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"
#define in std::cin
#define out std::cout
#define rep(i,N) for(int i=0;i<N;++i)
typedef long long int LL;
typedef std::pair<LL, LL> P;
struct edge { LL to, cost; };
 
const LL inf = 11234567890123;
LL N, M;
std::map<LL, LL>dist;
std::map<LL, std::vector<edge>>G;
 
void dijkstra(LL s)
{
	std::priority_queue<P, std::vector<P>, std::greater<P>>que;
	for (auto i : G) dist[i.first] = inf;
	dist[s] = 0;
	que.push(P(0, s));
	while (!que.empty())
	{
		P p = que.top(); que.pop();
		LL v = p.second;
		if (dist[v] < p.first) { continue; }
		rep(i, G[v].size())
		{
			edge e = G[v][i];
			if (dist[e.to] > dist[v] + e.cost)
			{
				dist[e.to] = dist[v] + e.cost;
				que.push(P(dist[e.to], e.to));
			}
		}
	}
}
 
int main()
{
	in >> N >> M;
	std::vector<LL>p(M), q(M), c(M);
	rep(i, M)
	{
		in >> p[i] >> q[i] >> c[i];
		G[p[i] + c[i] * N].push_back({ q[i] + c[i] * N,0 });
		G[q[i] + c[i] * N].push_back({ p[i] + c[i] * N,0 });
		G[p[i]].push_back({ p[i] + c[i] * N ,1 });
		G[p[i] + c[i] * N].push_back({ p[i] ,0 });
		G[q[i]].push_back({ q[i] + c[i] * N ,1 });
		G[q[i] + c[i] * N].push_back({ q[i] ,0 });
	}
	dist[N] = inf;
	dijkstra(1);
	out << (dist[N] >= inf ? -1 : dist[N]) << std::endl;
	return 0;
}