// In the name of Allah. Ya ali!
#include<bits/stdc++.h>
#define double long double
typedef long long ll;
const ll MAX_N = 1e5+10;
const ll MOD = 1e9+7;
using namespace std;
vector<pair<int,int>> g[MAX_N];
vector<int> g2[MAX_N];
vector<int> p[MAX_N];
ll dis[MAX_N];
ll m1[MAX_N];
ll d1[MAX_N];
ll d2[MAX_N];
ll m2[MAX_N];
int mark[MAX_N];
bool done[MAX_N];
int n,m,s,t,u,v;
ll ans = 1e18;
void dij(int start)
{
for(int i = 1;i<=n;++i)
dis[i] = 1e18;
dis[start] = 0;
set<pair<ll,int>> st;
for(int i = 1;i<=n;++i)
st.insert({dis[i],i});
while(st.size())
{
int v = (*st.begin()).second;
st.erase(st.begin());
for(auto x:g[v])
{
int u = x.first;
ll d = dis[v]+x.second;
if (dis[u]==d)
p[u].push_back(v);
else if (dis[u]>d)
{
p[u].clear();
p[u].push_back(v);
st.erase({dis[u],u});
dis[u] = d;
st.insert({dis[u],u});
}
}
}
}
void dfs(int v)
{
mark[v]++;
for(auto x:g2[v])
{
if (!mark[x])
dfs(x);
}
ans = min(ans,min(m1[v]+d2[v],m2[v]+d1[v]));
}
void addedges(int v)
{
done[v] = true;
for(auto x:p[v])
{
g2[x].push_back(v);
if (!done[x])
addedges(x);
}
}
int main()
{
cin >> n >> m >> s >> t >> u >> v;
for(int i = 1;i<=m;++i)
{
int u,v,w;
cin >> u >> v >> w;
g[u].push_back({v,w});
g[v].push_back({u,w});
}
dij(s);
addedges(t);
dij(u);
for(int i = 1;i<=n;++i)
d1[i] = m1[i] = dis[i];
dij(v);
for(int i = 1;i<=n;++i)
d2[i] = m2[i] = dis[i];
ans = dis[u];
dfs(s);
cout << ans;
return 0;
}
