#include<bits/stdc++.h>
const int MaxN = 1e5 + 10;
const long long Inf = 1e18;
struct Data{
long long vertex,w;
bool operator > (const Data &other) const{
return (w > other.w);
}
};
std::vector<std::pair<int,int>> adj[MaxN + 1];
int n,m;
long long f[4][MaxN + 1],s,t,s1,t1,ans = Inf;
std::pair<long long,long long> minPath[MaxN + 1],minPath1[MaxN + 1];
bool vis[MaxN + 1];
void readData(){
std::cin >> n >> m >> s >> t >> s1 >> t1;
for(int i = 1;i <= m;++i){
int u,v,w;
std::cin >> u >> v >> w;
adj[u].emplace_back(v,w);
adj[v].emplace_back(u,w);
}
}
void disjktra(int source,long long dist[]){
std::fill(dist + 1,dist + n + 1,Inf);
std::priority_queue<Data,std::vector<Data>,std::greater<Data>> pq;
pq.push({source,0});
dist[source] = 0;
while(!pq.empty()){
Data t = pq.top();
pq.pop();
if(t.w > dist[t.vertex]){
continue;
}
for(std::pair<int,int> v : adj[t.vertex]){
if(t.w + v.second < dist[v.first]){
dist[v.first] = t.w + v.second;
pq.push({v.first,dist[v.first]});
}
}
}
}
void disjktra1(){
std::fill(f[3] + 1,f[3] + n + 1,Inf);
for(int i = 1;i <= n;++i){
minPath[i] = {f[1][i],f[2][i]};
minPath1[i] = {f[2][i],f[1][i]};
}
std::priority_queue<Data,std::vector<Data>,std::greater<Data>> pq;
pq.push({s,0});
f[3][s] = 0;
while(!pq.empty()){
Data t = pq.top();
pq.pop();
if(t.w > f[3][t.vertex]){
continue;
}
for(std::pair<int,int> v : adj[t.vertex]){
if(t.w + v.second < f[3][v.first]){
f[3][v.first] = t.w + v.second;
pq.push({v.first,f[3][v.first]});
std::pair<long long,long long> first = {std::min(f[1][v.first],minPath[t.vertex].first),std::min(f[2][v.first],minPath[t.vertex].second)};
std::pair<long long,long long> second = {std::min(f[2][v.first],minPath1[t.vertex].first),std::min(f[1][v.first],minPath1[t.vertex].second)};
minPath[v.first] = first;
minPath1[v.first] = second;
// assert(std::min(first.first,first.second) > 0);
// assert(std::min(second.first,second.second) > 0);
}
if(t.w + v.second == f[3][v.first]){
std::pair<long long,long long> first = {std::min(f[1][v.first],minPath[t.vertex].first),std::min(f[2][v.first],minPath[t.vertex].second)};
std::pair<long long,long long> second = {std::min(f[2][v.first],minPath1[t.vertex].first),std::min(f[1][v.first],minPath1[t.vertex].second)};
minPath[v.first] = std::min(minPath[v.first],first);
minPath1[v.first] = std::min(minPath1[v.first],second);
}
}
}
}
void dfs(int u = t){
vis[u] = true;
ans = std::min(ans,minPath[u].first + minPath[u].second);
ans = std::min(ans,minPath1[u].first + minPath1[u].second);
for(std::pair<int,int> v : adj[u]){
if(f[3][v.first] + v.second == f[3][u] && !vis[v.first]){
dfs(v.first);
}
}
}
int main(){
std::ios_base::sync_with_stdio(false);
std::cin.tie(nullptr);std::cout.tie(nullptr);
readData();
disjktra(s1,f[1]);
disjktra(t1,f[2]);
disjktra1();
dfs();
ans = std::min(ans,f[2][s1]);
std::cout << ans;
return 0;
}
