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: Time Limit Exceeded)

#include <iostream>
#include <string>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <map>
#include <set>
#include <algorithm>
#include <ctime>
#include <queue>
#include <stack>
#include <functional>
#include <bitset>
#include <assert.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<char> vc;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef pair<ll,ll> P;
typedef vector<P> vpl;
typedef tuple<ll,ll,ll> tapu;
#define rep(i,n) for(ll i=0; i<(n); i++)
#define REP(i,a,b) for(int i=(a); i<(b); i++)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
const int inf = 1<<30;
const ll linf = 1LL<<62;
const int MAX = 510000;
ll dy[8] = {0,1,0,-1,1,-1,1,-1};
ll dx[8] = {1,0,-1,0,1,-1,-1,1};
const double pi = acos(-1);
const double eps = 1e-7;
template<typename T1,typename T2> inline bool chmin(T1 &a,T2 b){
	if(a>b){
		a = b; return true;
	}
	else return false;
}
template<typename T1,typename T2> inline bool chmax(T1 &a,T2 b){
	if(a<b){
		a = b; return true;
	}
	else return false;
}
template<typename T1,typename T2> inline void print2(T1 a, T2 b){cout << a << " " << b << "\n";}
template<typename T1,typename T2,typename T3> inline void print3(T1 a, T2 b, T3 c){
	cout << a << " " << b << " " << c << "\n";
}
const int mod = 1e9 + 7;
//const int mod = 998244353;

template <typename T> struct Compress{
    vector<T> comp;

    Compress(vector<T> v) : comp(v){
        sort(comp.begin(), comp.end());
        comp.erase(unique(comp.begin(), comp.end()), comp.end());
    }

    ll get(T x){
        if(!binary_search(all(comp),x)) return -1;
        return lower_bound(comp.begin(), comp.end(), x) - comp.begin();
    }

    T operator[](int id){
        return comp[id];
    }

    ll siz(){
        return comp.size();
    }
};

int main(){
    ll n,m; cin >> n >> m;
    vector<vpl> G(n);
    vvl color(n);
    color[0].push_back(0);
    rep(i,m){
        int u,v,c; scanf("%d%d%d",&u,&v,&c);
        u--; v--;
        G[u].emplace_back(v,c);
        G[v].emplace_back(u,c);
        color[u].push_back(c);
        color[v].push_back(c);
    }
    vector<Compress<ll>> cmp;
    rep(i,n){
        Compress<ll> v(color[i]);
        cmp.push_back(v);
    }
    vvl d(n);
    rep(i,n){
        d[i].resize(cmp[i].siz(),linf);
    }
    rep(i,n){
        for(auto &v : G[i]){
            v.second = cmp[v.first].get(v.second);
        }
    }
    d[0][0] = 0;
    priority_queue<pair<ll,P>,vector<pair<ll,P>>,greater<pair<ll,P>>> pq;
    pq.emplace(0,P(0,0));
    while(!pq.empty()){
        auto p = pq.top(); pq.pop();
        int u = p.second.first;
        int col = cmp[u][p.second.second];
        int cid = p.second.second;
        if(d[u][cid] < p.first) continue;
        for(auto v : G[u]){
            int plus = cmp[v.first][v.second] != col;
            if(d[v.first][v.second] > d[u][cid] + plus){
                d[v.first][v.second] = d[u][cid] + plus;
                pq.emplace(d[v.first][v.second], v);
            }
        }
    }
    ll ans = linf;
    rep(i,cmp[n-1].siz()) chmin(ans, d[n-1][i]);
    if(ans == linf) cout << -1 << endl;
    else cout << ans << endl;
}