#include <bits/stdc++.h>
using namespace std;
int n,m,S,T,U,V,x,y;
long long res;
long long w;
vector<pair<int,long long>> adj[100001];
long long inf = 1e18;
vector<int> g[100001];
bool c[100001];
long long dist[4][100001];
long long opt[2][100001];
void dik(int t,int sta){
for(int i = 1;i <= n;i++) dist[t][i] = inf;
dist[t][sta] = 0;
queue<int> q;
q.push(sta);
while(!q.empty()){
int u = q.front();
q.pop();
for(pair<int,long long> &v : adj[u]){
if(dist[t][v.first] > dist[t][u] + v.second){
dist[t][v.first] = dist[t][u] + v.second;
q.push(v.first);
}
}
}
}
void build(int u){
c[u] = true;
for(pair<int,long long> v : adj[u]){
if(dist[0][u] + v.second + dist[1][v.first] == dist[0][V]){
g[u].push_back(v.first);
if(!c[v.first]) build(v.first);
}
}
}
void dfs(int u){
c[u] = true;
opt[0][u] = dist[2][u];
opt[1][u] = dist[3][u];
for(int v : g[u]){
if(!c[v]) dfs(v);
opt[0][u] = min(opt[0][u],opt[0][v]);
opt[1][u] = min(opt[1][u],opt[1][v]);
}
//cout << S << " to " << u << " " <<dist[2][u] << " " << opt[1][u] << "\n";
//cout << T << " to " << u << " " << dist[3][u] << " " << opt[0][u] << "\n";
res = min(res,dist[2][u] + opt[1][u]);
res = min(res,dist[3][u] + opt[0][u]);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);cout.tie(0);
cin >> n >> m >> U >> V >> S >> T;
for(int i = 1;i <= m;i++){
cin >> x >> y >> w;
adj[x].push_back({y,w});
adj[y].push_back({x,w});
}
dik(0,U);
dik(1,V);
dik(2,S);
dik(3,T);
build(U);
res = dist[2][T];
for(int i = 1;i <= n;i++) c[i] = false;
dfs(U);
cout << res;
return 0;
}
