#include <bits/stdc++.h>
using namespace std;
#define int long long
using ll = long long;
using vi = vector<int>;
#define pb push_back
#define rsz resize
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
using pi = pair<int,int>;
#define endl "\n"
#define mp make_pair
void setIO(string name = "") {
ios_base::sync_with_stdio(0); cin.tie(0);
if(sz(name)){
freopen((name+".in").c_str(), "r", stdin);
freopen((name+".out").c_str(), "w", stdout);
}
}
const int maxn = 1e5+10;
const int inf = 1e18;
vector<pi> adj[100010];
int n,m,s,t,u,v;
vi du(maxn), dv(maxn), dend(maxn);
int ans;
vector<bool> visited(maxn);
vector<vi> dp(maxn, vi(2, 0));
void dj1(int start, vi&arr){
fill(arr.begin(), arr.end(), inf);
priority_queue<pi, vector<pi>, greater<pi>> pq;
pq.push({0, start});
arr[start] = 0;
while (!pq.empty()){
// cout<<1<<endl;
auto [c, node] = pq.top();
pq.pop();
if (c > arr[node]) continue;
for (auto i : adj[node]){
if (arr[i.first] > c + i.second){
arr[i.first] = c + i.second;
pq.push({arr[i.first], i.first});
}
}
}
}
void dj2(int start, int end){
dp.rsz(n+1, vi(2, inf));
visited.rsz(n+1, false);
priority_queue<pair<int, pi>, vector<pair<int, pi>>, greater<pair<int, pi>>> pq;
pq.push({0, {start, 0}});
dp[0][0] = dp[0][1] = inf;
while (!pq.empty()){
//cout<<2<<endl;
auto [cost, node ] = pq.top();
auto [cur, parent] = node;
pq.pop();
if (!visited[cur]){
visited[cur] = true;
dp[cur][0] = min(du[cur], dp[parent][0]);
dp[cur][1] = min(dv[cur], dp[parent][1]);
dend[cur] = cost;
for (auto i : adj[cur]){
pq.push({cost + i.second, {i.first, cur}});
}
}
else if (cost == dend[cur]){
if (min(du[cur], dp[parent][0]) + min(dv[cur], dp[parent][1]) <= dp[cur][0] + dp[cur][1]){
dp[cur][0] = min(du[cur], dp[parent][0]);
dp[cur][1] = min(dv[cur], dp[parent][1]);
}
}
}
ans = min(ans, dp[end][0] + dp[end][1]);
}
signed main(){
setIO();
cin>>n>>m>>s>>t>>u>>v;
for (int i = 0; i < m; i++){
int a,b,c;
cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
du.rsz(n+1);
dv.rsz(n+1);
dj1(u, du);
dj1(v, dv);
ans = du[v];
dj2(s,t);
dj2(t,s);
cout<<ans<<endl;
}
