#include <fstream>
#include <vector>
#include <queue>
using namespace std;

ifstream is("p1.in");
ofstream os("p1.out");

int N, X, Y, x, y, z;
vector <pair<int,int> > V[500];
int Cost[500];
int Nr[500];
priority_queue <pair<int,int>, vector <pair<int,int> > , greater <pair<int,int> > > P;

void Input();
void Dijkstra();

int main()
{
    Input();
    Dijkstra();
   /* for ( int i = 1; i <= N; ++i )
        os << Cost[i] << " "; */

    os << Nr[Y];

    is.close();
    os.close();
}

void Input()
{
    is >> N >> X >> Y;
    while ( is >> x )
    {
        is >> y >> z;
        V[x].push_back(make_pair(y,z));
        V[y].push_back(make_pair(x,z));
    }
    for ( int i = 2; i <= N; ++i )
        Cost[i] = 0x3f3f3f3f;


}

void Dijkstra()
{
    P.push(make_pair(0,X));
    int node;
    while ( !P.empty() )
    {
        node = P.top().second;
        P.pop();
        for ( const auto& v : V[node] )
        {
            if ( Cost[v.first] > Cost[node] + v.second )
            {
                Cost[v.first] = Cost[node] + v.second;
                Nr[v.first] = 1;
                P.push(make_pair(Cost[v.first],v.first));
            }
            else
                if ( Cost[v.first] == Cost[node] + v.second )
                    Nr[v.first]++;
        }
    }
}