#include <bits/stdc++.h>
using namespace std;
#define darvem ios_base::sync_with_stdio(false);cin.tie(NULL)
#define endl '\n'
#define ll long long
#define int long long
const int INF = 1e18;
typedef pair<int, int> pii;
int n, m, s, t, u, v;
vector<vector<pii>> g;
vector<int> d1(int st){
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.push({0, st});
vector<int> dst(n, INF);
while(!pq.empty()){
auto [d, x] = pq.top(); pq.pop();
if(dst[x] != INF) continue;
dst[x] = d;
for(auto e : g[x]){
pq.push({e.second + d, e.first});
}
}
return dst;
}
void dfs(vector<int> &visited, vector<int> &dst_u, vector<int> &dst_v, vector<vector<int>> &parents, vector<int> &dpu, vector<int> &dpv, int curr){
if(visited[curr]) return;
visited[curr] = 1;
for (auto p : parents[curr])
{
dfs(visited, dst_u, dst_v, parents, dpu, dpv, p);
dpu[curr] = min({dst_u[p], dpu[p], dpu[curr]});
dpv[curr] = min({dst_v[p], dpv[p], dpv[curr]});
}
}
int d2(){
priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, greater<tuple<int, int, int>>> pq;
vector<int> dst(n, INF), dpu(n, INF), dpv(n, INF), dst_u = d1(u), dst_v = d1(v);
vector<vector<int>> parents(n);
pq.push({0, s, -1});
while(!pq.empty()){
auto [d, x, p] = pq.top(); pq.pop();
if(dst[x] != INF){
if(dst[x] == d && p != -1) parents[x].push_back(p);
continue;
}
if(p!= -1) parents[x].push_back(p);
dst[x] = d;
for(auto e : g[x]){
pq.push({e.second + d, e.first, x});
}
}
vector<int> visited(n);
dfs(visited, dst_u, dst_v, parents, dpu, dpv, t);
int ans = 1e18;
for(int i = 0; i < n; i++){
ans = min({ans, dpu[i] + dst_v[i], dpv[i] + dst_u[i]});
}
return ans;
}
signed main(){
darvem;
cin >> n >> m >> s >> t >> u >> v;
s--;t--;u--;v--;
g.resize(n);
for(int i = 0; i<m; i++){
int a, b, c;
cin >> a >> b >> c;
a--;b--;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
auto dst = d1(u);
cout << min(dst[v], d2()) << endl;
}
