#include<bits/stdc++.h>
#define pb push_back
#define x first
#define y second
#define all(a) (a).begin(), (a).end()
using namespace std;
typedef long long ll;
typedef pair<int, int> ii;
const int maxn = 2e5 + 5;
const ll inf = 1e18;
int n, m, s, t, u, v;
vector<pair<int, ll>> adj[maxn];
vector<int> G[maxn];
ll D[5][maxn];
ll mini[maxn];
int deg[maxn];
void get_dist(int X, int p) {
vector<ll> dist(n, inf);
dist[X] = 0;
set<pair<ll, int>> q;
q.insert({0, X});
while(q.size()) {
auto state = *q.begin();
q.erase(state);
int x = state.y;
for(auto P : adj[x]) {
int y = P.x;
ll c = P.y;
if(dist[y] == inf) {
dist[y] = dist[x] + c;
q.insert({dist[y], y});
} else if(dist[x] + c < dist[y]) {
q.erase({dist[y], y});
dist[y] = dist[x] + c;
q.insert({dist[y], y});
}
}
}
for(int i = 0;i < n;i++)
D[p][i] = dist[i];
}
vector<int> get_topo() {
for(int i = 0;i < n;i++)
for(auto p : adj[i])
if(D[0][t] == D[0][i] + p.y + D[1][p.x])
G[i].pb(p.x), deg[p.x]++;
queue<int> q;
for(int i = 0;i < n;i++)
if(deg[i] == 0) q.push(i);
vector<int> V;
while(q.size()) {
int x = q.front();
q.pop(), V.pb(x);
for(int y : G[x]) {
deg[y]--;
if(deg[y] == 0)
q.push(y);
}
}
reverse(all(V));
return V;
}
int main() {
scanf("%d%d%d%d%d%d", &n, &m, &s, &t, &u, &v);
s--, t--, u--, v--;
for(int i = 0;i < m;i++) {
int x, y, c;
scanf("%d%d%d", &x, &y, &c);
x--, y--;
adj[x].pb({y, c}), adj[y].pb({x, c});
}
get_dist(s, 0);
get_dist(t, 1);
get_dist(u, 2);
get_dist(v, 3);
vector<int> topo = get_topo();
ll ans = inf;
for(int x : topo) {
mini[x] = D[3][x];
for(int y : G[x])
mini[x] = min(mini[x], mini[y]);
ans = min(ans, D[2][x] + mini[x]);
}
for(int x : topo) {
mini[x] = D[2][x];
for(int y : G[x])
mini[x] = min(mini[x], mini[y]);
ans = min(ans, D[3][x] + mini[x]);
}
printf("%lld\n", ans);
return 0;
}
