// 1
#include <bits/stdc++.h>
using namespace std;
#define int long long
const int N = 1e5+37;
vector<array<int, 2>> adj[N];
vector<int> ds, dt, dv, du, adj2[N];
vector<array<int, 2>> a1(N), a2(N);
vector<int> d(int x){
vector<int> dist(N, 1e18);
dist[x] = 0;
priority_queue<array<int, 2>> q;
q.push({0, x});
while (q.size()){
int u = -q.top()[0], v = q.top()[1];
q.pop();
for (auto i: adj[v]){
if(dist[i[0]] > u+i[1]){
dist[i[0]] = u + i[1];
q.push({-dist[i[0]], i[0]});
}
}
}
return dist;
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
int n, m; cin >> n >> m;
int s, t, u, v; cin >> s >> t >> u >> v;
s--; t--; u--; v--;
vector<array<int, 3>> e;
for (int i = 0; i < m; i++){
int x, y, z; cin >> x >> y >> z;
x--; y--;
adj[x].push_back({y, z});
adj[y].push_back({x, z});
e.push_back({x, y, z});
}
ds=d(s), dt=d(t), du=d(u), dv=d(v);
for (auto i: e){
if(i[2] + ds[i[0]] + dt[i[1]] == ds[t]) adj2[i[0]].push_back(i[1]), adj2[i[1]].push_back(i[0]);
if(i[2] + ds[i[1]] + dt[i[0]] == ds[t]) adj2[i[0]].push_back(i[1]), adj2[i[1]].push_back(i[0]);
}
int a=1e18;
for (int i = 0; i < n; i++){
a1[i] = {a, a};
a2[i] = {a, a};
}
queue<int> q;
q.push(s);
vector<int> vis(n);
vis[s]=1;
while (q.size()){
int c=q.front();
q.pop();
a1[c][0] = min(a1[c][0], dv[c]);
a1[c][1] = min(a1[c][1], du[c]);
for (auto i: adj2[c]){
if(ds[i] > ds[c]){
a1[i][0] = min(a1[i][0], a1[c][0]);
a1[i][1] = min(a1[i][1], a1[c][1]);
if(vis[i]==0) q.push(i), vis[i]=1;
}
}
}
q.push(t);
for(int i=0; i<n; i++) vis[i]=0;
vis[t]=1;
while (q.size()){
int c=q.front();
q.pop();
a2[c][0] = min(a2[c][0], dv[c]);
a2[c][1] = min(a2[c][1], du[c]);
for (auto i: adj2[c]){
if(dt[i] > dt[c]){
a2[i][0] = min(a2[i][0], a2[c][0]);
a2[i][1] = min(a2[i][1], a2[c][1]);
if(vis[i]==0) q.push(i), vis[i]=1;
}
}
}
int ans=dv[u];
for(int i=0; i<n; i++){
ans = min({a1[i][0] + a2[i][1], a1[i][1] + a2[i][0], ans});
}
cout<<ans;
}
