#include <bits/stdc++.h>
using namespace std;
#define DEBUG(x) //x
#define A(x) DEBUG(assert(x))
#define PRINT(x) DEBUG(cerr << x)
#define PV(x) DEBUG(cerr << #x << " = " << x << endl)
#define PAR(x) DEBUG(PRINT(#x << " = { "); for (auto y : x) PRINT(y << ' '); PRINT("}\n");)
#define PAR2(x) DEBUG(PRINT(#x << " = { "); for (auto [y, z] : x) PRINT(y << ',' << z << " "); PRINT("}\n");)
typedef int64_t i64;
const i64 INF = 1e18; //1000000007; //998244353;
struct S {
i64 n, m, s, t, u, v, ans;
vector<vector<pair<i64, i64>>> edges;
vector<i64> ds, du, dv, dpu, dpv;
array<vector<vector<i64>>, 2> sp;
void run() {
cin >> n >> m >> s >> t >> u >> v;
--s; --t; --u; --v;
edges.resize(n);
for (int i = 0; i < m; ++i) {
i64 a, b, c;
cin >> a >> b >> c;
--a; --b;
edges[a].push_back({b, c});
edges[b].push_back({a, c});
}
sp[0].resize(n);
sp[1].resize(n);
du = dijkstra(u); PAR(du);
dv = dijkstra(v); PAR(dv);
ans = du[v]; PV(ans);
dpu.resize(n);
dpv.resize(n);
dijkstra2(s, t); PAR(dpu); PAR(dpv);
dijkstra2(t, s); PAR(dpu); PAR(dpv);
cout << ans << '\n';
}
void dijkstra2(i64 start, i64 end) {
fill(dpu.begin(), dpu.end(), INF);
fill(dpv.begin(), dpv.end(), INF);
vector<i64> d(n, INF);
d[start] = 0;
vector<bool> visited(n, false);
priority_queue<array<i64, 3>> q;
q.push({0, start, 0});
while (!q.empty()) {
i64 dist = -q.top()[0];
i64 node = q.top()[1];
i64 prev = q.top()[2];
q.pop();
if (!visited[node]) {
visited[node] = true;
d[node] = dist;
dpu[node] = min(du[node], dpu[prev]);
dpv[node] = min(dv[node], dpv[prev]);
for (auto [next, wt] : edges[node]) {
q.push({-d[node] - wt, next, node});
}
} else if (dist == d[node]) {
if (min(du[node], dpu[prev]) + min(dv[node], dpv[prev])
<= dpu[node] + dpv[node]) {
dpu[node] = min(du[node], dpu[prev]);
dpv[node] = min(dv[node], dpv[prev]);
}
}
}
ans = min(ans, dpu[end] + dpv[end]);
}
vector<i64> dijkstra(i64 start) {
vector<i64> d(n, INF);
d[start] = 0;
vector<bool> visited(n, false);
priority_queue<pair<i64, i64>> q;
q.push({0, start});
while (!q.empty()) {
i64 dist = q.top().first;
i64 node = q.top().second;
q.pop();
if (visited[node]) continue;
visited[node] = true;
for (auto [next, wt] : edges[node]) {
if (d[node] + wt <= d[next]) {
d[next] = d[node] + wt;
q.push({-d[node] - wt, next});
}
}
}
return d;
}
};
int main() {
ios::sync_with_stdio(0); cin.tie(0);
auto sol = make_unique<S>();
sol->run();
}
