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 <vector>
#include <set>
#include <cassert>

int n, m;
std::vector <std::vector <std::pair <int, int>>> edge;
std::vector <int> dis;
std::vector <std::set <int>> vis;

int main () {
	std::cin >> n >> m;
	edge.resize (n);
	dis.assign (n, 1e9);
	vis.resize (n);
	while (m--) {
		int p, q, c;
		std::cin >> p >> q >> c;
		--p, --q;
		edge[p].push_back ({q, c});
		edge[q].push_back ({p, c});
	}
	std::set <std::pair <int,int>> q;
	q.insert ({0,0}); dis[0] = 0;
	while (!q.empty()) {
		int u = q.begin()->second, d = q.begin()->first;
		u = -u;
		assert (d == dis[u]);
		q.erase (q.begin());
		for (auto v : edge[u]) {
			int w = vis[u].count (v.second) ^ 1;
			if (dis[v.first] > dis[u] + w) {
				q.erase ({dis[v.first], -v.first});
				dis[v.first] = dis[u] + w;
				vis[v.first].clear ();
				vis[v.first].insert (v.second);
				q.insert ({dis[v.first], -v.first});
			} else if (dis[v.first] == dis[u] + w) {
				vis[v.first].insert (v.second);
			}
		}
	}
	if (dis[n-1] == 1e9) dis[n-1] = -1;
	std::cout << dis[n-1] << "\n";

	return 0;
}