#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;
#ifdef MY_DEBUG_FLAG
template<typename T> void debug(T a) { cerr << a << ' '; }
template<typename T, typename U> void debug(pair<T, U> a) { cerr << a.first << ' ' << a.second << ' '; }
template<typename T> void debug(vector<T> a) { for(auto it : a) debug(it);}
template<typename T> void debug(set<T> a) { for(auto it : a) debug(it);}
#define db(a) cerr << "DEBUG ( " << #a << " == "; debug(a); cerr << ")\n"
#else
#define db(...)
#endif
#define pb push_back
#define eb emplace_back
#define ff first
#define ss second
#define fast ios_base::sync_with_stdio(false), cout.tie(nullptr), cin.tie(nullptr)
#define sz(a) ((int)(a).size())
#define rep(i,a,b) for(int i=(a); i<(b); i++)
#define dec(i,n,a) for(int i=(n); i>=(a); i--)
#define clr(a,v) memset(a, v, sizeof(a))
#define all(a) (a).begin(),(a).end()
constexpr ll inf = 0x3f3f3f3f3f3f3f3f;
constexpr int MAXN = 1e5 + 10;
constexpr int mod = 1000000007;
struct Edge
{
int u, v, w;
} edges[2*MAXN];
vector<pii> g[MAXN];
ll dist[MAXN][4]; // 0 -> s, 1 -> t, 2 -> u, 3 -> v
void dijkstra(int s, int k) {
rep(i,0,MAXN) dist[i][k] = inf;
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> q;
q.push({0ll, s});
dist[s][k] = 0;
bool mark[MAXN]; clr(mark, 0);
while(!q.empty()) {
int u = q.top().ss;
q.pop();
if(mark[u]) continue;
mark[u] = 1;
for(auto nxt : g[u]) {
int v = nxt.ff, w = nxt.ss;
if(dist[v][k] > dist[u][k] + 1ll*w) {
dist[v][k] = dist[u][k] + 1ll*w;
q.push({dist[v][k], v});
}
}
}
}
vi dag[MAXN], inv_dag[MAXN], ord;
bool mark[MAXN];
void dfs(int u) {
mark[u] = 1;
for(auto v : dag[u])
if(!mark[v])
dfs(v);
ord.pb(u);
}
int main() {
int n, m, S, T, U, V; scanf("%d %d %d %d %d %d", &n, &m, &S, &T, &U, &V);
rep(i,0,m) {
int a, b, w; scanf("%d %d %d", &a, &b, &w);
edges[i] = {a,b,w};
g[a].pb({b,w});
g[b].pb({a,w});
}
dijkstra(S,0);
dijkstra(T,1);
dijkstra(U,2);
dijkstra(V,3);
ll menor = dist[T][0];
rep(i,0,m) {
int u = edges[i].u, v = edges[i].v, w = edges[i].w;
if(dist[u][0] + 1ll*w + dist[v][1] == menor)
dag[u].pb(v), inv_dag[v].pb(u);
if(dist[v][0] + 1ll*w + dist[u][1] == menor)
dag[v].pb(u), inv_dag[u].pb(v);
}
dfs(S);
reverse(all(ord));
vector<ll> d(n+1);
rep(i,1,n+1) d[i] = dist[i][2];
for(auto x : ord) {
for(auto y : dag[x]) {
dist[y][2] = min(dist[x][2], dist[y][2]);
}
}
reverse(all(ord));
for(auto x : ord) {
for(auto y : inv_dag[x]) {
d[y] = min(d[x], d[y]);
}
}
ll ans = inf;
rep(i,1,n+1) {
ans = min(ans, min(dist[i][2],d[i]) + dist[i][3]);
}
printf("%lld\n", ans);
}
