#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdio>
#include <iomanip>
#include <fstream>
#include <cassert>
#include <cstring>
#include <numeric>
#include <ctime>
#include <complex>
#include <bitset>
#include <random>
#include <climits>
#include <stack>
/*#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,sse4.1,sse4.2,popcnt,abm,mmx,avx,avx2,tune=native")*/
using namespace std;
typedef long long ll;
typedef long double ld;
#define int ll
#define double ld
#define loop(i, n) for(int i = 0; i < (int)n; ++i)
#define loop1(i, n) for(int i = 1; i <= (int)n; ++i)
#define F first
#define S second
#define pb push_back
#define pi pair <int, int>
#define all(x) begin(x), end(x)
#define ti tuple <int, int, int>
#define Point Vect
#define no {cout << -1; return;}
#define yes {cout << "Yes"; return;}
#define mkp make_pair
#define mkt make_tuple
#define cerr if(0) cerr
const int N = 1e5 + 7, INF = 1e18;
vector <pi> g[N];
vector <int> ng[N];
int dist[4][N];
ti ed[2 * N];
bool good[N], used[N];
void dijkstra(int fst, int f) {
priority_queue <pi, vector <pi>, greater <pi> > q;
q.push({ 0, fst });
loop(i, N)
dist[f][i] = INF;
dist[f][fst] = 0;
while (!q.empty()) {
int v = q.top().S, dv = q.top().F;
q.pop();
if (dv > dist[f][v])
continue;
for (pi u : g[v])
if (dist[f][u.F] > dist[f][v] + u.S) {
dist[f][u.F] = dist[f][v] + u.S;
q.push({ dist[f][u.F], u.F });
}
}
}
bool dfs(int v, int f) {
used[v] = 1;
if (v == f)
return true;
for (int u : ng[v])
if (!used[u] && dfs(u, f))
return true;
return false;
}
void solve() {
int n, m, s, t, a, b;
cin >> n >> m >> s >> t >> a >> b;
loop(i, m) {
int u, v, c;
cin >> u >> v >> c;
g[u].pb({ v, c });
g[v].pb({ u, c });
ed[i] = mkt(u, v, c);
}
dijkstra(s, 0);
dijkstra(t, 1);
dijkstra(a, 2);
dijkstra(b, 3);
int len = dist[0][t];
loop(i, m) {
int u, v, c;
tie(u, v, c) = ed[i];
if (dist[0][u] + c + dist[1][v] == len || dist[0][v] + c + dist[1][u] == len) {
good[u] = good[v] = 1;
if (dist[0][u] < dist[0][v])
ng[u].pb(v);
else
ng[v].pb(u);
}
}
int ans = dist[3][a];
if (n <= 300) {
loop1(i, n)
loop1(j, n) {
loop1(k, n)
used[k] = 0;
if (good[i] && good[j] && dfs(i, j))
ans = min({ ans, dist[2][i] + dist[3][j], dist[2][j] + dist[3][i] });
}
}
else if (s == a) {
loop1(i, n)
if (good[i])
ans = min(ans, dist[3][i]);
}
else {
int cla = s, clb = s;
loop1(i, n)
if (good[i]) {
if (dist[2][cla] > dist[2][i])
cla = i;
if (dist[3][clb] > dist[3][i])
clb = i;
}
ans = min(ans, dist[2][cla] + dist[3][clb]);
}
cout << ans;
}
signed main() {
//freopen("b2.txt", "r", stdin);
//freopen("ans9.txt", "w", stdout);
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
//int t; cin >> t; loop(i, t)
solve();
return 0;
}
