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 N (600009)
using namespace std;

struct Node
{
	int num,dis;
	bool operator < (const Node &a) const {return dis>a.dis;}
};
struct Edge{int to,next,len;}edge[N<<1];
int n,m,u,v,c,cnt,dis[N],vis[N];
int head[N],num_edge;
priority_queue<Node>q;
map<pair<int,int>,int>Map;

void add(int u,int v,int l)
{
	edge[++num_edge].to=v;
	edge[num_edge].next=head[u];
	edge[num_edge].len=l;
	head[u]=num_edge;
}

void Dijkstra(int s)
{
	memset(dis,0x7f,sizeof(dis));
	dis[s]=0; q.push((Node){s,0});
	while (!q.empty())
	{
		int x=q.top().num; q.pop();
		if (vis[x]) continue; vis[x]=1;
		for (int i=head[x]; i; i=edge[i].next)
			if (!vis[edge[i].to] && dis[x]+edge[i].len<dis[edge[i].to])
			{
				dis[edge[i].to]=dis[x]+edge[i].len;
				q.push((Node){edge[i].to,dis[edge[i].to]});
			}
	}
}

int getid(int x,int y)
{
	if (Map.find(make_pair(x,y))!=Map.end()) return Map[make_pair(x,y)];
	return Map[make_pair(x,y)]=++cnt;
}

int main()
{
	cin>>n>>m; cnt=n;
	for (int i=1; i<=m; ++i)
	{
		cin>>u>>v>>c;
		int id1=getid(u,c),id2=getid(v,c);
		add(id1,id2,0); add(id2,id1,0);
		add(u,id1,1); add(id1,u,1);
		add(v,id2,1); add(id2,v,1);
	}
	Dijkstra(1);
	cout<<(dis[n]>2e9?-1:dis[n]/2)<<endl;
}