#include<bits/stdc++.h>
#define inf 1e16
#define int long long
using namespace std;
const int N = 100010;
int dists[N], distt[N], dist[N][4];
vector <pair <int, int>> g[N];
int s, t, start, endd;
int32_t main(){
int n, m;
cin >> n >> m;
cin >> s >> t;
cin >> start >> endd;
for(int i = 0;i < m;i++){
int a, b, w;
cin >> a >> b >> w;
g[a].push_back({b, w});
g[b].push_back({a, w});
}
priority_queue <pair <int, int>> pq;
for(int i = 1;i <= n;i++){
dists[i] = distt[i] = inf;
dist[i][0] = dist[i][1] = dist[i][2] = dist[i][3] = inf;
}
dists[s] = 0;
pq.push({0, s});
while(!pq.empty()){
auto [d, v] = pq.top();
pq.pop();
if(-d != dists[v]) continue;
for(auto [x, w] : g[v]){
if(dists[x] > dists[v] + w){
dists[x] = dists[v] + w;
pq.push({-dists[x], x});
}
}
}
distt[t] = 0;
pq.push({0, t});
while(!pq.empty()){
auto [d, v] = pq.top();
pq.pop();
if(-d != distt[v]) continue;
for(auto [x, w] : g[v]){
if(distt[x] > distt[v] + w){
distt[x] = distt[v] + w;
pq.push({-distt[x], x});
}
}
}
dist[start][0] = 0;
priority_queue <array <int, 3>> pqq;
pqq.push({0, start, 0});
while(!pqq.empty()){
auto [d, v, flag] = pqq.top();
pqq.pop();
if(-d != dist[v][flag]) continue;
if(flag == 0){
if(dist[v][flag+1] > dist[v][flag]){
dist[v][flag+1] = dist[v][flag];
pqq.push({-dist[v][flag+1], v, flag+1});
}
if(dist[v][flag+2] > dist[v][flag]){
dist[v][flag+2] = dist[v][flag];
pqq.push({-dist[v][flag+2], v, flag+2});
}
}
if(flag == 1){
if(dist[v][flag+2] > dist[v][flag]){
dist[v][flag+2] = dist[v][flag];
pqq.push({-dist[v][flag+2], v, flag+2});
}
}
if(flag == 2){
if(dist[v][flag+1] > dist[v][flag]){
dist[v][flag+1] = dist[v][flag];
pqq.push({-dist[v][flag+1], v, flag+1});
}
}
for(auto [x, w] : g[v]){
if(flag == 0){
if(dist[x][0] > dist[v][0] + w){
dist[x][0] = dist[v][0] + w;
pqq.push({-dist[x][0], x, 0});
}
}
else if(flag == 1){
if(dists[v] + distt[x] + w == dists[t]){
if(dist[x][1] > dist[v][1]){
dist[x][1] = dist[v][1];
pqq.push({-dist[x][1], x, 1});
}
}
}
else if(flag == 2){
if(distt[v] + dists[x] + w == dists[t]){
if(dist[x][2] > dist[v][2]){
dist[x][2] = dist[v][2];
pqq.push({-dist[x][2], x, 2});
}
}
}
else{
if(dist[x][3] > dist[v][3] + w){
dist[x][3] = dist[v][3] + w;
pqq.push({-dist[x][3], x, 3});
}
}
}
}
cout << dist[endd][3] << '\n';
}
