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>
using namespace std;
struct Vertex {int s, c;};
struct Edge {Vertex to; int w;};
bool operator<(Vertex l, Vertex r) {return l.s!=r.s ? l.s<r.s : l.c<r.c;}
using Graph = map<Vertex, vector<Edge>>;
const int INF = 1e9;
int main() {
  int N, M;
  cin >> N >> M;
  Graph G;
  for(auto i=0; i<M; ++i) {
    int p, q, c;
    cin >> p >> q >> c;
    --p; --q; --c;
    Vertex u{p, c}, v{q, c};
    Vertex a{p, -1}, b{q, -1};
    G[u].push_back({v, 0});
    G[v].push_back({u, 0});
    G[u].push_back({a, 0});
    G[v].push_back({b, 0});
    G[a].push_back({u, 1});
    G[b].push_back({v, 1});
  }
  map<Vertex, int> d;
  deque<Vertex> q;
  q.push_front({0, -1});
  d[{0, -1}] = 0;
  while(!q.empty()) {
    auto v = q.front();
    q.pop_front();
    for(auto e: G[v]) {
      if(!d.count(e.to)) d[e.to] = INF;
      if(d[e.to] <= d[v] + e.w) continue;
      d[e.to] = d[v] + e.w;
      if(e.w) q.emplace_back(e.to);
      else    q.emplace_front(e.to);
    }
  }
  if(d.count({N-1, -1})) cout << d[{N-1, -1}] << endl;
  else                   cout << -1 << endl;
}