#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pll;
#define F first
#define S second
const int MN = 1e5+5, MM = 2e5+5;
int N, M, i, j, x, y, w, S, T, U, V, ww[MM], nd[4], deg[MN];
vector<pll> adj[MN]; vector<int> dag[MN]; ll dis[4][MN], dp[MN][2], ans;
priority_queue<pll,vector<pll>,greater<pll>> q;
queue<int> Q; pll ed[MM];
inline void dij(int idx){
memset(dis[idx],-1,sizeof(dis[idx]));
int st = nd[idx];
q.push({0, st});
while(q.size()){
pll cur = q.top(); q.pop();
if(dis[idx][cur.S]!=-1) continue;
dis[idx][cur.S] = cur.F;
for(auto v : adj[cur.S]){
if(dis[idx][v.F]!=-1) continue;
q.push({cur.F+v.S,v.F});
}
}
}
int main(){
scanf("%d%d%d%d%d%d",&N,&M,&S,&T,&U,&V);
nd[0]=S, nd[1]=T, nd[2]=U, nd[3]=V;
for(i=1;i<=M;i++){
scanf("%d%d%d",&x,&y,&w);
ed[i] = {x, y}; ww[i] = w;
adj[x].push_back({y, w});
adj[y].push_back({x, w});
}
for(i=0;i<4;i++) dij(i);
for(i=1;i<=M;i++){
x = ed[i].F, y = ed[i].S;
if(dis[0][x]>dis[0][y]) swap(x,y);
if(dis[0][x]+dis[1][y]+ww[i]==dis[0][T]){
dag[y].push_back(x);
deg[x]++;
}
}
ans = 1LL<<60;
for(i=1;i<=N;i++){
if(!deg[i]) Q.push(i);
}
memset(dp,0x3f,sizeof(dp));
while(Q.size()){
x = Q.front(); Q.pop();
for(i=0;i<2;i++) dp[x][i] = min(dp[x][i], dis[i^2][x]);
for(i=0;i<2;i++) ans = min(ans, dp[x][i]+dis[i^3][x]);
for(auto v : dag[x]){
deg[v] --;
if(!deg[v]) Q.push(v);
for(i=0;i<2;i++) dp[v][i] = min(dp[v][i], dp[x][i]);
}
}
printf("%lld\n",ans);
return 0;
}
