#include<iostream>

#include<cstring>

#include<cstdlib>

#include<cstdio>

#include<bitset>

#include<queue>

#include<map>

#define ll long long

using namespace std;

const int maxn=;

const ll inf=1e15;

struct tjm{int too, dis, pre;}e[maxn<<];

struct poi{int x; ll dis;};

priority_queue<poi>q;

bool operator<(poi a, poi b){return a.dis>b.dis;}

map<ll,bitset<maxn> >mp;

int n, m, s, t, x, y, z, tot, cnt, top;

int p[maxn], last[maxn], ru[maxn], pos[maxn], st[maxn];

ll ans, dist[][maxn], f[][maxn];

bitset<maxn>g[][maxn];

bool v[maxn];

inline void read(int &k)

{

    int f=; k=; char c=getchar();

    while(c<'' || c>'') c=='-' && (f=-), c=getchar();

    while(c<='' && c>='') k=k*+c-'', c=getchar();

    k*=f;

}

inline void add(int x, int y, int z){e[++tot]=(tjm){y, z, last[x]}; last[x]=tot;}

inline void dijkstra(int x, int ty)

{

    for(int i=;i<=n;i++) dist[ty][i]=inf;

    dist[ty][x]=; f[ty][x]=; q.push((poi){x, });

    while(!q.empty())

    {

        poi now=q.top(); q.pop();

        if(now.dis!=dist[ty][now.x]) continue;

        for(int i=last[now.x], too;i;i=e[i].pre)

        if(dist[ty][too=e[i].too]>dist[ty][now.x]+e[i].dis)

        {

            f[ty][too]=f[ty][x];

            dist[ty][too]=min(inf, dist[ty][now.x]+e[i].dis);

            q.push((poi){too, dist[ty][too]});

        }

        else if(dist[ty][too]==dist[ty][now.x]+e[i].dis) f[ty][too]+=f[ty][x];

    }

}

inline bool check(int x, int y, int dis, int ty){return v[y] && dist[ty][x]+dis==dist[ty][y];}

inline void topsort(int ty)

{

    memset(ru, , sizeof(ru)); top=;

    for(int i=;i<=cnt;i++) for(int j=last[p[i]], too;j;j=e[j].pre)

    if(check(p[i], too=e[j].too, e[j].dis, ty)) ru[too]++;

    for(int i=;i<=cnt;i++) if(!ru[p[i]]) st[++top]=p[i], pos[p[i]]=top;

    for(int i=;i<=top;i++)

    for(int j=last[st[i]], too;j;j=e[j].pre)

    if(check(st[i], too=e[j].too, e[j].dis, ty))

    {

        ru[too]--;

        if(!ru[too]) st[++top]=too, pos[too]=top;

    }

    for(int i=;i<=cnt;i++) g[ty][p[i]][p[i]-]=;

    for(int i=top;i;i--)

    for(int j=last[st[i]], too;j;j=e[j].pre)

    if(check(st[i], too=e[j].too, e[j].dis, ty) && pos[st[i]]<pos[too]) g[ty][st[i]]|=g[ty][too];

}

int main()

{

    read(n); read(m); read(s); read(t);

    for(int i=;i<=m;i++) read(x), read(y), read(z), add(x, y, z), add(y, x, z);

    dijkstra(s, ); if(dist[][t]==inf) return printf("%lld\n", 1ll*n*(n-)>>), ;

    dijkstra(t, );

    for(int i=;i<=n;i++) if(dist[][i]+dist[][i]==dist[][t]) p[++cnt]=i, v[i]=;

    for(int i=;i<=cnt;i++) mp[f[][p[i]]*f[][p[i]]]|=<<(p[i]-);

    topsort(); topsort();

    for(int i=;i<=cnt;i++) ans+=(((mp[f[][t]-f[][p[i]]*f[][p[i]]])>>(i-))&(~g[][p[i]]>>(i-))&(~g[][p[i]]>>(i-))).count();

    ll tmp=; for(int i=;i<=cnt;i++) if(f[][p[i]]*f[][p[i]]==f[][t]) tmp++; ans+=tmp*(n-cnt);

    printf("%lld\n", ans);

}