#include "bits/stdc++.h"
using namespace std;
int main() {
cin.tie(0)->sync_with_stdio(0);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
--s, --t;
--u, --v;
vector<vector<pair<int, int>>> g(n);
for (int i = 0; i < m; i++) {
int x, y, w;
cin >> x >> y >> w;
--x, --y;
g[x].emplace_back(y, w);
g[y].emplace_back(x, w);
}
const int64_t inf = 1e18;
using P = pair<int64_t, int>;
auto dijkstra = [&](int s) {
const int64_t inf = int64_t(1e18);
vector<int64_t> d(n, inf);
priority_queue<P, vector<P>, greater<>> pq;
pq.emplace(d[s] = 0, s);
while (pq.size()) {
int64_t d_v;
int v;
tie(d_v, v) = pq.top();
pq.pop();
if (d_v != d[v])
continue;
for (auto &it : g[v]) {
int u = it.first;
int w = it.second;
if (d[v] + w < d[u]) {
pq.emplace(d[u] = d[v] + w, u);
}
}
}
return d;
};
auto du = dijkstra(u);
auto dv = dijkstra(v);
auto dijkstra2 = [&](int s, int t) {
vector<array<int64_t, 2>> dp(n, {inf, inf});
vector<int64_t> d(n, inf);
priority_queue<P, vector<P>, greater<>> pq;
dp[s][0] = du[s];
dp[s][1] = dv[s];
pq.emplace(d[s] = 0, s);
while (pq.size()) {
int64_t d_v;
int v;
tie(d_v, v) = pq.top();
pq.pop();
if (d_v != d[v])
continue;
for (auto &it : g[v]) {
int u, w;
tie(u, w) = it;
if (d[u] > d[v] + w) {
dp[u][0] = min(dp[v][0], du[u]);
dp[u][1] = min(dp[v][1], dv[u]);
pq.emplace(d[u] = d[v] + w, u);
} else if (d[u] == d[v] + w) {
if (min(dp[v][0], du[u]) + min(dp[v][1], dv[u]) <=
dp[u][0] + dp[u][1]) {
dp[u][0] = min(dp[v][0], du[u]);
dp[u][1] = min(dp[v][1], dv[u]);
}
}
}
}
return dp[t][0] + dp[t][1];
};
int64_t res = du[v];
res = min(res, dijkstra2(s, t));
res = min(res, dijkstra2(t, s));
cout << res;
}
