#include <bits/stdc++.h>
#define fi first
#define se second
#define mp make_pair
using namespace std;
const int N = 1e5 + 5;
const long long oo = 1e18;
vector <pair <int, int>> adj[N];
long long f[N];
long long g[N];
long long dis[2][N];
long long dp[2][N];
long long invdp[2][N];
vector <int> order;
int n,m,s,t,u,v;
template <typename T>
bool mini(T &a, T b)
{
if (a > b) {
a = b;
return true;
}
return false;
}
void dijkstra(int s, long long dis[])
{
for (int i = 1; i <= n; i++)
dis[i] = oo;
dis[s] = 0;
priority_queue <pair <long long, int>> heap;
heap.push(mp(0, s));
while (heap.size()) {
int u = heap.top().se;
long long cur = -heap.top().fi;
heap.pop();
if (dis[u] != cur)
continue;
for (pair <int, int> e : adj[u])
if (mini(dis[e.fi], cur + e.se))
heap.push(mp(-dis[e.fi], e.fi));
}
}
void dfs(int u)
{
for (pair <int, int> e : adj[u]) {
int v = e.fi;
int w = e.se;
if (f[u] + g[v] + w == f[t])
dfs(v);
}
order.push_back(u);
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
//freopen("file.inp","r",stdin);
cin >> n >> m;
cin >> s >> t >> u >> v;
for (int i = 1; i <= m; i++) {
int u,v,w;
cin >> u >> v >> w;
adj[u].push_back(mp(v, w));
adj[v].push_back(mp(u, w));
}
dijkstra(s, f);
dijkstra(t, g);
dijkstra(u, dis[0]);
dijkstra(v, dis[1]);
dfs(s);
reverse(order.begin(), order.end());
for (int j = 0; j <= 1; j++)
for (int i = 1; i <= n; i++)
dp[j][i] = oo;
for (int i : order) {
for (int j = 0; j <= 1; j++) {
dp[j][i] = dis[j][i];
for (pair <int, int> e : adj[i]) {
int pre = e.fi;
int w = e.se;
if (f[pre] + g[i] + w == f[t])
dp[j][i] = min(dp[j][i], dp[j][pre]);
}
}
}
reverse(order.begin(), order.end());
for (int i : order) {
for (int j = 0; j <= 1; j++) {
invdp[j][i] = dis[j][i];
for (pair <int, int> e : adj[i]) {
int pre = e.fi;
int w = e.se;
if (f[i] + g[pre] + w == f[t])
invdp[j][i] = min(invdp[j][i], invdp[j][pre]);
}
}
}
long long ans = dis[0][v];
for (int i = 1; i <= n; i++)
for (int j = 0; j <= 1; j++)
ans = min(ans, dp[j][i] + invdp[j ^ 1][i]);
cout << ans;
return 0;
}
