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;

typedef long long ll;
typedef unsigned long long ull;

ll conv(int station, int company){
    return station*10000000LL+company;
}

int main(){
    int N,M;
    cin >> N >> M;
    map<ll,vector<ll>> E;
    for(int i=0;i<M;i++){
        int p,q,c;
        cin >> p >> q >> c;
        E[conv(p,c)].push_back(conv(q,c));
        E[conv(p,c)].push_back(conv(p,0));
        E[conv(p,0)].push_back(conv(p,c));
        E[conv(q,c)].push_back(conv(p,c));
        E[conv(q,c)].push_back(conv(q,0));
        E[conv(q,0)].push_back(conv(q,c));
    }

    deque<pair<ll,ll>> Q;
    unordered_set<ll> checked;
    Q.push_back(make_pair(conv(1,0),0));
    while(!Q.empty()){
        auto t=Q.front();
        Q.pop_front();
        if(t.first/10000000LL==N){
            cout << t.second << endl;
            return 0;
        }
        if(checked.count(t.first)>0) continue;
        checked.insert(t.first);
        for(ll x:E[t.first]){
            if(checked.count(x)>0) continue;
            if(t.first%10000000LL==0){
                Q.push_back(make_pair(x,t.second+1));
            }else{
                Q.push_front(make_pair(x,t.second));
            }
        }
    }
    cout << "-1" << endl;
    return 0;
}