#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define vi vector<int>
#define pii pair<int,int>
#define vii vector<pair<int,int>>
#define vll vector<long long>
#define pb push_back
#define pll pair<long long ,long long>
#define pf push_front
#define ql cout<<endl;
#define int long long
const ll inf=1e18;
const int maxn= 1e5+5;
int n,m,s,t,u,v;
int par[maxn];
vii g[maxn];
vll dists,distu,distv;
int dp[2][maxn];
bool bt[maxn];
int ans=inf;
void dijkstra(int start,vll &dist){
dist.resize(n+1);
priority_queue<pii,vii,greater<pii>> q;
fill(dist.begin(),dist.end(),inf);
dist[start]=0;
q.push({0,start});
fill(bt,bt+n+1,0);
while(!q.empty()){
auto[du,u]=q.top();
q.pop();
if(bt[u])continue;
bt[u]=1;
for(auto[viz , d] : g[u]){
if (dist[viz] > du + d) {
dist[viz] = du + d;
q.push({dist[viz], viz});
}
}
}
}
void dijkstra2(int start,int end){
fill(bt,bt+n+1,0);
fill(dp[0],dp[0]+n+1,inf);
fill(dp[1],dp[1]+n+1,inf);
priority_queue<pair<int,pii>,vector<pair<int,pii>>,greater<pair<int,pii>>>q;
q.push({0,{start,0}});
dp[0][start]=distu[start];
dp[1][start]=distu[start]+distv[start];
while(!q.empty()){
auto[du,p]=q.top();
auto[u,paru]=p;
q.pop();
if (!bt[u]) {
bt[u] = true;
dists[u] = du;
if (paru == 0) {
dp[0][u] = distu[u];
dp[1][u] = distu[u] + distv[u];
} else {
dp[0][u] = min(distu[u], dp[0][paru]);
dp[1][u] = min(dp[0][u] + distv[u], dp[1][paru]);
}
for (auto [v, w] : g[u]) {
q.push({du + w, {v, u}});
}
}
else if (du == dists[u]) {
dp[0][u] = min(dp[0][u], dp[0][paru]);
dp[1][u] = min({dp[1][u], dp[0][u] + distv[u], dp[1][paru]});
}
}
ans=min(ans,dp[1][end]);
}
int32_t main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin>>n>>m>>s>>t>>u>>v;
for(int i=0;i<m;i++){
int a,b,c;
cin>>a>>b>>c;
g[a].pb({b,c});
g[b].pb({a,c});
}
dijkstra(u,distu);
dijkstra(v,distv);
ans=distu[v];
dists.resize(n+1);
dijkstra2(s,t);
dijkstra2(t,s);
cout<<ans;
}
