#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define ii pair<int,int>
#define pii pair<int,ii>
#define fi first
#define se second
#define pb push_back
#define all(x) x.begin(), x.end()
#define RUN_FAST ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
const int N = 1e6+5;
const int M = log2(N)+5;
const ll oo = 1e18;
const int maxn = 5010;
const ll mod = 1000000007;
const int base = 311;
ll n, m, s, t, u, v;
ll dis[3][N], best[N][3];
vector<ii> g[N];
ll ans;
void dijk(int start, int type)
{
for(int i = 1; i <= n; i++)
{
dis[type][i] = 3e9;
}
dis[type][start] = 0;
priority_queue<ii, vector<ii>, greater<ii> > q;
q.push({dis[type][start], start});
while(!q.empty())
{
int u = q.top().se;
int cost = q.top().fi;
q.pop();
if(cost > dis[type][u]) continue;
for(auto it : g[u])
{
int v = it.fi;
int w = it.se;
if(dis[type][v] > dis[type][u] + w)
{
dis[type][v] = dis[type][u] + w;
q.push({dis[type][v], v});
}
}
}
}
void dfs(int t)
{
best[t][0] = dis[1][t];
best[t][1] = dis[2][t];
// cout << best[t][1] << " " << best[t][0] << '\n';
for(auto it : g[t])
{
int v = it.fi;
int w = it.se;
if(dis[0][v] + w != dis[0][t]) continue;
dfs(v);
// cout << best[t][0] << " " << best[v][0] << " " << best[t][1] << " " << best[v][1] << '\n';
best[t][0] = min(best[t][0], best[v][0]);
best[t][1] = min(best[t][1], best[v][1]);
}
ans = min(ans, dis[1][t] + best[t][1]);
ans = min(ans, dis[2][t] + best[t][0]);
}
int main()
{
RUN_FAST
// freopen("test.inp","r",stdin);
// freopen("test.out","w",stdout);
cin >> n >> m >> s >> t >> u >> v;
for(int i = 1; i <= m; i++)
{
int u, v, w;
cin >> u >> v >> w;
g[u].pb({v, w});
g[v].pb({u, w});
}
dijk(s, 0);
dijk(u, 1);
dijk(v, 2);
ans = dis[1][v];
dfs(t);
cout << ans;
return 0;
}
// 2zzz;
// codelozd
//⣿⣿⣿⡇⢩⠘⣴⣿⣥⣤⢦⢁⠄⠉⡄⡇⠛⠛⠛⢛⣭⣾⣿⣿⡏
//⣿⣿⣿⡇⠹⢇⡹⣿⣿⣛⣓⣿⡿⠞⠑⣱⠄⢀⣴⣿⣿⣿⣿⡟
//⣿⣿⣿⣧⣸⡄⣿⣪⡻⣿⠿⠋⠄⠄⣀⣀⢡⣿⣿⣿⣿⡿⠋
//⠘⣿⣿⣿⣿⣷⣭⣓⡽⡆⡄⢀⣤⣾⣿⣿⣿⣿⣿⡿⠋
//⠄⢨⡻⡇⣿⢿⣿⣿⣭⡶⣿⣿⣿⣜⢿⡇⡿⠟⠉
//⠄⠸⣷⡅⣫⣾⣿⣿⣿⣷⣙⢿⣿⣿⣷⣦⣚⡀
//⠄⠄⢉⣾⡟⠙❤️⠈⢻⣿⣷⣅⢻⣿⣿⣿⣿⣿⣶⣶⡆⠄⡀
//⠄⢠⣿⣿⣧⣀⣀⣀⣀⣼⣿⣿⣿⡎⢿⣿⣿⣿⣿⣿⣿⣇❤️⠄
//⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣎⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶
//⠄⠄⠻⢿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣾⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⡟
//⠄⠄⠄⠄⢮⣭⣍⡭⣭⡵⣾⣿⣿⣿⡎⣿⣿⣌⠻⠿⠿⠿⠟⠋
//⠄⠄⠄⠄⠈⠻⣿⣿⣿⣿⣹⣿⣿⣿⡇⣿⣿⡿
//⠄⠄⣀⣴⣾⣶⡞⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠃
//⣠⣾⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⡟⣹⣿⣳⡄
