#pragma GCC optimize("O3,unroll-loops,Ofast")
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define endl '\n'
#define fii first
#define sei second
const ll inf = 1e18;
const int N = 100005;
int n, m, s, t, x, y;
ll d[4][N], ans = inf;
bool vst[N];
vector<pair<int, ll>> adj[N];
vector<int> adj2[N];
struct Edge { int u, v; ll w; };
vector<Edge> edges;
ll minx[N], miny[N];
void dijkstra(int st, int id) {
for (int i = 1; i <= n; i++) d[id][i] = inf;
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
d[id][st] = 0;
pq.push({0, st});
while (!pq.empty()) {
auto [dist, u] = pq.top(); pq.pop();
if (dist > d[id][u]) continue;
for (auto &pr : adj[u]) {
int v = pr.fii; ll w = pr.sei;
if (d[id][v] > dist + w) {
d[id][v] = dist + w;
pq.push({d[id][v], v});
}
}
}
}
void dfs2(int u) {
vst[u] = true;
minx[u] = miny[u] = inf;
for (int v : adj2[u]) {
if (!vst[v]) dfs2(v);
ans = min(ans, d[2][u] + miny[v]);
ans = min(ans, d[3][u] + minx[v]);
minx[u] = min(minx[u], minx[v]);
miny[u] = min(miny[u], miny[v]);
}
minx[u] = min(minx[u], d[2][u]);
miny[u] = min(miny[u], d[3][u]);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(NULL);
cin >> n >> m >> s >> t >> x >> y;
edges.reserve(m);
for (int i = 0; i < m; i++) {
int u, v; ll w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
edges.push_back({u, v, w});
}
dijkstra(s, 0);
dijkstra(t, 1);
dijkstra(x, 2);
dijkstra(y, 3);
ll ST = d[0][t];
for (int i = 1; i <= n; i++) {
adj2[i].clear();
vst[i] = false;
}
for (auto &e : edges) {
int u = e.u, v = e.v; ll w = e.w;
if (d[0][u] + w + d[1][v] == ST) adj2[u].push_back(v);
if (d[0][v] + w + d[1][u] == ST) adj2[v].push_back(u);
}
ans = d[2][y];
dfs2(s);
cout << ans;
return 0;
}
