#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;
typedef long long ll;
#define st first
#define nd second
#define f(a, c, b) for (int a = c; b > a; a++)
#define pb push_back
#define all(a) a.begin(), a.end()
#define wczytaj(a, c, n) a.resize(n); f(i, c, n) cin >> a[i];
#define sz(a) int(a.size())
#define wypisz(a, c) f(i, c, sz(a)) cout << a[i] << " "; cout << "\n";
int n, m, s, t, u, v; //zerujemy wybrane z s do t
vector<vector<pair<int, ll>>> sasiedzi;
vector<vector<ll>> min_odl(4);
vector<ll> dp;
vector<ll> dp_tyl;
vector<int> odw;
vector<int> odw2;
void dijkstra(int ind, int zrodlo) {
min_odl[ind].resize(n + 1);
f(i, 1, n + 1) min_odl[ind][i] = -1;
priority_queue<pair<ll, int>> kolejka;
kolejka.push({0, zrodlo});
pair<ll, int> p1;
while (kolejka.size()) {
p1 = kolejka.top();
kolejka.pop();
if (min_odl[ind][p1.nd] != -1) continue;
p1.st = -p1.st;
min_odl[ind][p1.nd] = p1.st;
for (pair<int, ll> sasd: sasiedzi[p1.nd]) {
if (min_odl[ind][sasd.st] != -1) continue;
kolejka.push({-(p1.st + sasd.nd), sasd.st});
}
}
}
void dfs_dp(int w) { //mamy juz gwarancje ze lezy na najkrotszej sciezce z s do t
odw[w] = 1;
dp[w] = min_odl[1][w];
for (pair<int, ll> sasd: sasiedzi[w]) {
if ((min_odl[2][w] + sasd.nd + min_odl[3][sasd.st]) > min_odl[2][t]) continue; //krawedz nie lezy na najkrotszej sciezce
if (!odw[sasd.st]) {
dfs_dp(sasd.st);
}
dp[w] = min(dp[w], dp[sasd.st]);
}
}
void dfs_od_tylu(int w) {
dp_tyl[w] = min_odl[1][w];
odw2[w] = 1;
for (pair<int, ll> sasd: sasiedzi[w]) {
if ((min_odl[3][w] + sasd.nd + min_odl[2][sasd.st]) > min_odl[3][s]) continue; //krawedz nie jest na minimalnej sciezce z t do s
if (!odw2[sasd.st]) {
dfs_od_tylu(sasd.st);
}
dp_tyl[w] = min(dp_tyl[w], dp_tyl[sasd.st]);
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m >> s >> t >> u >> v;
sasiedzi.resize(n + 1);
int w1, w2;
ll w3;
f(i, 0, m) {
cin >> w1 >> w2 >> w3;
sasiedzi[w1].pb({w2, w3});
sasiedzi[w2].pb({w1, w3});
}
dijkstra(0, u); dijkstra(1, v); dijkstra(2, s); dijkstra(3, t);
dp.resize(n + 1, -1);
dp_tyl.resize(n + 1, -1);
odw.resize(n + 1, 0);
odw2.resize(n + 1, 0);
dfs_dp(s);
dfs_od_tylu(t);
ll wnk = 1000000000000000000;
/*f(i, 1, n + 1) {
cout << dp[i] << " ";
}*/
f(i, 1, n + 1) {
if (dp[i] != -1) {
wnk = min(wnk, min_odl[0][i] + min(dp_tyl[i], dp[i]));
}
}
cout << wnk;
return 0;
}
