/*
K stands for "Khongbietcode"
grade 11 computer science
Tran Dai Nghia Highschool for the gifted
*/
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#define endl '\n'
#define fastIO ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define ll long long
#define pb push_back
#define ull unsigned long long
#define llll pair<ll,ll>
#define llllm map<ll,ll>
#define gcd(a,b) __gcd(a,b)
#define lcm(a,b) a*b/gcd(a,b)
#define X first
#define Y second
#define INF 1LL<<60
using namespace std;
using namespace __gnu_pbds;
const ll N=1e5+1;
vector<llll> a[N],b[N*4];
ll d[2][N],d1[N*4];
ll n,m,s,t,x,y;
void dijkstra(ll id,ll u)
{
for(int i=1;i<=n;i++)
{
d[id][i]=INF;
}
d[id][u]=0;
priority_queue<llll,vector<llll>,greater<llll>> pq;
pq.push({0,u});
while(!pq.empty())
{
llll top=pq.top();
pq.pop();
if(d[id][top.Y]!=top.X)
continue;
for(auto v:a[top.Y])
{
if(d[id][v.X]>d[id][top.Y]+v.Y)
{
pq.push({d[id][v.X]=d[id][top.Y]+v.Y,v.X});
}
}
}
}
void solve(){
cin >> n >> m >> s >> t >> x >> y;
for(int i=0;i<m;i++)
{
ll u,v,w;
cin >> u >> v >> w;
a[u].pb({v,w});
a[v].pb({u,w});
}
dijkstra(0,s);
dijkstra(1,t);
for(int u=1;u<=n;u++)
{
b[u].pb({n+u,0});
b[u].pb({2*n+u,0});
b[n+u].pb({3*n+u,0});
b[2*n+u].pb({3*n+u,0});
for(auto i:a[u])
{
ll v=i.X,w=i.Y;
b[u].pb({v,w});
b[3*n+u].pb({3*n+v,w});
if(d[0][u]+w+d[1][v]==d[0][t])
{
b[n+u].pb({n+v,0});
b[n*2+v].pb({2*n+u,0});
}
}
}
for(int i=1;i<=n*4;i++)
{
d1[i]=INF;
}
priority_queue<llll,vector<llll> ,greater<llll>> pq;
pq.push({d1[x]=0,x});
while(pq.size())
{
auto top=pq.top();
pq.pop();
if(d1[top.Y]!=top.X) continue;
for(auto i:b[top.Y])
{
if(d1[i.X]>d1[top.Y]+i.Y)
{
pq.push({d1[i.X]=d1[top.Y]+i.Y,i.X});
}
}
}
cout << d1[3*n+y];
}
int main(){
fastIO;
// freopen("tdk.inp","r",stdin);
// freopen("tdk.out","w",stdout);
//freopen("tdk.err","b",stderr);
int t=1;
//cin>>t;
while(t--){
solve();
cout << endl;
}
// cout << "\n" << (double)clock() / CLOCKS_PER_SEC * 1000 << " ms";
return 0;
}
