#include<bits/stdc++.h>
using namespace std;
#define fast ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define in insert
#define all(x) x.begin(),x.end()
#define pb push_back
#define eb emplace_back
#define ff first
#define ss second
#define int long long
typedef long long ll;
typedef vector<int> vi;
typedef set<int> si;
typedef multiset<int> msi;
typedef pair<int, int> pii;
typedef vector<pii> vpii;
template<typename T, typename U>
ostream & operator << (ostream &out, const pair<T, U> &c) {
out << c.first << ' ' << c.second;
return out;
}
template<typename T>
ostream & operator << (ostream &out, vector<T> &v) {
const int sz = v.size();
for (int i = 0; i < sz; i++) {
if (i) out << ' ';
out << v[i];
}
return out;
}
template<typename T>
istream & operator >> (istream &in, vector<T> &v) {
for (T &x : v) in >> x;
return in;
}
template<typename T>
void mxx(T &a, T b){if(b > a) a = b;}
template<typename T>
void mnn(T &a, T b){if(b < a) a = b;}
const int mxn = 2e5 + 10, inf = 1e18 + 10;
int vis[mxn], mn[mxn][4], n, cnt[mxn][3], dp[mxn][3];
vector<pair<int, int>> g[mxn];
void dfs(int x) {
vis[x] = 1;
for(auto [y, t] : g[x]) {
if(mn[y][0] + t == mn[x][0] && !vis[y]) {
dfs(y);
}
}
}
void bfs(int st, int tp) {
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> q;
for(int i = 1; i <= n; i++) {
mn[i][tp] = inf;
}
mn[st][tp] = 0;
q.push({0, st});
while(q.size()) {
int cs = q.top().ff, x = q.top().ss; q.pop();
if(mn[x][tp] != cs) continue;
for(auto [y, t] : g[x]) {
if(mn[y][tp] > cs + t) {
mn[y][tp] = cs + t;
q.push({mn[y][tp], y});
}
}
}
}
void topsort(int st, int tp) {
queue<int> q;
q.push(st);
while(q.size()) {
int x = q.front(); q.pop();
for(auto [y, t] : g[x]) {
if(tp == 0 && mn[y][0] + t == mn[x][0] && vis[y]) {
cnt[y][tp]--;
mnn(dp[y][tp], dp[x][tp]);
if(cnt[y][tp] == 0) q.push(y);
}
if(tp == 1 && mn[y][0] == mn[x][0] + t && vis[y]) {
cnt[y][tp]--;
mnn(dp[y][tp], dp[x][tp]);
if(cnt[y][tp] == 0) q.push(y);
}
}
}
}
void go() {
int m;
cin >> n >> m;
int s, t, u, v;
cin >> s >> t >> u >> v;
for(int i = 1; i <= m; i++) {
int x, y, c;
cin >> x >> y >> c;
g[x].pb({y, c});
g[y].pb({x, c});
}
bfs(s, 0);
dfs(t);
bfs(u, 1);
bfs(v, 2);
for(int i = 1; i <= n; i++) {
if(vis[i]) {
for(auto [y, t] : g[i]) {
if(mn[y][0] + t == mn[i][0] && vis[y]) cnt[y][0]++;
if(mn[y][0] == mn[i][0] + t && vis[y]) cnt[y][1]++;
}
}
dp[i][0] = dp[i][1] = mn[i][1];
}
topsort(s, 1);
topsort(t, 0);
int ans = inf;
for(int i = 1; i <= n; i++) {
mnn(ans, min(dp[i][0], dp[i][1]) + mn[i][2]);
}
cout << ans << '\n';
}
signed main() {
// #ifndef ONO
// freopen("file.in", "r", stdin);
// freopen("file.out", "w", stdout);
// #endif
fast;
int t = 1;
// cin >> t;
while(t--) {
go();
}
return 0;
}
