#include <bits/stdc++.h>
#define coutf(n, m) cout << fixed << setprecision(n) << m
#define forr(i, a, n) for (int i = a; i < n; i++)
#define forl(i, a, n) for (int i = a; i > n; i--)
#define macos ios::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define endll "\n"
#define sp " "
typedef long long ll;
using namespace std;
struct Non{
int v;
ll w;
bool operator < (const Non &rhs)const{
if(w!=rhs.w)return w>rhs.w;
return v>rhs.v;
}
};
const int N = 1e5 + 10;
int n,m,x,y,st,des,a,b;
int p[N];
ll dis[3][N],c,ans,ans1=1e18,ans2=1e18;
vector<pair<int,ll>> adj[N];
priority_queue<Non> q;
void dijkstra(int z, int s){
forr(i,1,n+1)dis[s][i] = 1e18;
q.push({z,dis[s][z]=0LL});
while(!q.empty()){
int u = q.top().v;
q.pop();
for(auto [v,w]:adj[u]){
if(dis[s][v]>dis[s][u]+w){
q.push({v,dis[s][v]=dis[s][u]+w});
if(!s)p[v] = u;
}
}
}
}
int main(){macos;
cin >> n >> m >> x >> y >> st >> des;
forr(i,1,n+1)p[i] = i;
forr(i,0,m){
cin >> a >> b >> c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
dijkstra(x,0);
dijkstra(st,1);
dijkstra(des,2);
for(int u=y;u!=p[u];u=p[u])ans1 = min(ans1,dis[1][u]),ans2 = min(ans2,dis[2][u]);
ans1 = min(ans1,dis[1][x]),ans2 = min(ans2,dis[2][x]);
cout << min(dis[1][des],ans1+ans2);
return 0;
}
