_visit = []
        for j in range(len(routes)):
            if source in routes[j]:
                lines_to_visit.append(j)
        if len(lines_to_visit) == 0:
            return -1
        number_of_lines = 1
        lines_visited = []
        while len(lines_to_visit) > 0:
            for line in lines_to_visit:
                if target in routes[line]:
                    return number_of_lines
            number_of_lines += 1
            lines_visited.extend(lines_to_visit.copy())
            new_lines_to_visit = []
            for line in lines_to_visit:
                for elem in crossroads[line]:
                    if (elem not in new_lines_to_visit) and (elem not in lines_visited):
                        new_lines_to_visit.append(elem)
            lines_to_visit = new_lines_to_visit
        return -1

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