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<iostream>
#include<cstdio>
#include<algorithm>
#include<set>
#include<map>
#include<queue>
#include<cassert>
#define PB push_back
#define MP make_pair
#define sz(v) (in((v).size()))
#define forn(i,n) for(in i=0;i<(n);++i)
#define forv(i,v) forn(i,sz(v))
#define fors(i,s) for(auto i=(s).begin();i!=(s).end();++i)
#define all(v) (v).begin(),(v).end()
using namespace std;
typedef long long in;
typedef vector<in> VI;
typedef vector<VI> VVI;
vector<set<in> > usd;
VI dst;
VVI egt;
vector<map<in,VI> > eso;
queue<in> q;
void ttk(in u, in c, in d){
  if(usd[u].find(c)!=usd[u].end())
    return;
  usd[u].insert(c);
  if(dst[u]>d){
    dst[u]=d;
    q.push(u);
  }
  VI& tp=eso[u][c];
  forv(i,tp){
    ttk(tp[i],c,d);
  }
}
int main(){
  ios::sync_with_stdio(0);
  cin.tie(0);
  in n,m;
  cin>>n>>m;
  in x,y,c;
  egt.resize(n);
  const in inf=1e9;
  usd.resize(n);
  dst.resize(n,inf);
  q.push(0);
  dst[0]=0;
  eso.resize(n);
  forn(z,m){
    cin>>x>>y>>c;
    --x;
    --y;
    eso[x][c].PB(y);
    eso[y][c].PB(x);
    egt[x].PB(c);
    egt[y].PB(c);
  }
  in u;
  while(!q.empty()){
    u=q.front();
    q.pop();
    forv(i,egt[u]){
      c=egt[u][i];
      if(usd[u].find(c)!=usd[u].end())
	continue;
      ttk(u,c,dst[u]+1);
    }
  }
  if(dst[n-1]==inf)
    cout<<-1<<endl;
  else
    cout<<dst[n-1]<<endl;
  return 0;
}