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 500010
#define inf 0x3f3f3f3f
#define mp make_pair
using namespace std;
struct node
{
	int to,nxt,belong;
}e[N<<2];
int n,m,x,y,c,head[N<<2],cnt,d[N*2] ;
void ins(int u,int v,int c)
{
	e[++cnt].to=v;
	e[cnt].nxt=head[u];
	e[cnt].belong=c;
	head[u]=cnt;
}
std::set<int> st[N];
priority_queue<pair<int,int> > q;
void spfa()
{
	for (int i=1;i<=n;i++) d[i]=inf;
	d[1]=0;
	q.push(mp(0,1));
	while (!q.empty())
	{
		int u=q.top().second,ans=-q.top().first;
		q.pop();
		if (d[u]<ans) continue;
		for (int i=head[u];i;i=e[i].nxt)
		{
			int v=e[i].to;
			int num=ans+!st[u].count(e[i].belong);
			if (d[v]>num)
			{
				d[v]=num;
				q.push(mp(-num,v));
				st[v].clear();
				st[v].insert(e[i].belong);
			}
			else if (d[v]==num) st[v].insert(e[i].belong);
		}
	}
	if (d[n]==inf) cout<<"-1";
	else cout<<d[n];
}
int main()
{
	cin>>n>>m;
	for (int i=0;i<m;i++)
	{
		cin>>x>>y>>c;
		ins(x,y,c);
		ins(y,x,c);
	}
	spfa();
	return 0;
}