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;

template<class T> using pqueue = priority_queue<T, vector<T>, greater<T>>;
const int inf = 1e9;

int main() {
	int n, m;
	cin >> n >> m;

	vector<map<int, vector<int>>> g(1000000);
	vector<vector<int>> color(n);
	for (int i = 0; i < m; i++) {
		int p, q, c;
		scanf("%d %d %d", &p, &q, &c);
		p--; q--; c--;
		g[p][c].push_back(q);
		g[q][c].push_back(p);
	}

	vector<map<int, int>> dist(n);
	vector<queue<pair<int, int>>> q(101010);

	for (auto kv : g[0]) {
		dist[0][kv.first] = 1;
		q[1].emplace(0, kv.first);
	}

	for (int i = 1; i < 101010 - 1; i++) {
		queue<int> Q;
		while (!q[i].empty()) {
			int v, c;
			tie(v, c) = q[i].front(); q[i].pop();
			Q.push(v);
			for (auto u : g[v][c]) {
				if (dist[u].count(c) == 0) {
					dist[u][c] = i;
					q[i].emplace(u, c);
				}
			}
			g[v][c].clear();
		}
		while (!Q.empty()) {
			int v = Q.front(); Q.pop();
			for (auto kv : g[v]) {
				for (int u : kv.second) {
					if (dist[u].count(kv.first) == 0) {
						dist[u][kv.first] = i + 1;
						q[i + 1].emplace(u, kv.first);
					}
				}
			}
			g[v].clear();
		}
	}

	int ans = inf;

	for (auto kv : dist[n - 1]) {
		ans = min(ans, kv.second);
	}

	if (ans == inf) ans = -1;

	cout << ans << endl;
}