#include<bits/stdc++.h>
#define fo(i,d,c) for(int i=d;i<=c;i++)
#define fod(i,c,d) for(int i=c;i>=d;i--)
#define maxn 1000010
#define N 1010
#define fi first
#define se second
#define pb emplace_back
#define en cout<<"\n";
#define int long long
#define inf (int)2e18
#define pii pair<int,int>
#define vii vector<pii>
#define lb(x) x&-x
#define bit(i,j) ((i>>j)&1)
#define offbit(i,j) (i^(1<<j))
#define onbit(i,j) (i|(1<<j))
#define vi vector<int>
template <typename T1, typename T2> bool minimize(T1 &a, T2 b){if (a > b) {a = b; return true;} return false;}
template <typename T1, typename T2> bool maximize(T1 &a, T2 b){if (a < b) {a = b; return true;} return false;}
using namespace std;
int n,m;
vii ke[maxn];
void dijkstra1(int inp,int d[])
{
priority_queue<pii,vii,greater<pii>> q;
fo(i,1,n) d[i] = inf;
d[inp] = 0;
q.push({0,inp});
while(q.size())
{
auto [du,u] = q.top();
q.pop();
if(du != d[u]) continue;
for(auto [v,w] : ke[u])
{
if(d[v] > d[u] + w)
{
d[v] = d[u] + w;
q.push({d[v],v});
}
}
}
}
int du[maxn],dv[maxn],ds[maxn],dt[maxn];
int dpu[maxn],dpv[maxn];
vi adj[maxn];
array<int,3> edge[maxn];
int ans;
int vis[maxn];
void dfs(int u)
{
vis[u] = 1;
for(int v : adj[u])
{
if(!vis[v]) dfs(v);
dpu[u] = min(dpu[u],min(dpu[v],du[v]));
dpv[u] = min(dpv[u],min(dpv[v],dv[v]));
}
ans = min({ans,dpu[u] + dv[u],dpv[u] + du[u]});
}
int s,t,u,v;
main()
{
#define name "TASK"
if(fopen(name".inp","r"))
{
freopen(name".inp","r",stdin);
freopen(name".out","w",stdout);
}
ios_base::sync_with_stdio(false);cin.tie(NULL);
cin >> n >> m;
cin >> s >> t >> u >> v;
fo(i,1,m)
{
cin >> edge[i][0] >> edge[i][1] >> edge[i][2];
ke[edge[i][0]].pb(edge[i][1],edge[i][2]);
ke[edge[i][1]].pb(edge[i][0],edge[i][2]);
}
dijkstra1(u,du);
dijkstra1(v,dv);
dijkstra1(s,ds);
dijkstra1(t,dt);
fo(i,1,m)
{
if(ds[edge[i][0]] + edge[i][2] + dt[edge[i][1]] == ds[t]) adj[edge[i][0]].pb(edge[i][1]);
if(ds[edge[i][1]] + edge[i][2] + dt[edge[i][0]] == ds[t]) adj[edge[i][1]].pb(edge[i][0]);
}
fo(i,1,n) dpu[i] = dpv[i] = 2e18;
ans = du[v];
dfs(s);
cout << ans;
}
