/*
this question is BFS final bos :sob:
*/
#include <iostream>
#include <vector>
#include <queue>
using namespace std;
bool debug=0;
#define dout if(debug)cout
#define ll long long
#define pb push_back
#define mp make_pair
ll min_dist=1e18;
vector<ll> distS, distT, distU, distV;
vector<ll> mdistU, mdistV;
vector<vector<ll>> below;
ll minDU(int n){
// what is the shortest distance between U and some node on some free path from S to `n`?
// a.k.a.
// with the option of using the free path, what is the smallest cost to get from U to `n`?
if(mdistU[n] != -1){
return mdistU[n];
}
ll answer=distU[n];
for(int e:below[n]){
answer = min(answer, minDU(e));
}
return mdistU[n]=answer;
}
ll minDV(int n){
// what is the shortest distance between V and some node on some free path from S to `n`?
if(mdistV[n] != -1){
return mdistV[n];
}
ll answer=distV[n];
for(int e:below[n]){
answer = min(answer, minDV(e));
}
return mdistV[n]=answer;
}
int main(){
// input
ll n,m, s,t, u,v;
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
s--;t--;u--;v--;
ll a,b,c;
vector<vector<pair<ll, ll>>> adj(n);
for(int i=0; i<m; i++){
cin>>a>>b>>c;
a--;b--;
adj[a].pb(mp(b,c));
adj[b].pb(mp(a,c));
}
mdistU = vector<ll>(n, -1);
mdistV = vector<ll>(n, -1);
// bfs to initialise distances from S/T/U/V to each node
priority_queue<pair<ll, ll>> q;
ll cur_dist, node;
distS = vector<ll>(n, -1);
q.push(mp(0, s));
while(!q.empty()){
cur_dist = q.top().first*-1;
node = q.top().second;
q.pop();
if(distS[node] != -1)continue;
distS[node] = cur_dist; // guaranteed minimum.
for(int i=0; i<adj[node].size(); i++){
if(distS[adj[node][i].first]==-1){
q.push(mp(-1 * (cur_dist+adj[node][i].second), adj[node][i].first));
}
}
}
distT = vector<ll>(n, -1);
q.push(mp(0, t));
while(!q.empty()){
cur_dist = q.top().first*-1;
node = q.top().second;
q.pop();
if(distT[node] != -1)continue;
distT[node] = cur_dist;
for(int i=0; i<adj[node].size(); i++){
if(distT[adj[node][i].first]==-1){
q.push(mp(-1 * (cur_dist+adj[node][i].second), adj[node][i].first));
}
}
}
distU = vector<ll>(n, -1);
q.push(mp(0, u));
while(!q.empty()){
cur_dist = q.top().first*-1;
node = q.top().second;
q.pop();
if(distU[node] != -1)continue;
distU[node] = cur_dist;
for(int i=0; i<adj[node].size(); i++){
if(distU[adj[node][i].first]==-1){
q.push(mp(-1 * (cur_dist+adj[node][i].second), adj[node][i].first));
}
}
}
distV = vector<ll>(n, -1);
q.push(mp(0, v));
while(!q.empty()){
cur_dist = q.top().first*-1;
node = q.top().second;
q.pop();
if(distV[node] != -1)continue;
distV[node] = cur_dist;
for(int i=0; i<adj[node].size(); i++){
if(distV[adj[node][i].first]==-1){
q.push(mp(-1 * (cur_dist+adj[node][i].second), adj[node][i].first));
}
}
}
// find the shortest distance by finding the minimum value of distS[i]+distT[i]
for(int i=0; i<n; i++){
min_dist = min(min_dist, distS[i]+distT[i]);
}
if(debug)
{
cout<<"shortest dist: "<<min_dist<<"\n";
cout<<"debug distS: ";
for(int i=0; i<n; i++){
cout<<distS[i]<<" ";
}cout<<"\n";
}
int e,cost;
// compute `below` (directed graph of shortest paths from T to S)
vector<int> onpath;
below = vector<vector<ll>>(n);
for(int i=0; i<n; i++){
if(distS[i]+distT[i] == min_dist){ // node `i` lies on a path
onpath.pb(i);
for(int j=0; j<adj[i].size(); j++){
e = adj[i][j].first;
cost = adj[i][j].second;
if(distS[e]+distT[e] == min_dist && distS[i]-cost == distS[e]){
below[i].pb(e);
}
}
}
}
// find minimum distance from U to V without considering the bridge between S and T
ll minUV = 1e18;
for(int i=0; i<n; i++){
minUV = min(minUV, distU[i]+distV[i]);
}
ll answer = minUV;
ll node1;
for(int i=0; i<onpath.size(); i++){
node1 = onpath[i];
answer = min(answer, minDU(node1)+distV[node1]);
answer = min(answer, minDV(node1)+distU[node1]);
minDU(node1);
}
cout<<answer<<"\n";
return 0;
}
