#include <bits/stdc++.h>
#define pb push_back
#define ll long long
#define pii pair<int, int>
#define pll pair<ll, ll>
#define xx first
#define yy second
#define MAXN 100010
#define INF 1000000000000000LL
#define MALON 310
using namespace std;
ll n, m, s, t, x, y, d[MAXN], ds[MAXN], dt[MAXN], dx[MAXN], dy[MAXN], p[MAXN], fw[MALON][MALON], minn[5][MAXN], minmin[MAXN], ress=INF;
vector<ll> g[MAXN];
map<pii, ll> w;
void dijkstra(int s, ll d[], int dal)
{
for (int i=1; i<=n; i++) { d[i]=INF; p[i]=-1; }
priority_queue< pll, vector<pll>, greater<pll> > pq;
pq.push({0, s});
d[s]=0;
p[s]=-1;
if (dal) minn[dal][s]=dx[s];
while (!pq.empty())
{
ll td=pq.top().xx, u=pq.top().yy;
pq.pop();
if (td!=d[u]) continue;
for (int i=0; i<g[u].size(); i++)
{
ll v, ww;
v=g[u][i];
pii par={u, v};
ww=w[par];
if (d[u]+ww<d[v])
{
d[v]=d[u]+ww;
//if (dal) { /*cout<<u<<" "<<v<<" "<<minn[dal][u]<<" "<<minn[dal][v]<<endl;*/ minn[dal][v]=min(minn[dal][u], min(minn[dal][v], dx[v])); /*cout<<"a sad "<<minn[dal][v]<<endl;*/ }
p[v]=u;
pq.push({d[v], v});
}
if (dal && (d[u]+ww)<=d[v]) { minn[dal][v]=min(minn[dal][u], min(minn[dal][v], dx[v])); }
}
}
}
int main(){
ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
cin>>n>>m>>s>>t>>x>>y;
for (int i=0; i<m; i++)
{
int u, v, ww; cin>>u>>v>>ww;
g[u].pb(v);
g[v].pb(u);
w[{u, v}]=ww;
w[{v, u}]=ww;
}
for (int i=1; i<=n; i++) { minn[1][i]=minn[2][i]=INF; }
dijkstra(x, dx, 0); dijkstra(y, dy, 0); dijkstra(s, ds, 1); dijkstra(t, dt, 2);
//cout<<"GLEEEEEEE "<<ds[t]<<endl;
for (int i=1; i<=n; i++) { minmin[i]=min(minn[1][i], minn[2][i]); /*cout<<i<<" "<<minmin[i]<<endl;*/ }
ress=dx[y];
for (int i=1; i<=n; i++)
{
if (ds[i]+dt[i]==ds[t])
{
ress=min(ress, dy[i]+minmin[i]);
}
}
cout<<ress;
exit(0);
if (s==x)
{
dijkstra(s, ds, 0); dijkstra(t, dt, 0); dijkstra(y, dy, 0);
ress=ds[y];
for (int i=1; i<=n; i++) if ((ds[i]+dt[i])==ds[t]) ress=min(ress, dy[i]);
cout<<ress;
exit(0);
}
if (n<=300)
{
for (int i=1; i<=n; i++) for (int j=1; j<=n; j++) fw[i][j]=INF;
for (int i=1; i<=n; i++)
{
fw[i][i]=0;
for (int j=0; j<g[i].size(); j++) fw[i][g[i][j]]=w[{i, g[i][j]}];
}
for (int v=1; v<=n; v++)
for (int i=1; i<=n; i++)
for (int j=1; j<=n; j++)
fw[i][j]=min(fw[i][j], fw[i][v]+fw[v][j]);
//for (int i=1; i<=n; i++) for (int j=1; j<=n; j++) cout<<i<<" "<<j<<" "<<fw[i][j]<<endl;
ress=fw[x][y];
for (int i=1; i<=n; i++)
{
for (int j=1; j<=n; j++)
{
if (fw[s][i]+fw[i][j]+fw[j][t]==fw[s][t]) ress=min(ress, min(fw[x][i]+fw[j][y], fw[x][j]+fw[i][y]));
}
}
cout<<ress;
exit(0);
}
dijkstra(s, d, 0);
//cout<<d[1]<<" "<<d[2]<<" "<<d[3]<<" "<<d[4]<<" "<<d[5]<<" "<<d[6]<<endl;
int u=t;
while(p[u]!=-1)///p[u] ili u?
{
//cout<<u<<" "<<p[u]<<endl;
w[{u, p[u]}]=0;
w[{p[u], u}]=0;
u=p[u];
}
dijkstra(x, d, 0);
//cout<<d[1]<<" "<<d[2]<<" "<<d[3]<<" "<<d[4]<<" "<<d[5]<<" "<<d[6];
cout<<d[y];
}
