/*
In the name of Allah
made by: Ahmed_Solyman
*/
#include <bits/stdc++.h>
#include <ext/rope>
using namespace std;
using namespace __gnu_cxx;
#pragma GCC optimize("-Ofast")
#pragma GCC optimize("-O1")
//-------------------------------------------------------------//
typedef long long ll;
typedef unsigned long long ull;
#define fast ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define PI acos(-1)
#define lb lower_bound
#define ub upper_bound
#define endl '\n'
#define all(v) v.begin(),v.end()
#define allr(v) v.rbegin(),v.rend()
#define sum_to(n) (n*(n+1))/2
#define pb push_back
#define pf push_front
#define fil(arr,x) memset(arr,x,sizeof(arr))
#define REP(i,a,b) for (int i=a;i<=b;i++)
#define F first
#define S second
#define MP make_pair
const ll mod=1e9+7;
int dx[8]={0,1,0,-1,1,1,-1,-1};
int dy[8]={1,0,-1,0,1,-1,-1,1};
//-------------------------------------------------------------//
ll lcm(ll a,ll b)
{
return (max(a,b)/__gcd(a,b))*min(a,b);
}
void person_bool(bool x)
{
cout<<(x?"YES":"NO")<<endl;
}
const int N=1e5+5;
int n,m,s,t,u,v;
vector<pair<int,int>>adj[N];
vector<ll>dijkstra(int node){
vector<ll>dist(n+1,4e18);
dist[node]=0;
priority_queue<pair<ll,int>>pq;
pq.push({0,node});
while(pq.size()){
ll w=-pq.top().first;
int node=pq.top().second;
pq.pop();
if(w>dist[node])continue;
for(auto i:adj[node]){
if(w+i.second<dist[i.first]){
dist[i.first]=w+i.second;
pq.push({-dist[i.first],i.first});
}
}
}
return dist;
}
int main()
{
//freopen("input.txt","r",stdin);
//freopen("output.txt","w",stdout);
fast
cin>>n>>m>>s>>t>>u>>v;
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});
}
vector<ll>dist1=dijkstra(s);
vector<ll>dist2=dijkstra(t);
vector<vector<ll>>dist(n+1,vector<ll>(3,4e18));
dist[u][0]=0;
priority_queue<pair<pair<ll,int>,int>>pq;
pq.push({{0,u},0});
while(pq.size()){
ll w=-pq.top().first.first;
int node=pq.top().first.second;
int type=pq.top().second;
pq.pop();
if(w>dist[node][type])continue;
for(auto i:adj[node]){
if(type==0){
if(dist[i.first][0]>w+i.second){
dist[i.first][0]=w+i.second;
pq.push({{-dist[i.first][0],i.first},0});
}
if(dist[i.first][1]>w && dist1[i.first] + dist2[i.first] == dist1[t] && dist1[node] + i.second == dist1[i.first]){
dist[i.first][1]=w;
pq.push({{-dist[i.first][1],i.first},1});
}
}
if(type==1){
if(dist[i.first][2]>w+i.second){
dist[i.first][2]=w+i.second;
pq.push({{-dist[i.first][2],i.first},2});
}
if(dist[i.first][1]>w && dist1[i.first] + dist2[i.first] == dist1[t] && dist1[node] + i.second == dist1[i.first]){
dist[i.first][1]=w;
pq.push({{-dist[i.first][1],i.first},1});
}
}
if(type==2){
if(dist[i.first][2]>w+i.second){
dist[i.first][2]=w+i.second;
pq.push({{-dist[i.first][2],i.first},2});
}
}
}
}
cout<<min({dist[v][0],dist[v][1],dist[v][2]})<<endl;
return 0;
}
