#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int maxn = 1e5 + 10;
vector<pair<int, int>> g[maxn];
ll dist[4][maxn];
int n, m, s, t, u, v;
void dijkstra(int src, ll dist[]) {
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> q;
for (int i=1; i<=n; ++i) dist[i] = 1e18;
dist[src] = 0;
q.push({0ll, src});
while (!q.empty()) {
auto [dv, v] = q.top(); q.pop();
if (dv != dist[v]) continue;
for (auto [u, w] : g[v]) {
if (dv + w < dist[u]) {
dist[u] = dv + w;
q.push({dist[u], u});
}
}
}
}
vector<int> dag[maxn];
ll dp[maxn][4];
bool vis[maxn][4];
ll dfs(int x, int r) {
if (x == t) {
if (r == 0) return dist[2][t] + dist[3][t];
if (r == 1) return dist[3][t];
if (r == 2) return dist[2][t];
if (r == 3) return 0;
}
if (vis[x][r]) return dp[x][r];
vis[x][r] = 1;
ll& ans = dp[x][r] = 1e18;
for (auto y : dag[x]) {
if (r == 0) {
ans = min(ans, dfs(y, 0));
ans = min(ans, dfs(y, 1) + dist[2][x]);
ans = min(ans, dfs(y, 2) + dist[3][x]);
ans = min(ans, dfs(y, 3) + dist[2][x] + dist[3][x]);
}
if (r == 1) {
ans = min(ans, dfs(y, 1));
ans = min(ans, dfs(y, 3) + dist[3][x]);
}
if (r == 2) {
ans = min(ans, dfs(y, 2));
ans = min(ans, dfs(y, 3) + dist[2][x]);
}
if (r == 3) {
ans = min(ans, dfs(y, 3));
}
}
return ans;
}
int main() {
cin>>n>>m>>s>>t>>u>>v;
vector<tuple<int, int, int>> edges;
for (int i=0; i<m; ++i) {
int a, b, c;
cin>>a>>b>>c;
edges.push_back({a, b, c});
g[a].push_back({b, c});
g[b].push_back({a, c});
}
dijkstra(s, dist[0]);
dijkstra(t, dist[1]);
dijkstra(u, dist[2]);
dijkstra(v, dist[3]);
for (auto [a, b, c] : edges) {
if (dist[0][a] + c + dist[1][b] == dist[0][t]) {
dag[a].push_back(b);
}
if (dist[0][b] + c + dist[1][a] == dist[1][s]) {
dag[b].push_back(a);
}
}
ll ans = dist[2][v];
ans = min(ans, dfs(s, 0));
cout << ans << '\n';
return 0;
}
