#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ff first
#define ss second
#define N 200005
#define INF 0x3f3f3f3f3f3f3f3f
int e[N], d[N], n, m, s, t, u, v;
vector<int> adj[N];
priority_queue<pair<ll, int> > p;
void dij(int v, ll* dis){
memset(dis, 0x3f3f, N << 3);
dis[v] = 0;
p.push({0, v});
while(!p.empty()){
v = p.top().ss;
if(p.top().ff != -dis[v]){
p.pop();
continue;
}
p.pop();
for(int& x : adj[v]){
int u = e[x] ^ v;
if(dis[u] > dis[v] + d[x]){
dis[u] = dis[v] + d[x];
p.push({-dis[u], u});
}
}
}
}
ll dis[3][N], dp[2][N], res;
void dfs(int v){
if(dp[0][v] != INF) return;
dp[1][v] = dis[1][v];
dp[0][v] = dis[0][v];
for(int& x : adj[v]){
int u = e[x] ^ v;
if(dis[2][u] == dis[2][v] - d[x]){
dfs(u);
dp[1][v] = min(dp[1][u], dp[1][v]);
dp[0][v] = min(dp[0][u], dp[0][v]);
}
}
res = min(res, min(dp[1][v] + dis[0][v], dp[0][v] + dis[1][v]));
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cin>>n>>m>>s>>t>>u>>v;
for(int a, b, i = 1; i <= m; i++){
cin>>a>>b>>d[i];
e[i] = a ^ b;
adj[a].push_back(i);
adj[b].push_back(i);
}
memset(dp, 0x3f3f, sizeof dp);
dij(u, dis[0]);
dij(v, dis[1]);
dij(s, dis[2]);
res = dis[1][u];
dfs(t);
cout<<res;
}
