#include <bits/stdc++.h>
#define lsb(x) (x & (-x))
#define ll long long
#define ull unsigned long long
// 217
// 44
using namespace std;
const ll INF = 1e18;
vector < vector < pair <int, int> > > g;
vector <ll> dst[4];
int n;
inline void dijkstra(int nod, vector <ll> &dst) {
dst.resize(n + 1);
fill(dst.begin(), dst.end(), INF);
priority_queue < pair <ll, int> > pq;
pq.push({0, nod});
dst[nod] = 0;
vector <bool> vis(n + 1);
fill(vis.begin(), vis.end(), 0);
while(pq.size()) {
pair <ll, int> cur = pq.top();
pq.pop();
if(vis[cur.second]) {
continue;
}
vis[cur.second] = 1;
for(auto it : g[cur.second]) {
if(dst[it.first] > -cur.first + it.second) {
dst[it.first] = -cur.first + it.second;
pq.push({-dst[it.first], it.first});
}
}
}
}
vector <bool> vis;
vector <int> top;
void dfs(int nod) {
vis[nod] = 1;
for(auto it : g[nod]) {
if(vis[it.first] == 0) {
dfs(it.first);
}
}
top.push_back(nod);
}
int main() {
//ifstream cin("A.in");
//ofstream cout("A.out");
int i, m, s, t, u, v;
ios::sync_with_stdio(false);
cin.tie(0), cout.tie(0);
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
g.resize(n + 1);
for(i = 1; i <= m; i++) {
int x, y, c;
cin >> x >> y >> c;
g[x].push_back({y, c});
g[y].push_back({x, c});
}
vis.resize(n + 1);
ll ans = INF;
for(int p = 0; p < 2; p++) {
swap(u, v);
dijkstra(s, dst[0]); // s
dijkstra(t, dst[1]); // t
dijkstra(u, dst[2]); // u
dijkstra(v, dst[3]); // v
ans = min(ans, dst[2][v]);
vector < vector <int> > dag(n + 1);
for(i = 1; i <= n; i++) {
for(auto it : g[i]) {
if(dst[0][it.first] + it.second + dst[1][i] == dst[0][t]) {
dag[it.first].push_back(i);
}
}
}
fill(vis.begin(), vis.end(), 0);
top.clear();
dfs(1);
vector <ll> dp(n + 1, INF);
for(auto nod : top) {
if(dst[0][nod] + dst[1][nod] != dst[0][t]) {
continue;
}
dp[nod] = min(dp[nod], dst[3][nod]);
for(auto it : dag[nod]) {
dp[nod] = min(dp[nod], dp[it]);
}
ans = min(ans, dp[nod] + dst[2][nod]);
}
}
cout << ans;
//cin.close();
//cout.close();
return 0;
}
