#include<bits/stdc++.h>
#define int long long
#define fi first
#define se second
using namespace std;
vector<int>adj[100005], par[100005];
int dist[100005], distx[100005], ans=1e18;
bool vis[100005];
int n, m, s, t, u, v;map<pair<int, int>, int> mp;
void dfs(int node)
{
ans=min(ans, distx[node]);
// printf("%lld %lld %lld %lld\n", node, dist[v], dist[node], distx[node]);
for(auto x:par[node])
{
if(!vis[x])
{
vis[x]=1;
dfs(x);
}
}
}
signed main()
{
scanf("%lld %lld %lld %lld %lld %lld", &n, &m, &s, &t, &u, &v);
for(int i=1; i<=m; i++)
{
int a, b, c;
scanf("%lld %lld %lld", &a, &b, &c);
if(a>b)swap(a, b);
adj[a].push_back(b);
adj[b].push_back(a);
mp[{a, b}]=c;
}
if(s==u)
{
priority_queue<pair<int, int> > pq;
pq.push({0, s});
for(int i=1; i<=n; i++)
{
dist[i]=1e18;
distx[i]=1e18;
}
dist[s]=0;
while(!pq.empty())
{
int step=-pq.top().fi;
int node=pq.top().se;
// int p=pq.top().se.se;
// par[node].push_back(p);
pq.pop();
if(vis[node])
{
continue;
}
vis[node]=1;
for(auto x:adj[node])
{
if(dist[x]==step+mp[{min(node, x), max(node, x)}])
{
par[x].push_back(node);
}
else if(dist[x]>step+mp[{min(node, x), max(node, x)}])
{
par[x].clear();
par[x].push_back(node);
dist[x]=step+mp[{min(node, x), max(node, x)}];
pq.push({-(step+mp[{min(node, x), max(node, x)}]), x});
}
}
}
for(int i=1; i<=n; i++)vis[i]=0;
distx[v]=0;
pq.push({0, v});
while(!pq.empty())
{
int step=-pq.top().fi;
int node=pq.top().se;
// int p=pq.top().se.se;
// par[node].push_back(p);
pq.pop();
if(vis[node])
{
continue;
}
vis[node]=1;
for(auto x:adj[node])
{
if(distx[x]>step+mp[{min(node, x), max(node, x)}])
{
distx[x]=step+mp[{min(node, x), max(node, x)}];
pq.push({-(step+mp[{min(node, x), max(node, x)}]), x});
}
}
}
for(int i=1; i<=n; i++)vis[i]=0;
ans=distx[u];
vis[t]=1;
dfs(t);
printf("%lld\n", ans);
}
else
{
priority_queue<pair<int, int> > pq;
pq.push({0, s});
for(int i=1; i<=n; i++)dist[i]=1e18;
dist[s]=0;
while(!pq.empty())
{
int step=-pq.top().fi;
int node=pq.top().se;
// int p=pq.top().se.se;
// par[node].push_back(p);
pq.pop();
if(vis[node])
{
continue;
}
vis[node]=1;
for(auto x:adj[node])
{
if(dist[x]==step+mp[{min(node, x), max(node, x)}])
{
par[x].push_back(node);
}
else if(dist[x]>step+mp[{min(node, x), max(node, x)}])
{
par[x].clear();
par[x].push_back(node);
dist[x]=step+mp[{min(node, x), max(node, x)}];
pq.push({-(step+mp[{min(node, x), max(node, x)}]), x});
}
}
}
int now=t;
while(now!=s)
{
// printf("%lld\n", now);
mp[{min(par[now][0], now), max(par[now][0], now)}]=0;
now=par[now][0];
}
for(int i=1; i<=n; i++)
{
// printf("%lld\n", i);
vis[i]=0;
dist[i]=1e18;
}
dist[u]=0;
priority_queue<pair<int, int> > q;q.push({0, u});
while(!q.empty())
{
int step=-q.top().fi;
int node=q.top().se;
q.pop();
if(vis[node])
{
continue;
}
vis[node]=1;
for(auto x:adj[node])
{
if(dist[x]>step+mp[{min(node, x), max(node, x)}])
{
dist[x]=step+mp[{min(node, x), max(node, x)}];
q.push({-(step+mp[{min(node, x), max(node, x)}]), x});
}
}
}
printf("%lld\n", dist[v]);
}
}
