#include <iostream>
#include <vector>
#include <queue>
#include <tuple>
#include <climits>
using namespace std;
int n, m, s, t, u, v;
vector<vector<pair<int, int>>> adj;
vector<long long>distU, distV, dpU, dpV;
long long ans = 1e15;
long long const INF = 1e15;
void dijkstras_ST(int start, int end){
fill(dpU.begin(), dpU.end(), INF);
fill(dpV.begin(), dpV.end(), INF);
vector<bool> visited(n+1);
priority_queue<tuple<long long, int, int>> q; //dist, node, parent
vector<long long>dist(n+1,LONG_LONG_MAX);
q.push({0,start, 0});
dist[s] = 0;
while(!q.empty()){
long long dist_node;
int node, parent;
tie(dist_node, node, parent) = q.top();
dist_node *= -1;
q.pop();
if(!visited[node]){
visited[node] = true;
dpU[node] = min(distU[node], distU[parent]);
dpV[node] = min(distU[node], distV[parent]);
for(auto edge : adj[node]){
int next = edge.first;
int weight = edge.second;
if(dist[node] + weight < dist[next]){
dist[next] = dist[node] + next;
q.push({-dist[next], next, node});
}
}
}else if(min(distU[node], distU[parent]) + min(distU[node], distV[parent]) <= dpU[node] + dpV[node]){
dpU[node] = min(distU[node], distU[parent]);
dpV[node] = min(distU[node], distV[parent]);
}
}
ans = min(ans, dpU[v] + dpV[v]);
}
void dijkstras_UV(int start, vector<long long> &dist){
vector<bool> visited(n+1);
priority_queue<pair<long long, int>> q;
q.push({0,start});
dist[start] = 0;
while(!q.empty()){
int node = q.top().second;
q.pop();
if(visited[node])
continue;
visited[node] = true;
for(auto edge : adj[node]){
int next = edge.first;
int weight = edge.second;
if(dist[node] + weight < dist[next]){
dist[next] = dist[node] + weight;
q.push({-dist[next],next});
}
}
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
//freopen("in.txt","r",stdin);
cin >> n >> m >> s >> t >> u >> v;
adj = vector<vector<pair<int, int>>>(n+1);
for(int i = 0; i < m; i++){
int a, b, c;
cin >> a >> b >> c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
distU = vector<long long>(n+1, INF);
dijkstras_UV(u, distU);
//base case, travel without pass
ans = distU[v];
distV = vector<long long> (n+1, INF);
dijkstras_UV(v, distV);
dijkstras_ST(s,t);
dijkstras_ST(t,s);
cout << ans << '\n';
return 0;
}
