#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pb push_back
#define ins insert
#define all(x) x.begin(), x.end()
#define F first
#define S second
const int N = 2e5 + 7;
int d[N], d1[N], d2[N], n, m, used[N], s, t, u, v, ans = 1e18, used1[N], used2[N];
int dp[N][2];
vector<int>ord;
vector<pair<int, int>>g[N], g1[N];
void dfs(int v){
used1[v] = 1;
for(auto [to, w] : g1[v]){
if(used1[to]) continue;
dfs(to);
}
ord.pb(v);
}
void dfs1(int v){
used2[v] = 1;
for(auto [to, w] : g[v]){
if(d[to] + w == d[v]){
g1[to].pb({v, 0});
if(!used2[to]){
dfs1(to);
}
}
}
}
void dijkstra(){
for(int i = 1; i <= n; i++){
d[i] = 1e18;
used[i] = 0;
dp[i][0] = dp[i][1] = 1e18;
}
priority_queue<array<int, 3>>q;
d[s] = 0;
q.push({0, s, s});
while(q.size()){
int we = -q.top()[0], v = q.top()[1], pr = q.top()[2];
q.pop();
if(!used[v]){
used[v] = 1;
for(auto [to, w] : g[v]){
if(d[to] >= d[v] + w){
d[to] = d[v] + w;
q.push({-d[to], to, v});
}
}
}
}
dfs1(t);
}
void dijkstra1(int s){
for(int i = 1; i <= n; i++){
used[i] = 0;
d1[i] = 1e18;
}
d1[s] = 0;
priority_queue<pair<int, int>>q;
q.push({0, s});
while(q.size()){
int v = q.top().second;
q.pop();
if(used[v]) continue;
used[v] = 1;
for(auto [to, w] : g[v]){
if(d1[to] > d1[v] + w){
d1[to] = d1[v] + w;
q.push({-d1[to], to});
}
}
}
dfs1(t);
}
void dijkstra2(int s){
for(int i = 1; i <= n; i++){
used[i] = 0;
d2[i] = 1e18;
}
d2[s] = 0;
priority_queue<pair<int, int>>q;
q.push({0, s});
while(q.size()){
int v = q.top().second;
q.pop();
if(used[v]) continue;
used[v] = 1;
for(auto [to, w] : g[v]){
if(d2[to] > d2[v] + w){
d2[to] = d2[v] + w;
q.push({-d2[to], to});
}
}
}
}
void solve(){
cin>>n>>m>>s>>t>>u>>v;
for(int i = 1; i <= m; i++){
int a, b, w;
cin>>a>>b>>w;
g[a].pb({b, w});
g[b].pb({a, w});
}
dijkstra1(u);
dijkstra2(v);
dijkstra();
dfs(s);
int ans = d1[v];
for(auto a : ord){
ans = min(ans, d1[a] + d2[a]);
dp[a][0] = d2[a];
dp[a][1] = d1[a];
for(auto [to, w] : g1[a]){
dp[a][0] = min(dp[a][0], dp[to][0]);
dp[a][1] = min(dp[a][1], dp[to][1]);
ans = min({ans, dp[a][0] + d1[a], dp[a][1] + d2[a]});
}
}
cout<<ans<<'\n';
}
signed main(){
ios_base :: sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
int t = 1;
//cin>>t;
while(t--){
solve();
}
}
