#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, int> pli;
#define ff first
#define ss second
const ll inf = 1e18;
const int N = 1e5 + 9;
int n, m, s, t, U, V;
vector<pii> g[N];
vector<int> G[N];
ll dist[4][N];
void dijkstra(int u, ll dist[]) {
fill(dist + 1, dist + n + 1, inf);
priority_queue<pli> q;
q.emplace(dist[u] = 0, u);
while (!q.empty()) {
ll d = -q.top().ff;
u = q.top().ss; q.pop();
if (d != dist[u]) continue;
for (pii v : g[u]) {
if (dist[v.ff] > dist[u] + v.ss) {
dist[v.ff] = dist[u] + v.ss;
q.emplace(-dist[v.ff], v.ff);
}
}
}
}
int idx[N];
bool cmp(int i, int j) { return dist[1][i] < dist[1][j]; }
void init_idx() {
for (int i = 1; i <= n; ++i) idx[i] = i;
sort(idx + 1, idx + n + 1, cmp);
}
ll dp[2][N];
int main() {
cin.tie(NULL)->sync_with_stdio(false);
cin >> n >> m >> s >> t >> U >> V;
for (int i = 0, u, v, c; i < m; ++i) {
cin >> u >> v >> c;
g[u].emplace_back(v, c);
g[v].emplace_back(u, c);
}
dijkstra(s, dist[0]);
dijkstra(t, dist[1]);
for (int u = 1; u <= n; ++u)
for (pii v : g[u])
if (dist[0][u] + v.ss + dist[1][v.ff] == dist[0][t])
G[u].push_back(v.ff);
dijkstra(U, dist[2]);
dijkstra(V, dist[3]);
ll ans = dist[2][V];
init_idx();
for (int i = 1, u; i <= n; ++i) {
u = idx[i];
//// U -> u -> v -> V
// edge v -> V
dp[0][u] = dist[3][u];
// edge u -> v
for (int v : G[u])
dp[0][u] = min(dp[0][u], dp[0][v]);
// edge U -> u
ans = min(ans, dp[0][u] + dist[2][u]);
//// U -> v -> u -> V
// edge U -> v
dp[1][u] = dist[2][u];
// edge v -> u
for (int v : G[u])
dp[1][u] = min(dp[1][u], dp[1][v]);
// edge u -> V
ans = min(ans, dp[1][u] + dist[3][u]);
}
cout << ans;
}
