#include <bits/stdc++.h>
#define fo(i,a,b) for(int i=(a);i<=(b);++i)
#define fd(i,a,b) for(int i=(a);i>=(b);--i)
#define rep(i,a,b) for(int i=(a);i<(b);++i)
#define fi first
#define se second
#define LL unsigned long long
#define uint unsigned int
#define pb push_back
#define eb emplace_back
#define bit(s,i) ((s >> i) & 1)
#define off(s,i) (s & (~ (1 << i)))
#define ii pair <long long , int>
#define iii1 pair <ii , int>
#define iii2 pair <int , ii>
#define TASK "commuter"
using namespace std;
const long long inf = 0x3f3f3f3f3f3f3f3f;
const int maxn = 1e5 + 5;
int n , m , tim , s , t;
long long d[maxn][4] , dp[maxn] , res , ans;
ii a[maxn];
bool vs[maxn] ;
vector < ii > g[maxn];
vector < int > adj[maxn];
///--------------------------
void dijkstra(int u,int ty) {
priority_queue < ii , vector < ii > , greater < ii > > pt;
d[u][ty] = 0;
pt.push({d[u][ty] , u});
while (!pt.empty()) {
ii x = pt.top();
pt.pop();
long long dis = x.fi;
int u = x.se;
if (dis != d[u][ty]) continue;
for (auto v : g[u]) {
if (d[v.fi][ty] > dis + v.se) {
d[v.fi][ty] = dis + v.se;
pt.push({d[v.fi][ty] , v.fi});
}
}
}
}
///--------------------------
void readf() {
int u , v;
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1 ; i <= m ; ++i) {
int u , v , w;
cin >> u >> v >> w;
g[u].eb(v , w);
g[v].eb(u , w);
}
memset(d,inf,sizeof(d));
memset(dp,inf,sizeof(dp));
dijkstra(s,0);
dijkstra(u,1);
dijkstra(v,2);
dijkstra(t,3);
ans = res = d[v][1];
}
///--------------------------
bool in(int u) {
return (d[u][0] + d[u][3] == d[t][0]);
}
///--------------------------
void solve() {
for (int i = 1 ; i <= n ; ++i) a[i] = ii(d[i][0] , i);
sort(a + 1 , a + n + 1);
for (int u = 1 ; u <= n ; ++u)
if (in(u)) dp[u] = d[u][2];
for (int i = n ; i > 0 ; --i) {
int u = a[i].se;
if (!in(u)) continue;
for (auto v : g[u])
if (in(v.fi) && d[v.fi][0] == d[u][0] + v.se) {
dp[u] = min(dp[u] , dp[v.fi]);
}
}
for (int u = 1 ; u <= n ; ++u)
if (in(u)) res = min(res , dp[u] + d[u][1]);
memset(dp,inf,sizeof(dp));
for (int u = 1 ; u <= n ; ++u)
if (in(u)) dp[u] = d[u][1];
for (int i = n ; i > 0 ; --i) {
int u = a[i].se;
if (!in(u)) continue;
for (auto v : g[u])
if (in(v.fi) && d[v.fi][0] == d[u][0] + v.se) {
dp[u] = min(dp[u] , dp[v.fi]);
}
}
for (int u = 1 ; u <= n ; ++u)
if (in(u)) res = min(res , dp[u] + d[u][2]);
cout << res << '\n';
}
///--------------------------
void solve1() {
for (int u = 1 ; u <= n ; ++u)
for (int v = 1 ; v <= n ; ++v)
if (in(u) && in(v)) ans = min(ans , d[u][1] + d[v][2]);
cout << ans << '\n';
}
///--------------------------
int main() {
#ifdef BDP0509
freopen(TASK".inp", "r", stdin);
freopen(TASK".out", "w", stdout);
#endif // ONLINE_JUDGE
ios::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
readf();
solve();
//solve1();
}
