#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define all(x) x.begin(), x.end()
#define L(i, b, e) for (int i = b; i < e; ++i)
#define R(i, b, e) for (int i = b; i >= e; --i)
#define pb emplace_back
#define vi vector<int>
#define sz(x) ((int) x.size())
const int N = 1e5 + 7, Mx = 1e9 + 9;
int n, m;
int s, t, u, v;
vector<pair<int, int>> g[N];
ll dis1[N], dis2[N];
void dijkstra(int x, ll d[]){
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
d[x] = 0;
pq.push({0, x});
while (!pq.empty()){
auto [w, y] = pq.top();
pq.pop();
if (d[y] != w)continue;
for (auto &i : g[y]){
if (w + i.second < d[i.first]){
d[i.first] = w + i.second;
pq.push({d[i.first], i.first});
}
}
}
}
ll dis3[N];
ll mn1[N], mn2[N];
ll res1[N], res2[N];
bool vis[N];
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m >> s >> t >> u >> v;
s--;
t--;
u--;
v--;
L(i, 0, m){
int a, b, w;
cin >> a >> b >> w;
a--;
b--;
g[a].pb(b, w);
g[b].pb(a, w);
}
L(i, 0, n)dis1[i] = dis2[i] = dis3[i] = 1LL * Mx * Mx;
L(i, 0, n)res1[i] = res2[i] = 1LL * Mx * Mx;
dijkstra(u, dis1);
dijkstra(v, dis2);
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
dis3[s] = 0;
pq.push({0, s});
while (!pq.empty()){
auto [d, y] = pq.top();
pq.pop();
if (vis[y])continue;
vis[y] = true;
mn1[y] = dis1[y];
mn2[y] = dis2[y];
for (auto &i : g[y]){
if (d + i.second < dis3[i.first]){
dis3[i.first] = d + i.second;
pq.push({dis3[i.first], i.first});
}else if (i.second + dis3[i.first] == d){
mn1[y] = min(mn1[y], mn1[i.first]);
res1[y] = min(res1[y], res1[i.first]);
mn2[y] = min(mn2[y], mn2[i.first]);
res2[y] = min(res2[y], res2[i.first]);
}
}
res1[y] = min(res1[y], mn1[y] + dis2[y]);
res2[y] = min(res2[y], mn2[y] + dis1[y]);
}
cout << min({dis1[v], res1[t], res2[t]});
}
