#include <bits/stdc++.h>
#define int long long
#define FOR(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define REV(i, a, b) for (int i = (a), _b = (b); i >= _b; --i)
using namespace std;
int n, m;
#define MAXN 200005
int S, T, U, V, ST;
vector<pair<int, int>> g[MAXN], adj[MAXN];
int d[MAXN][4];
int dp[MAXN][2];
bool vi[MAXN];
int res = 1e15;
vector<int> topo;
struct edge {
int u, v, w;
};
vector<edge> edges;
void dijkstra(int s, int id){
memset(vi, false, sizeof vi);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
pq.push(make_pair(0, s));
d[s][id] = 0;
while (pq.size()){
int w, u; tie(w, u) = pq.top();
pq.pop();
if (vi[u]) continue;
vi[u] = 1;
for (pair<int, int> &x : g[u]){
int v, ww; tie(v, ww) = x;
if (d[v][id] > w + ww){
d[v][id] = w + ww;
pq.push(make_pair(d[v][id], v));
}
}
}
}
void dfs(int u){
vi[u] = 1;
for (pair<int, int> &x : g[u]){
int v, w; tie(v, w) = x;
if (vi[v] || d[u][0] + w + d[v][1] != ST) continue;
dfs(v);
}
topo.push_back(u);
}
void solve(){
memset(d, 0x3f, sizeof d);
cin >> n >> m >> S >> T >> U >> V;
FOR(i, 1, m){
int u, v, w; cin >> u >> v >> w;
g[u].push_back(make_pair(v, w));
g[v].push_back(make_pair(u, w));
edges.push_back({u, v, w});
}
dijkstra(S, 0);
dijkstra(T, 1);
dijkstra(U, 2);
dijkstra(V, 3);
ST = d[T][0];
res = d[V][2];
FOR(i, 1, n){
dp[i][0] = d[i][2];
dp[i][1] = d[i][3];
}
memset(vi, false, sizeof vi);
dfs(S);
reverse(topo.begin(), topo.end());
for (int &u : topo){
for (pair<int, int> &x : g[u]){
int v, w; tie(v, w) = x;
if (d[u][0] + w + d[v][1] != ST) continue;
dp[v][0] = min(dp[v][0], dp[u][0]);
dp[v][1] = min(dp[v][1], dp[u][1]);
}
}
FOR(i, 1, n){
if (d[i][0] + d[i][1] != ST) continue;
res = min({res, d[i][2] + dp[i][1], dp[i][0] + d[i][3]});
}
cout << res;
}
/**
6 6
1 6
3 4
1 2 1
2 3 1
3 5 1
2 4 1
4 5 1
5 6 1
6 6
1 6
1 4
1 2 1
2 3 1
3 5 1
2 4 3
4 5 2
5 6 1
**/
#define task "PATH"
int32_t main(){
if (fopen(task".inp","r")){
freopen(task".inp","r",stdin);
freopen(task".out","w",stdout);
}
ios_base::sync_with_stdio(false);
cin.tie(nullptr); cout.tie(nullptr);
solve();
return 0;
}
