#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){
vi dpu(size,MOD);
vi dpv(size,MOD);
visited.assign(size,false);
priority_queue<pair<int,pii>> pq;
int ans = du[end2];
pq.push({0,{u,0}});
while(!pq.empty()){
pair<int,pii> x = pq.top();
pq.pop();
int node = x.s.f;
int parent = x.s.s;
int c = -x.f;
if(!visited[node]){
visited[node] = true;
dpu[node] = min(du[node],dpu[parent]);
dpv[node] = min(dv[node],dpv[parent]);
for(pii t : graph[node]){
pq.push({-c-t.s,{t.f,node}});
}
}
else if(c == ds[node]){
if(min(du[node],dpu[parent]) + min(dv[node],dpv[parent]) < dpu[node] + dpv[node]){
dpu[node] = min(du[node],dpu[parent]);
dpv[node] = min(dv[node],dpv[parent]);
}
}
}
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;
}
