Problem:
Score : 600 points

Problem Statement

Snuke's town has a subway system, consisting of N stations and M railway lines. The stations are numbered 1 through N. Each line is operated by a company. Each company has an identification number.

The i-th ( 1 \leq i \leq M ) line connects station p_i and q_i bidirectionally. There is no intermediate station. This line is operated by company c_i.

You can change trains at a station where multiple lines are available.

The fare system used in this subway system is a bit strange. When a passenger only uses lines that are operated by the same company, the fare is 1 yen (the currency of Japan). Whenever a passenger changes to a line that is operated by a different company from the current line, the passenger is charged an additional fare of 1 yen. In a case where a passenger who changed from some company A's line to another company's line changes to company A's line again, the additional fare is incurred again.

Snuke is now at station 1 and wants to travel to station N by subway. Find the minimum required fare.

Constraints

2 \leq N \leq 10^5

0 \leq M \leq 2×10^5

1 \leq p_i \leq N (1 \leq i \leq M)

1 \leq q_i \leq N (1 \leq i \leq M)

1 \leq c_i \leq 10^6 (1 \leq i \leq M)

p_i \neq q_i (1 \leq i \leq M)

Input

The input is given from Standard Input in the following format:

N M
p_1 q_1 c_1
:
p_M q_M c_M

Output

Print the minimum required fare. If it is impossible to get to station N by subway, print -1 instead.

Sample Input 1

3 3
1 2 1
2 3 1
3 1 2

Sample Output 1

1

Use company 1's lines: 1 → 2 → 3. The fare is 1 yen.

Sample Input 2

8 11
1 3 1
1 4 2
2 3 1
2 5 1
3 4 3
3 6 3
3 7 3
4 8 4
5 6 1
6 7 5
7 8 5

Sample Output 2

2

First, use company 1's lines: 1 → 3 → 2 → 5 → 6. Then, use company 5's lines: 6 → 7 → 8. The fare is 2 yen.

Sample Input 3

2 0

Sample Output 3

-1

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <queue>
#include <vector>
#include <functional>

using ll=long long int;

constexpr int MAX_N=(int)1e5;

constexpr ll INF=(ll)1e9;

struct edge{

    int to,com;

    edge()=default;

    edge(int _t,int _c) : to(_t),com(_c) {}
};

struct Node{

    int v,com;

    ll cost;

    Node()=default;

    Node(int _v,ll _cost,int _com) : v(_v),cost(_cost),com(_com) {}

    bool operator< (const Node& rhs) const{

        return cost<rhs.cost;
    }

    bool operator> (const Node& rhs) const{

        return cost>rhs.cost;
    }
};

int n,m;

std::vector<edge> G[MAX_N];

ll d[MAX_N];

ll dijkstra(int s,int g){

    for(int i=0;i<n;++i)
        d[i]=INF;

    std::priority_queue<Node,std::vector<Node>,std::greater<Node>> que;

    que.emplace(s,d[s]=0,0);

    while(!que.empty()){

        Node node=que.top();

        que.pop();

        if(node.v==g)
            return d[g];

        if(node.cost>d[node.v])
            continue;
        
        for(auto& e : G[node.v]) {

            int cost=(e.com!=node.com);

            if(d[e.to]>d[node.v]+cost){

                d[e.to]=d[node.v]+cost;

                que.emplace(e.to,d[e.to],e.com);
            }
        }
    }
    return -1;
}

int main() {

    std::cin>>n>>m;

    int p,q,c;

    for(int i=0;i<m;++i) {

        std::cin>>p>>q>>c;

        G[p-1].emplace_back(q-1,c);

        G[q-1].emplace_back(p-1,c);
    }

    ll ans=dijkstra(0,n-1);

    std::cout<<ans<<std::endl;

    return 0;
}