Problem: 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.

Examples

Input

3 3
1 2 1
2 3 1
3 1 2


Output

1


Input

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


Output

2


Input

2 0


Output

-1

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define pii pair<int,int>
#define F first
#define S second
#define vi vector<pii>
#define pb push_back
using namespace std;
const int N=6e5+5;
vi v[N];
int n,m,id;
map<pair<int,int>,int>mp;
void add_edge(int a,int b,int c,int d)
{
	v[a].pb(make_pair(b,c));
	v[b].pb(make_pair(a,d));
}
int getid(int a,int pos)
{
	if(mp[make_pair(a,pos)])return mp[make_pair(a,pos)];
	int res=id++;
	add_edge(a,res,1,0);
	return (mp[make_pair(a,pos)]=res);
}
priority_queue<pii,vi,greater<pii> >pq;
bool visit[N];
int main()
{
	cin>>n>>m;
	id = n;
	for(int i=0;i<m;i++)
	{
		int a,b,c;
		cin>>a>>b>>c;
		a--,b--;
		int x=getid(a,c);
		int y=getid(b,c);
		add_edge(x,y,0,0);
	}
/*	for(int i=0;i<id;++i)
	{
		cout<<"Vertex "<<i<<" connact:  ";
		for(int j=0;j<v[i].size();j++)cout<<v[i][j].F<<' '<<v[i][j].S<<'\n';
		cout<<endl;
	}*/
	pq.push(make_pair(0,0));
	while(!pq.empty())
	{
		int move=pq.top().F;
		int now=pq.top().S;
		pq.pop();
		if(visit[now])continue;
		visit[now]=true;
		if(now==n-1)
		{
			cout<<move<<endl;
			return 0;
		}
		for(int i=0;i<v[now].size();i++)
		{
			int to=v[now][i].F;
			pq.push(make_pair(move+v[now][i].S,to));
		}
	}
	cout<<"-1\n";
	return 0;
}