#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
#define ll long long
ll mod = 1e9+7;
//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
ll binpow(ll a, ll b)
{
ll res = 1;
while (b>0)
{
if (b&1)
res = (res*a)%mod;
a = (a*a)%mod;
b>>=1;
}
return res;
}
ll gcd(ll x, ll y)
{
if (y==0)
return x;
return gcd(y, x%y);
}
ll maxi = 202020;
vector<vector<pair<ll,ll>>>g(maxi);
vector<vector<ll>>adj(maxi);
vector<ll>dp1(maxi, LLONG_MAX), dp2(maxi, LLONG_MAX);
vector<ll>dist;
ll n,m,s,t,u,v;
vector<ll>du(maxi, LLONG_MAX), dv(maxi, LLONG_MAX);
vector<ll> dijkstra1(ll x)
{
for (int i=1 ; i<=n ; i++)
dist[i] = dp1[i] = LLONG_MAX;
dist[x] = 0;
priority_queue<pair<ll,ll>, vector<pair<ll,ll>>, greater<pair<ll,ll>>>pq;
pq.push({0, x});
dp1[x] = du[x];
while (!pq.empty())
{
auto it = pq.top();
pq.pop();
ll d = it.first;
ll v = it.second;
if (d!=dist[v]) continue;
for (auto to:g[v])
{
ll i = to.first;
ll w = to.second;
if (dist[i]>dist[v]+w)
{
dist[i] = dist[v]+w;
pq.push({dist[i], i});
dp1[i] = min(du[i], dp1[v]);
}
if (dist[i]==dist[v]+w)
dp1[i] = min({dp1[i], du[i], dp1[v]});
}
}
return dist;
}
vector<ll> dijkstra2(ll x)
{
for (int i=1 ; i<=n ; i++)
dist[i] = dp2[i] = LLONG_MAX;
dist[x] = 0;
priority_queue<pair<ll,ll>, vector<pair<ll,ll>>, greater<pair<ll,ll>>>pq;
pq.push({0, x});
dp2[x] = dv[x];
while (!pq.empty())
{
auto it = pq.top();
pq.pop();
ll d = it.first;
ll v = it.second;
if (d!=dist[v]) continue;
for (auto to:g[v])
{
ll i = to.first;
ll w = to.second;
if (dist[i]>dist[v]+w)
{
dist[i] = dist[v]+w;
pq.push({dist[i], i});
dp2[i] = min(dv[i], dp2[v]);
}
if (dist[i]==dist[v]+w)
dp2[i] = min({dp2[i], dv[i], dp2[v]});
}
}
return dist;
}
vector<ll>dijkstra(ll x)
{
for (int i=1 ; i<=n ; i++)
dist[i] = LLONG_MAX;
dist[x] = 0;
priority_queue<pair<ll,ll>, vector<pair<ll,ll>>, greater<pair<ll,ll>>>pq;
pq.push({0, x});
while (!pq.empty())
{
auto it = pq.top();
pq.pop();
ll d = it.first;
ll v = it.second;
if (d!=dist[v]) continue;
for (auto to:g[v])
{
ll i = to.first;
ll w = to.second;
if (dist[i]>dist[v]+w)
{
dist[i] = dist[v]+w;
pq.push({dist[i], i});
}
}
}
return dist;
}
ll func(ll s, ll t)
{
du = dijkstra(u);
dv = dijkstra(v);
// for (int i=1 ;i<=n ;i++)
// cout<<du[i]<<" ";
// cout<<endl;
// for (int i=1 ; i<=n ;i++)
// cout<<dv[i]<<" ";
// cout<<endl;
vector<ll>ds = dijkstra1(s);
vector<ll>dt = dijkstra2(t);
ll sp = ds[t];
ll res = du[v];
for (int i=1 ; i<=n ;i++)
{
if (ds[i]+dt[i]==sp)
res = min(res, dp1[i]+dp2[i]);
}
return res;
}
void solve()
{
cin>>n>>m>>s>>t>>u>>v;
for (int i=1 ; i<=m ; i++)
{
ll x,y,z;
cin>>x>>y>>z;
g[x].push_back({y, z});
g[y].push_back({x, z});
}
dist.assign(n+1, LLONG_MAX);
cout<<min(func(s, t), func(t, s))<<endl;
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
ll tt = 1;
// cin>>tt;
while (tt--)
{
solve();
}
return 0;
}
