#include<bits/stdc++.h>
using namespace std;
#define ii pair < int , int >
#define iii pair < int , ii >
#define int long long
const int N = 1e5 + 5;
int n , m , s , t , u , v;
vector < ii > g[N];
priority_queue < iii , vector < iii > , greater < iii > > q;
int dists[N] , distt[N] , dist[N][5];
void dijkstra(int start , int dist[N])
{
priority_queue < ii , vector < ii > , greater < ii > > q;
while(!q.empty())
q.pop();
for(int i = 1 ; i <= n ; i++)
dist[i] = 1e18;
dist[start] = 0;
q.push(ii(dist[start] , start));
while(!q.empty())
{
int u = q.top().second;
int cost = q.top().first;
q.pop();
if(cost > dist[u])
continue;
for(auto e: g[u])
{
int v = e.first;
int w = e.second;
if(dist[v] > dist[u] + w)
{
dist[v] = dist[u] + w;
q.push(ii(dist[v] , v));
}
}
}
}
void dijkstra2(int start)
{
for(int i = 1 ; i <= n ; i++)
for(int j = 0 ; j <= 2 ; j++)
dist[i][j] = 1e18;
dist[start][0] = 0;
q.push(iii(dist[start][0] , ii(start , 0)));
while(!q.empty())
{
int u = q.top().second.first;
int k = q.top().second.second;
int cost = q.top().first;
//cout << u << " " << k << " " << cost << endl;
q.pop();
if(cost > dist[u][k])
continue;
if(u == v)
{
cout << dist[v][k];
exit(0);
}
if(k == 0)
{
for(auto e: g[u])
{
int v = e.first;
int w = e.second;
if(dist[v][k] > dist[u][k] + w)
{
dist[v][k] = dist[u][k] + w;
q.push(iii(dist[v][k] , ii(v , k)));
}
if(dists[u] + w + distt[v] == dists[t]
|| dists[v] + w + distt[u] == dists[t])
{
if(dist[v][k + 1] > dist[u][k])
{
dist[v][k + 1] = dist[u][k];
q.push(iii(dist[v][k + 1] , ii(v , k + 1)));
}
}
}
}
else if(k == 1)
{
for(auto e: g[u])
{
int v = e.first;
int w = e.second;
if(dist[v][k + 1] > dist[u][k] + w)
{
dist[v][k + 1] = dist[u][k] + w;
q.push(iii(dist[v][k + 1] , ii(v , k + 1)));
}
if(dists[u] + w + distt[v] == dists[t]
|| dists[v] + w + distt[u] == dists[t])
{
if(dist[v][k] > dist[u][k])
{
dist[v][k] = dist[u][k];
q.push(iii(dist[v][k] , ii(v , k)));
}
}
}
}
else
{
for(auto e: g[u])
{
int v = e.first;
int w = e.second;
if(dist[v][k] > dist[u][k] + w)
{
dist[v][k] = dist[u][k] + w;
q.push(iii(dist[v][k] , ii(v , k)));
}
}
}
}
}
main()
{
ios::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
for(int i = 1 ; i <= m ; i++)
{
int u , v , w;
cin >> u >> v >> w;
g[u].push_back(ii(v , w));
g[v].push_back(ii(u , w));
}
dijkstra(s , dists);
dijkstra(t , distt);
dijkstra2(u);
}
