#include <bits/stdc++.h>
#define fi first
#define se second
using namespace std;
const int N = 1e5;
int n, m, S, T, U, V;
long long d[2][N + 2], f[N + 2][3];
vector<pair<int, int> > adj[N + 2];
void input() {
cin >> n >> m;
cin >> S >> T;
cin >> U >> V;
int u, v, w;
for(int i = 1; i <= m; i++) {
cin >> u >> v >> w;
adj[u].push_back(make_pair(v, w));
adj[v].push_back(make_pair(u, w));
}
}
bool minimize(long long &x, long long y) {
if(x > y) {
x = y;
return true;
}
return false;
}
void dijkstra(int x, int type) {
priority_queue<pair<long long, int> > pq;
memset(d[type], 0x3f, sizeof d[type]);
d[type][x] = 0;
pq.push(make_pair(0, x));
while(pq.size()) {
long long l = -pq.top().fi;
int u = pq.top().se;
pq.pop();
if(d[type][u] != l) continue;
for(pair<int, int> e : adj[u]) {
int v = e.fi;
int w = e.se;
if(minimize(d[type][v], d[type][u] + w))
pq.push(make_pair(-d[type][v], v));
}
}
}
void calc(int x) {
priority_queue<pair<pair<long long, int>, int > > pq;
memset(f, 0x3f, sizeof f);
f[x][0] = 0;
pq.push(make_pair(make_pair(0, 0), x));
while(pq.size()) {
long long l = -pq.top().fi.fi;
int type = pq.top().fi.se;
int u = pq.top().se;
pq.pop();
if(f[u][type] != l) continue;
for(pair<int, int> e : adj[u]) {
int v = e.fi;
int w = e.se;
if(d[0][u] + w + d[1][v] == d[0][T] && type != 2) {
if(minimize(f[v][1], f[u][type]))
pq.push(make_pair(make_pair(-f[v][1], 1), v));
}
if(type != 1) {
if(minimize(f[v][type], f[u][type] + w))
pq.push(make_pair(make_pair(-f[v][type], type), v));
} else if(minimize(f[v][2], f[u][type] + w))
pq.push(make_pair(make_pair(-f[v][2], 2), v));
}
}
}
void solve() {
dijkstra(S, 0);
dijkstra(T, 1);
calc(U);
long long res = min({f[V][0], f[V][1], f[V][2]});
calc(V);
cout << min({res, f[U][0], f[U][1], f[U][2]});
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
//freopen(".inp", "r", stdin);
//freopen(".out", "w", stdout);
input();
solve();
return 0;
}
