#include <bits/stdc++.h>
using namespace std;
#define int long long
const int inf = 1e18;
vector<vector<pair<int, int>>> graph(1e5 + 1);
vector<int> du(1e5 + 1, inf), dv(1e5 + 1, inf), ds(1e5 + 1, inf);
vector<vector<int>> dp(2, vector<int>(1e5 + 1));
vector<bool> vis(1e5 + 1);
int ans;
void dijkstra1(int start, vector<int> &arr) {
// Reset the visited vector for this run.
fill(vis.begin(), vis.end(), false);
arr[start] = 0;
priority_queue<pair<int, int>> pq;
pq.push({0, start});
while (!pq.empty()) {
auto [c, node] = pq.top();
pq.pop();
if (vis[node]) continue;
vis[node] = true;
for (auto [b, wt] : graph[node]) {
if (arr[node] + wt < arr[b]) {
arr[b] = arr[node] + wt;
pq.push({-arr[b], b});
}
}
}
}
void dijkstra2(int start, int end) {
// Reset dp arrays with "inf" for this run.
fill(dp[0].begin(), dp[0].end(), inf);
fill(dp[1].begin(), dp[1].end(), inf);
// Reset the visited vector.
fill(vis.begin(), vis.end(), false);
priority_queue<pair<int, pair<int, int>>> pq;
pq.push({0, {start, 0}});
// Set the dp value for the dummy parent (index 0) to inf.
dp[0][0] = dp[1][0] = inf;
while (!pq.empty()) {
auto [c, p] = pq.top();
auto [node, par] = p;
pq.pop();
if (!vis[node]) {
vis[node] = true;
ds[node] = -c;
// Propagate the best hook-in costs.
dp[0][node] = min(du[node], dp[0][par]);
dp[1][node] = min(dv[node], dp[1][par]);
for (auto &edge : graph[node]) {
int next = edge.first, w = edge.second;
pq.push({c - w, {next, node}});
}
} else if (-c == ds[node]) {
// If we reach node with the same corridor distance,
// update dp values if the candidate parent's values are better.
if (min(du[node], dp[0][par]) + min(dv[node], dp[1][par]) <= dp[0][node] + dp[1][node]) {
dp[0][node] = min(du[node], dp[0][par]);
dp[1][node] = min(dv[node], dp[1][par]);
}
}
}
ans = min(ans, dp[0][end] + dp[1][end]);
}
void solve() {
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
for (int i = 0; i < m; i++) {
int a, b, c;
cin >> a >> b >> c;
graph[a].push_back({b, c});
graph[b].push_back({a, c});
}
dijkstra1(u, du);
dijkstra1(v, dv);
ans = du[v];
dijkstra2(s, t);
dijkstra2(t, s);
cout << ans << endl;
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t = 1;
while (t--) solve();
return 0;
}
