#include <bits/stdc++.h>
using namespace std;
const int MAXN = 100000;
const long long LL_INF = 1000000000ll * 1000000000;
struct Edge {
int v,w;
bool in;
Edge() {};
Edge(int _v,int _w,int _in) : v(_v), w(_w), in(_in) {};
};
long long dis[4][MAXN+2];
vector<Edge> adj[MAXN+2];
int n,m;
int s,t,l,r;
void dijkstra(int st,int id) {
for (int i=1;i<=n;i++) dis[id][i] = LL_INF;
dis[id][st] = 0;
priority_queue<pair<long long,int>> pq;
pq.push(make_pair(0,st));
while (pq.size()) {
int u = pq.top().second;
long long cur_w = -pq.top().first;
pq.pop();
if (cur_w > dis[id][u]) continue;
for (int i=0;i<adj[u].size();i++) {
int v = adj[u][i].v;
int w = adj[u][i].w;
if (dis[id][v] > cur_w + w) {
dis[id][v] = cur_w + w;
pq.push(make_pair(-dis[id][v],v));
}
}
}
}
bool vst[MAXN+2];
int topo_pos[MAXN+2];
int topo[MAXN+2];
int sz = 0;
void dfs(int u) {
vst[u] = 1;
for (int i=0;i<adj[u].size();i++) {
if (adj[u][i].in == 0) continue;
int v = adj[u][i].v;
if (vst[v]) continue;
dfs(v);
}
topo[++sz] = u;
}
long long dp[2][MAXN+2];
int main() {
cin.tie(0) -> sync_with_stdio(0);
cin >> n >> m;
cin >> s >> t >> l >> r;
for (int i=1;i<=m;i++) {
int x,y,w; cin >> x >> y >> w;
adj[x].push_back(Edge(y,w,0));
adj[y].push_back(Edge(x,w,0));
}
dijkstra(s,0);
dijkstra(t,1);
dijkstra(l,2);
dijkstra(r,3);
long long short_s_t = dis[0][t];
long long ans = dis[2][r];
for (int u=1;u<=n;u++) {
for (int i=0;i<adj[u].size();i++) {
int v = adj[u][i].v;
int w = adj[u][i].w;
if (dis[0][u] + dis[1][v] + w == short_s_t) {
adj[u][i].in = 1;
}
}
}
dfs(s);
reverse(topo+1,topo+sz+1);
for (int i=1;i<=sz;i++) {
topo_pos[topo[i]] = i;
dp[0][i] = dp[1][i] = LL_INF;
}
// cout << short_s_t << ' ' << ans << '\n';
for (int i=1;i<=sz;i++) {
int u = topo[i];
// cerr << u << ' ' << i << '\n';
dp[0][i] = min(dp[0][i], dis[2][u]);
dp[1][i] = min(dp[1][i], dis[3][u]);
ans = min(ans, dp[0][i] + dis[3][u]);
ans = min(ans, dp[1][i] + dis[2][u]);
for (int j=0;j<adj[u].size();j++) {
if (!adj[u][j].in) continue;
int v = adj[u][j].v;
int id = topo_pos[v];
dp[0][id] = min(dp[0][id], dp[0][i]);
dp[1][id] = min(dp[1][id], dp[1][i]);
}
}
cout << ans;
return 0;
}
