<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>

const int N = 1E5, M = 501;
int dist[N + 1][M + 1];
bool st[N + 1][M + 1];
class Solution {
public:
    int numBusesToDestination(vector<vector<int>>& routes, int source, int target) {
        if (source == target) {
            return 0;
        }
        int n = routes.size();
        for (auto& r : routes) {
            for (int v : r) {
                n = max(n, v);
            }
        }
        n += 10;
        vector<vector<pair<int, int>>> adj(n);
        for (int i = 0; i < routes.size(); i++) {
            int m = routes[i].size();
            for (int j = 0; j < m; j++) {
                adj[routes[i][j]].push_back({routes[i][(j + 1) % m], i});
            }
        }
        const int inf = 0x3f3f3f3f;
        memset(dist, 0x3f, sizeof(dist));
        memset(st, 0, sizeof(st));
        dist[source][routes.size()] = 0;
        priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, greater<tuple<int, int, int>>> hp;
        hp.emplace(0, source, routes.size());
        while (!hp.empty()) {
            auto [_, x, i] = hp.top();
            hp.pop();
            if (st[x][i]) {
                continue;
            }
            st[x][i] = true;
            for (auto& [y, j] : adj[x]) {
                if (dist[y][j] > dist[x][i] + (i != j)) {
                    dist[y][j] = dist[x][i] + (i != j);
                    hp.emplace(dist[y][j], y, j);
                }
            }
        }
        int ans = inf;
        for (int i = 0; i < routes.size(); i++) 
            ans = min(ans, dist[target][i]);
        if (ans >= inf) 
            ans = -1;
        return ans;
    }
};
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