#include <iostream>
#include <vector>
#include <queue>
#define f first
#define se second
#define pll pair<long long,long long>
using namespace std;
long long n, m, s, t, ss, tt, dist[100010], disu[100010], disv[100010], vis[100010], in[100010], minu[100010], minv[100010], minn[100010];
vector<pll> edge[100010];
vector<long long> dag[100010];
priority_queue<pll,vector<pll>,greater<pll>> pq;
void dijk(int st, long long (&dis)[100010]) {
pq.push({0,st});
for (int i = 1; i <= n; i++) dis[i] = 1e18, vis[i] = 0;
dis[st] = 0;
while (pq.size()) {
long long u = pq.top().se;
pq.pop();
if (vis[u]) continue;
vis[u] = 1;
for (int i = 0; i < edge[u].size(); i++) {
if (dis[edge[u][i].f] > dis[u]+edge[u][i].se) {
dis[edge[u][i].f] = dis[u]+edge[u][i].se;
pq.push({dist[edge[u][i].f],edge[u][i].f});
}
}
}
}
void dfs(int u) {
minu[u] = min(minu[u],disu[u]);
minv[u] = min(minv[u],disv[u]);
minn[u] = min(minn[u],min(minu[u]+disv[u],minv[u]+disu[u]));
for (int i = 0; i < dag[u].size(); i++) {
long long v = dag[u][i];
in[v]--;
minu[v] = min(minu[v],minu[u]);
minv[v] = min(minv[v],minv[u]);
minn[v] = min(minn[v],minn[u]);
if (!in[v]) dfs(v);
}
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
cin >> n >> m >> s >> t >> ss >> tt;
for (int i = 1; i <= m; i++) {
long long u, v, w;
cin >> u >> v >> w;
edge[u].push_back({v,w});
edge[v].push_back({u,w});
}
dijk(ss,disu);
dijk(tt,disv);
dijk(s,dist);
for (int i = 1; i <= n; i++) {
for (int j = 0; j < edge[i].size(); j++) {
if (dist[i]+edge[i][j].se == dist[edge[i][j].f]) {
dag[i].push_back(edge[i][j].f);
in[edge[i][j].f]++;
}
}
}
for (int i = 1; i <= n; i++) minu[i] = minv[i] = minn[i] = 1e18;
dfs(s);
cout << min(disu[tt],minn[t]) << endl;
}
