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<bits/stdc++.h>
#define pii pair<int,int>
#define piii pair<int,pii>
#define F first
#define S second
#define mp make_pair
#define pb push_back
#define vii vector<pii>
using namespace std;
const int N=1e5+5;
bool visit[N];
vii v[N];
int n,m,dist[N];
deque<piii>q;
void BFS()
{
	q.push_front(mp(0,mp(0,0)));
	while(!q.empty())
	{
		piii p=q.front();q.pop_front();
		int now=p.F;
		int color=p.S.F;
		int move=p.S.S;
		dist[now]=min(dist[now],move);
		visit[now]=true;
		for(int i=0;i<v[now].size();i++)
		{
			int to=v[now][i].F;
			if(!visit[to])
			{
				if(v[now][i].S==color)q.push_front(mp(to,mp(color,move)));
				else q.push_back(mp(to,mp(v[now][i].S,move+1)));
			}
		}
	}
	return;
}
int main()
{
	cin>>n>>m;
	for(int i=0;i<m;i++)
	{
		int a,b,c;
		cin>>a>>b>>c;
		a--,b--;
		v[a].pb(mp(b,c));
		v[b].pb(mp(a,c));
	}
	for(int i=0;i<n;i++)dist[i]=1e9;
	BFS();
	int ans=n-1;
	if(dist[ans]==1e9)dist[ans]=-1;
	cout<<dist[ans]<<endl;
	return 0;
}
/*
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
*/