#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int MXN = 1e5+5;
const ll inf = 1e18;
int n, m, S, T, U, V;
vector<pii> g[MXN];
ll dis[6][MXN];
inline void dijkstra(int v, int id) {
fill(dis[id]+1, dis[id]+n+1, inf);
dis[id][v] = 0;
priority_queue<pll> pq;
pq.push({0, v});
while(!pq.empty()) {
ll d = -pq.top().first;
int v = pq.top().second;
pq.pop();
if(d!=dis[id][v]) continue;
for(auto [u, w] : g[v])
if(dis[id][u]>d+w)
pq.push({-(dis[id][u]=d+w), u});
}
}
int32_t main() {
cin.tie(0); cout.tie(0); ios_base::sync_with_stdio(0);
cin >> n >> m >> S >> T >> U >> V;
for(int i=0,u,v,w; i<m; i++) {
cin >> u >> v >> w;
g[u].push_back({v, w});
g[v].push_back({u, w});
}
dijkstra(S, 0);
dijkstra(T, 1);
fill(dis[2]+1, dis[2]+n+1, inf);
fill(dis[3]+1, dis[3]+n+1, inf);
fill(dis[4]+1, dis[4]+n+1, inf);
fill(dis[5]+1, dis[5]+n+1, inf);
priority_queue<pair<ll, pii>> pq;
dis[2][U] = 0; pq.push({0, {2, U}});
if(dis[0][U]+dis[1][U]==dis[0][T])
dis[3][U] = 0, pq.push({0, {3, U}});
dis[4][U] = 0, pq.push({0, {4, U}});
dis[5][U] = 0, pq.push({0, {5, U}});
while(!pq.empty()) {
ll d = -pq.top().first;
int type = pq.top().second.first;
int v = pq.top().second.second;
pq.pop();
if(d != dis[type][v]) continue;
if(type==2) {
for(auto [u, w] : g[v]) {
if(dis[2][u]>d+w)
pq.push({-(dis[2][u]=d+w), {2, u}});
if(dis[0][u]+dis[1][u]==dis[0][T]) {
if(dis[3][u]>d+w) pq.push({-(dis[3][u]=d+w), {3, u}});
if(dis[4][u]>d+w) pq.push({-(dis[4][u]=d+w), {4, u}});
}
}
}
else if(type==3) {
for(auto [u, w] : g[v]) {
if(dis[0][v]+w+dis[1][u]==dis[0][T] && dis[3][u]>d)
pq.push({-(dis[3][u]=d), {3, u}});
if(dis[5][u]>d+w)
pq.push({-(dis[5][u]=d+w), {5, u}});
}
}
else if(type==4) {
for(auto [u, w] : g[v]) {
if(dis[1][v]+w+dis[0][u]==dis[0][T] && dis[4][u]>d)
pq.push({-(dis[4][u]=d), {4, u}});
if(dis[5][u]>d+w)
pq.push({-(dis[5][u]=d+w), {5, u}});
}
}
else if(type==5) {
for(auto [u, w] : g[v])
if(dis[5][u]>d+w)
pq.push({-(dis[5][u]=d+w), {5, u}});
}
}
cout << min({dis[3][V], dis[4][V], dis[5][V]}) << '\n';
return 0;
}
