#include <bits/stdc++.h>
#define loop(i,a,b) for(int i = (a); i < (b); i ++)
#define pb push_back
#define ins insert
#define pii pair<int,int>
#define ff first
#define ss second
//#define op(x) cerr << #x << " = " << x << endl;
//#define opa(x) cerr << #x << " = " << x << ", ";
//#define ops(x) cerr << x;
//#define entr cerr << endl;
//#define spac cerr << ' ';
//#define STL(x) cerr << #x << " : "; for(auto &qwe:x) cerr << qwe << ' '; cerr << endl;
//#define ARR(x, nnn) cerr << #x << " : "; loop(qwe,0,nnn) cerr << x[qwe] << ' '; cerr << endl;
#define BAE(x) x.begin(), x.end()
#define unilize(x) x.resize(unique(BAE(x)) - x.begin())
#define unisort(x) sort(BAE(x)); unilize(x);
using namespace std;
typedef long long ll;
const int mxn = (int)(1e5) + 10;
const ll INF = 1e18;
struct EDGE{ int u, w; };
struct three_edge{ int ff, ss, w; };
vector<EDGE> E[mxn], F[mxn], G[mxn];
ll dp[mxn], d1[mxn], d2[mxn];
vector<three_edge> EV;
bool vis[mxn], n_vis[mxn];
void dfs(int v){
vis[v] = true;
for(auto &i:F[v]){
if(!vis[i.u]){
dfs(i.u);
}
}
}
void n_dfs(int v){
n_vis[v] = true;
for(auto &i:G[v]){
if(!n_vis[i.u]){
n_dfs(i.u);
}
}
}
int main(){
// freopen("in.txt", "r", stdin);
ios::sync_with_stdio(false); cin.tie(0);
int n, m, S, T, U, V;
cin >> n >> m >> S >> T >> U >> V;
loop(i,0,m){
int ia, ib, w;
cin >> ia >> ib >> w;
E[ia].pb({ib, w});
E[ib].pb({ia, w});
EV.pb({ia, ib, w});
}
loop(i,1,n+1) dp[i] = INF; dp[S] = 0;
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
pq.push({0, S});
while(!pq.empty()){
int now = pq.top().ss;
ll dis = pq.top().ff;
pq.pop();
if(dis != dp[now]) continue;
for(auto &i:E[now]){
if(dis + i.w < dp[i.u]){
dp[i.u] = dis + i.w;
pq.push({dp[i.u], i.u});
}
}
}
for(auto &i:EV){
if(min(dp[i.ff], dp[i.ss]) + i.w == max(dp[i.ff], dp[i.ss])){
int near = (dp[i.ff] < dp[i.ss]) ? i.ff : i.ss;
int far = i.ff + i.ss - near;
F[near].pb({far, 0});
// opa(far) op(near)
// opa(near) op(far)
G[far].pb({near, 0});
}
}
dfs(S);
n_dfs(T);
loop(i,1,n+1){
F[i].clear();
G[i].clear();
}
for(auto &i:EV){
if(min(dp[i.ff], dp[i.ss]) + i.w == max(dp[i.ff], dp[i.ss])
&& vis[i.ff] && vis[i.ss] && n_vis[i.ff] && n_vis[i.ss]){
int near = (dp[i.ff] < dp[i.ss]) ? i.ff : i.ss;
int far = i.ff + i.ss - near;
F[near].pb({far, 0});
G[far].pb({near, 0});
}
}
loop(i,1,n+1) dp[i] = INF; dp[U] = 0;
pq.push({0, U});
while(!pq.empty()){
int now = pq.top().ss;
ll nd = pq.top().ff;
pq.pop();
if(nd != dp[now]) continue;
for(auto &i:E[now]){
if(dp[i.u] > nd + i.w){
dp[i.u] = nd + i.w;
pq.push({dp[i.u], i.u});
}
}
}
ll ans = dp[V];
loop(i,1,n+1){
d1[i] = dp[i];
pq.push({d1[i], i});
}
while(!pq.empty()){
int now = pq.top().ss;
ll nd = pq.top().ff;
pq.pop();
if(nd != d1[now]) continue;
for(auto &i:F[now]){
if(d1[i.u] > nd + i.w){
d1[i.u] = nd + i.w;
pq.push({d1[i.u], i.u});
}
}
}
loop(i,1,n+1){
d2[i] = dp[i];
pq.push({d2[i], i});
}
while(!pq.empty()){
int now = pq.top().ss;
ll nd = pq.top().ff;
pq.pop();
if(nd != d2[now]) continue;
for(auto &i:G[now]){
if(d2[i.u] > nd + i.w){
d2[i.u] = nd + i.w;
pq.push({d2[i.u], i.u});
}
}
}
loop(i,1,n+1){
dp[i] = min(d1[i], d2[i]);
pq.push({dp[i], i});
}
while(!pq.empty()){
int now = pq.top().ss;
ll nd = pq.top().ff;
pq.pop();
if(nd != dp[now]) continue;
for(auto &i:E[now]){
if(dp[i.u] > nd + i.w){
dp[i.u] = nd + i.w;
pq.push({dp[i.u], i.u});
}
}
}
ans = min(ans, dp[V]);
cout << ans << '\n';
}
