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 <cstdio>
#include <iostream>
#include <string>
#include <vector>
#include <sstream>
#include <map>
#include <set>
#include <queue>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <typeinfo>
#include <numeric>
#include <functional>
#include <unordered_map>
#include <bitset>
#include <stack>


using namespace std;
using ll = long long;
using ull = unsigned long long;

const ll INF = 1e16;
const ll MOD = 1e9 + 7;

#define REP(i, n) for(ll i = 0; i < n; i++)





using P = pair<ll, ll>;

int main() {
    ll n, m;
    cin >> n >> m;
    vector<vector<P>> g(n);
    REP(i, m){
        ll p, q, c;
        cin >> p >> q >> c;
        p--;q--;
        g[p].push_back({q, c});
        g[q].push_back({p, c});
    }
    vector<ll> dist(n, INF);
    dist[0] = 0;
    priority_queue<P, vector<P>, greater<P>> que;
    que.push({0, 0});
    vector<set<ll>> st(n);
    while(!que.empty()){
        auto tmp = que.top(); que.pop();
        ll d = tmp.first, now = tmp.second;
        if(dist[now] < d) continue;
        for(auto &edge : g[now]){
            ll to = edge.first, c = edge.second;
            ll dd = dist[now];
            if(st[now].count(c) == 0) dd++;
            if(dist[to] > dd){
                dist[to] = dd;
                st[to].clear();
                st[to].insert(c);
                que.push({dd, to});
            }
            else if(dist[to] == dd) st[to].insert(c);
        }
    }
    cout << ((dist[n - 1] <= 1e15)? dist[n - 1] : -1) << endl;
}