#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
// #define _GLIBCXX_DEBUG 1
// #define _GLIBCXX_DEBUG_PEDANTIC 1
// #pragma GCC optimize("trapv")
// #define dbg(TXTMSG) cerr << "\n" << TXTMSG
// #define dbgv(VARN) cerr << "\n" << #VARN << " = "<< VARN << ", line: " << __LINE__ << "\n"
#define ld long double
#define int long long
#define forn(i,j) for(int i = 0; i < j; i++)
#define forrange(i,j,k) for(int i = j; i < k; ++i)
#define rof(i,j) rof(int i = j; i >= 0; --i)
#define pii pair<int,int>
#define vi vector<int>
#define vpii vector<pii>
#define vvi vector<vi>
#define vvpii vector<vector<pii>>
#define vb vector<bool>
#define pb push_back
#define p push
#define f first
#define s second
#define all(x) x.begin(), x.end()
#define eb emplace_back
#define qi queue<int>
#define qpii queue<pii>
#define pqpii priority_queue<pii>
#define pqi priority_queue<int>
#define MOD 1000000007
void setIO(string name = ""){
ios_base::sync_with_stdio(0);
cin.tie(0);
if(!name.empty()){
freopen((name + ".in").c_str(), "r", stdin);
freopen((name + ".out").c_str(), "w", stdout);
}
}
vi du;
vi dv;
vi ds;
vector<vector<pii>> graph;
vb visited;
vi djikstra1(int u, int size){
vi dist(size);
visited.assign(size,false);
dist[u] = 0;
pqpii pq;
pq.push({0,u});
while(!pq.empty()){
pii x = pq.top();
pq.pop();
if(!visited[x.s]){
dist[x.s] = -x.f;
visited[x.s] = true;
for(pii y: graph[x.s]){
int node = y.f;
int cost = y.s;
pq.push({x.f - cost, node});
}
}
}
return dist;
}
int djikstra2(int u, int size, int end,int end2){
visited.assign(size,false);
pqpii pq;
vi dpu(size);
vi dpv(size);
int ans = du[end2];
pq.push({0,u});
forn(i,size){
dpu[i] = du[i];
dpv[i] = dv[i];
}
while(!pq.empty()){
pii x = pq.top();
pq.pop();
if(!visited[x.s]){
visited[x.s] = true;
for(pii j : graph[x.s]){
int node = j.f;
int cost = j.s;
if(-x.f + cost == ds[node]){
if(min(du[node],dpu[x.s]) + min(dv[node],dpv[x.s]) <= dpu[node] + dpv[node]){
dpu[node] = min(du[node],dpu[x.s]);
dpv[node] = min(dv[node],dpv[x.s]);
}
pq.push({-ds[node],node});
}
}
}
}
ans = min(ans,dpu[end]+dpv[end]);
return ans;
}
signed main(){
setIO();
int n,m,s,t,u,v;
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
s--;
t--;
u--;
v--;
graph.resize(n);
visited.resize(n);
forn(i,m){
int a,b,c;
cin >> a >> b >> c;
a--,b--;
graph[a].pb({b,c});
graph[b].pb({a,c});
}
ds = djikstra1(s,n);
du = djikstra1(u,n);
dv = djikstra1(v,n);
int res = djikstra2(s,n,t,v);
cout << res << endl;
}
