#include<bits/stdc++.h>
#define endl '\n'
#define fi first
#define se second
using namespace std;
typedef long long ll;
const int N=1e5+5;
const ll INF=1e15;
int n,m,s,t,x,y;
vector<pair<int,int>> graph[N],g[4*N];
ll d[2][N],d1[4*N];
void dijkstra(int s,int k)
{
for(int i=1;i<=n;i++) d[k][i]=INF;
d[k][s]=0;
priority_queue<pair<ll,pair<int,int>>,vector<pair<ll,pair<int,int>>>,greater<pair<ll,pair<int,int>>>> pq;
pq.push({d[k][s],{k,s}});
while((int)pq.size())
{
ll temp=pq.top().fi;
int k=pq.top().se.fi,u=pq.top().se.se;
pq.pop();
if(temp!=d[k][u]) continue;
for(int i=0;i<(int)graph[u].size();i++)
{
int v=graph[u][i].fi,w=graph[u][i].se;
if(d[k][v]>d[k][u]+w)
{
d[k][v]=d[k][u]+w;
pq.push({d[k][v],{k,v}});
}
}
}
}
void solve()
{
cin >> n >> m >> s >> t >> x >> y;
for(int i=1;i<=m;i++)
{
int u,v,w;
cin >> u >> v >> w;
graph[u].push_back({v,w});
graph[v].push_back({u,w});
}
dijkstra(s,0);dijkstra(t,1);
for(int u=1;u<=n;u++)
{
g[u].push_back({n+u,0});
g[u].push_back({2*n+u,0});
g[n+u].push_back({3*n+u,0});
g[2*n+u].push_back({3*n+u,0});
for(int i=0;i<(int)graph[u].size();i++)
{
int v=graph[u][i].fi,w=graph[u][i].se;
if(d[0][u]+w+d[1][v]==d[0][t])
{
g[n+u].push_back({n+v,0});
g[2*n+v].push_back({2*n+u,0});
}
g[u].push_back({v,w});g[3*n+u].push_back({3*n+v,w});
}
}
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>> pq;
for(int i=1;i<=4*n;i++) d1[i]=INF;
d1[x]=0;
pq.push({d1[x],x});
while((int)pq.size())
{
ll temp=pq.top().fi;
int u=pq.top().se;
pq.pop();
if(temp!=d1[u]) continue;
for(int i=0;i<(int)g[u].size();i++)
{
int v=g[u][i].fi,w=g[u][i].se;
if(d1[v]>d1[u]+w)
{
d1[v]=d1[u]+w;
pq.push({d1[v],v});
}
}
}
cout << d1[3*n+y] << endl;
}
int main()
{
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
//freopen("hanhhhh.inp","r",stdin);
//freopen("hanhhhh.out","w",stdout);
int t=1;
//cin >> t;
while(t--)
solve();
return 0;
}
