#include<bits/stdc++.h>
#define ll long long
#define pll pair<long long,long long>
using namespace std;
const ll maxn = 1e5 + 5;
const ll mod = 1e9 + 7;
const ll base = 13;
const ll inf = 1e14;
ll n,m,x,y,z,s,t,u,v;
vector<pll>a[maxn];
ll dist[maxn][5];
ll ans;
ll best[maxn][5];
priority_queue<pll,vector<pll>,greater<pll>>pe;
void dijk(ll st,ll type)
{
for(ll i = 1;i<=n;i++)
{
dist[i][type] = inf;
}
dist[st][type] = 0;
pe.push({0,st});
while(!pe.empty())
{
ll u = pe.top().second;
ll cur = pe.top().first;
pe.pop();
if(dist[u][type] < cur)
{
continue;
}
for(pll v : a[u])
{
if(dist[v.first][type] > dist[u][type] + v.second)
{
dist[v.first][type] = dist[u][type] + v.second;
pe.push({dist[v.first][type],v.first});
}
}
}
}
void dfs(ll u)
{
best[u][2] = dist[u][2];
best[u][3] = dist[u][3];
for(auto [v,w] : a[u])
{
if(dist[v][1] + w == dist[u][1])
{
dfs(v);
best[u][2] = min(best[u][2],best[v][2]);
best[u][3] = min(best[u][3],best[v][3]);
}
}
ans = min(ans,min(best[u][2] + dist[u][3],best[u][3] + dist[u][2]));
}
void solve()
{
cin>>n>>m>>s>>t>>u>>v;
for(ll i = 1;i<=m;++i)
{
cin>>x>>y>>z;
a[x].push_back({y,z});
a[y].push_back({x,z});
}
dijk(s,1);
dijk(u,2);
dijk(v,3);
ans = dist[u][3];
dfs(t);
cout<<ans;
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
//freopen("BUS.INP","r",stdin);
//freopen("BUS.OUT","w",stdout);
ll t = 1;
//cin>>t;
while(t--)
{
solve();
}
return 0;
}
