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: Accepted)

#include  <functional>
#include  <algorithm>
#include  <exception>
#include  <stdexcept>
#include  <streambuf>
#include  <iterator>
#include  <string.h>
#include  <stdlib.h>
#include  <typeinfo>
#include  <valarray>
#include  <iostream>
#include  <sstream>
#include  <istream>
#include  <stdio.h>
#include  <climits>
#include  <clocale>
#include  <complex>
#include  <csetjmp>
#include  <csignal>
#include  <cstdarg>
#include  <cstddef>
#include  <ctype.h>
#include  <cassert>
#include  <cstdlib>
#include  <utility>
#include  <cstring>
#include  <numeric>
#include  <ostream>
#include  <cwctype>
#include  <fstream>
#include  <iomanip>
#include  <math.h>
#include  <bitset>
#include  <cctype>
#include  <string>
#include  <vector>
#include  <limits>
#include  <memory>
#include  <cerrno>
#include  <time.h>
#include  <iosfwd>
#include  <cfloat>
#include  <cstdio>
#include  <cwchar>
#include  <cmath>
#include  <ctime>
#include  <deque>
#include  <queue>
#include  <stack>
#include  <ios>
#include  <map>
#include  <set>
#include  <new>
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define ll long long
#define pii pair<int,int>
using namespace std;
const int maxn=1000005;
int par[maxn],vis[maxn],hei[maxn],id[maxn];
int n,m,cols,sz,ans[maxn];
vector<pii> col[maxn];
vector<int> gra[maxn];
int findfa(int x)
{
    if(x==par[x])
    return x;
    else
    return par[x]=findfa(par[x]);
}
void unio(int x,int y)
{
    int fx=findfa(x),fy=findfa(y);
    if(fx==fy)
    return;
    if(hei[fx]<hei[fy])
    par[fx]=fy;
    else
    {
        par[fy]=fx;
        if(hei[fx]==hei[fy])
        hei[fx]++;
    }
}
inline void init(int i,int j)
{
    par[i]=i;
    par[j]=j;
    hei[i]=hei[j]=0;
    id[i]=id[j]=-1;
    vis[i]=vis[j]=0;
}
inline void clea(int i)
{
    for(int j=0;j<col[i].size();j++)
    init(col[i][j].fi,col[i][j].se);
    for(int j=0;j<col[i].size();j++)
    unio(col[i][j].fi,col[i][j].se);
}
inline void built(int i,int j)
{
    gra[i].pb(j);
    gra[j].pb(i);
}
int main()
{
    cin>>n>>m;
    for(int i=0;i<m;i++)
    {
        int x,y,c;
        scanf("%d%d%d",&x,&y,&c);
        x--;y--;c--;
        cols=max(cols,c);
        col[c].pb(mp(x,y));
    }
    sz=n;
    for(int i=0;i<=cols;i++)
    {
        if(col[i].empty())
        continue;
        clea(i);
        for(int j=0;j<col[i].size();j++)
        {
            pii p=col[i][j];
            if(!vis[p.fi])
            {
                vis[p.fi]=1;
                int fa=findfa(p.fi);
                if(id[fa]==-1)
                id[fa]=sz++;
                built(p.fi,id[fa]);
            }
            if(!vis[p.se])
            {
                vis[p.se]=1;
                int fa=findfa(p.se);
                if(id[fa]==-1)
                id[fa]=sz++;
                built(p.se,id[fa]);
            }
        }
    }
    queue<int> q;
    q.push(0);
    memset(ans,-1,sizeof(ans));
    ans[0]=0;
    while(!q.empty())
    {
        int u=q.front();
        q.pop();
        for(int i=0;i<gra[u].size();i++)
        {
            int v=gra[u][i];
            if(ans[v]==-1)
            {
                ans[v]=ans[u]+1;
                q.push(v);
            }
        }
    }
    if(ans[n-1]<0)
    cout<<-1;
    else
    cout<<ans[n-1]/2;
    return 0;
}