#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
#define INF (1000000000ll * 200000ll)
typedef long long ll;
struct adj_t {
int nx;
ll w;
};
int n, m;
vector<adj_t> adj[100001], adj_inv[100001];
vector<ll> dijkstra(int start, vector<adj_t> *adj_mat) {
vector<ll> dist(n + 1, INF);
priority_queue<pair<ll, int>> heap;
heap.push({-0ll, start});
dist[start] = 0ll;
while (!heap.empty()) {
int nw = heap.top().second;
ll d = -heap.top().first;
heap.pop();
if (d > dist[nw])
continue;
for (int i = 0; i < adj_mat[nw].size(); i++) {
auto nex = adj_mat[nw][i];
ll new_cost = d + nex.w;
if (new_cost < dist[nex.nx]) {
heap.push({-new_cost, nex.nx});
dist[nex.nx] = new_cost;
}
}
}
return dist;
}
vector<pair<int, int>> shortest_path(int start, int end, vector<adj_t> *adj_mat) {
vector<ll> dist(n + 1, INF);
vector<int> memo[100001];
vector<pair<int, int>> edge;
priority_queue<pair<ll, int>> heap;
heap.push({-0, start});
dist[start] = 0;
while (!heap.empty()) {
int nw = heap.top().second;
ll d = -heap.top().first;
heap.pop();
if (d > dist[nw])
continue;
for (int i = 0; i < adj_mat[nw].size(); i++) {
auto nex = adj_mat[nw][i];
ll new_cost = d + nex.w;
if (new_cost < dist[nex.nx]) {
heap.push({-new_cost, nex.nx});
dist[nex.nx] = new_cost;
memo[nex.nx].clear();
memo[nex.nx].push_back(nw);
}
else if (new_cost == dist[nex.nx])
memo[nex.nx].push_back(nw);
}
}
bool visit[100001] = {false};
queue<int> bfsQ;
bfsQ.push(end);
visit[end] = true;
while (!bfsQ.empty()) {
int nw = bfsQ.front();
bfsQ.pop();
for (int i = 0; i < memo[nw].size(); i++) {
int nex = memo[nw][i];
if (!visit[nex]) {
bfsQ.push(nex);
visit[nex] = true;
}
edge.push_back({nex, nw});
}
}
return edge;
}
int main(void) {
int s, t, u, v;
scanf("%d %d %d %d %d %d", &n, &m, &s, &t, &u, &v);
for (int i = 0; i < m; i++) {
int a, b, c;
scanf("%d %d %d", &a, &b, &c);
adj[a].push_back({b, (ll)c});
adj[b].push_back({a, (ll)c});
adj_inv[a].push_back({b, (ll)c});
adj_inv[b].push_back({a, (ll)c});
}
auto edge = shortest_path(s, t, adj);
for (int i = 0; i < edge.size(); i++) {
adj[edge[i].first].push_back({edge[i].second, 0ll});
adj_inv[edge[i].second].push_back({edge[i].first, 0ll});
}
auto udis1 = dijkstra(u, adj), vdis1 = dijkstra(v, adj_inv);
auto udis2 = dijkstra(u, adj_inv), vdis2 = dijkstra(v, adj);
ll ans = INF;
for (int i = 1; i <= n; i++)
ans = min(ans, min(udis1[i] + vdis1[i], udis2[i] + vdis2[i]));
printf("%lld\n", ans);
return 0;
}
