#include <bits/stdc++.h>
using namespace std;
#define int long long
#define all(x) x.begin(), x.end()
#define size(x) (int)x.size()
template<class S, class T>
bool chmin(S &a, const T &b) {
return a > b && (a = b) == b;
}
template<class S, class T>
bool chmax(S &a, const T &b) {
return a < b && (a = b) == b;
}
const int inf = 1e9 + 7;
const int INF = 1e18 + 7;
const int mod = 1e9 + 7;
const int N = 1e5 + 1;
vector<pair<int, int>> g[N];
vector<int> du(N, INF), dv(N, INF);
vector<vector<int>> dp(2, vector<int> (N, INF));
int res;
void dijkstra(int init, vector<int> &d) {
priority_queue<pair<int, int>,
vector<pair<int, int>>,
greater<pair<int, int>>> q;
q.push({0, init});
d[init] = 0;
while (!q.empty()) {
int v = q.top().second;
q.pop();
for (auto [to, w] : g[v]) {
if (chmin(d[to], d[v] + w)) {
q.push({d[to], to});
}
}
}
}
void compute(int s, int t) {
vector<int> d(N, INF);
priority_queue<pair<int, int>,
vector<pair<int, int>>,
greater<pair<int, int>>> q;
q.push({0, s});
d[s] = 0;
while (!q.empty()) {
int v = q.top().second;
q.pop();
for (auto [to, w] : g[v]) {
if (chmin(d[to], d[v] + w)) {
dp[0][to] = min(du[to], dp[0][v]);
dp[1][to] = min(dv[to], dp[1][v]);
q.push({d[to], to});
} else if (d[to] == d[v] + w) {
if (min(du[to], dp[0][v]) + min(dv[to], dp[1][v]) < dp[0][to] + dp[1][to]) {
dp[0][to] = min(du[to], dp[0][v] + w);
dp[1][to] = min(dv[to], dp[1][v] + w);
}
}
}
}
//cout << s << ' ' << t << ' ' << dp[0][t] + dp[1][t] << '\n';
chmin(res, dp[0][t] + dp[1][t]);
}
signed main() {
cin.tie(nullptr)->sync_with_stdio(false);
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;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
dijkstra(u, du), dijkstra(v, dv);
res = min(du[v], dv[u]);
compute(s, t), compute(t, s);
cout << res;
}
