#include <bits/stdc++.h>
using namespace std;
using P = pair<int,int>;
using ll = long long;
const int N=1e5+5;
const int M=2e5+6;
const ll INF = 1e18;
int n,m;
int s1,s2;
int t1,t2;
vector<P> adj[N];
ll distsc[N],dist1[N],dist2[N];
ll dp[N][2][2];
void djisktra(int a, ll* dist) {
priority_queue<pair<ll,int>> pq;
for(int i=1; i<=n; i++) {
dist[i] = INF;
}
dist[a] = 0;
pq.emplace(0,a);
while(!pq.empty()) {
auto [w,u] = pq.top();
pq.pop();
if(w > dist[u]) {
continue;
}
for(auto [v,d] : adj[u]) {
// cerr << u << "->" << v << " " << d << '\n';
if(dist[v] > w+d) {
dist[v] = w+d;
pq.emplace(dist[v],v);
}
}
}
}
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
cin >> n >> m;
cin >> s1 >> s2;
cin >> t1 >> t2;
int u,v,w;
for(int i=0; i<m; i++) {
cin >> u >> v >> w;
adj[u].emplace_back(v,w);
adj[v].emplace_back(u,w);
}
djisktra(s1,distsc);
djisktra(t1,dist1);
djisktra(t2,dist2);
vector<int> topo;
for(int i=1; i<=n; i++) {
topo.emplace_back(i);
}
sort(topo.begin(),topo.begin()+n, [](int a,int b) {
return distsc[a] < distsc[b];
});
// for(int i=0; i<n; i++) {
// cerr << topo[i] << ' ';
// }
// cerr << '\n';
for(int cur = 1; cur <= n; cur++) {
for(int x=0; x<2; x++) {
for(int y=0; y<2; y++) {
dp[cur][x][y] = INF;
}
}
}
dp[s1][0][0] = 0;
for (int cur : topo) {
for(int x = 0 ; x < 2; x++) {
for(int y = 0; y < 2; y++) {
if(x==0) {
// If haven't connected to house
dp[cur][1][y] = min(dp[cur][1][y],dp[cur][x][y] + dist1[cur]);
}
if(y==0) {
// If haven't connected to Library
dp[cur][x][1] = min(dp[cur][x][1],dp[cur][x][y] + dist2[cur]);
}
}
}
// See which way should take train to work;
for (auto [v,w] : adj[cur]) {
if(distsc[v] != distsc[cur]+w) continue; /*Did not take this path*/
for(int x=0; x<2; x++){
for(int y=0; y<2; y++) {
dp[v][x][y] = min(dp[v][x][y], dp[cur][x][y]);
}
}
}
}
cout << min(dp[s2][1][1],dist1[t2]);
}
