#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
#define mod 1000000007
#define ull unsigned long long
#define mll map<int,int>
#define vll vector<int>
#define pll pair<int, int>
#define FOR(i, a, b) for(int i = a; i < b; i++)
#define FOR1(i, a, b) for(int i = a; i <= b; i++)
#define UNF(i, a, b) for(int i = b; i >= a; i--)
#define UNF1(i, a, b) for(int i = b; i > a; i--)
#define ll long long
#define pb push_back
#define mp make_pair
#define X first
#define Y second
#define name "QUADQUERY"
#define fast ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
const int MAXN = 3e6 + 5;
int n, m, s, t, x, y;
vector<pll> g[MAXN];
ll d[MAXN], ans = LLONG_MAX;
map<pll, bool> check;
vector<int> edge[MAXN];
void Dijkstra(int p, int end) {
fill(d, d + n + 1, LLONG_MAX);
d[p] = 0;
priority_queue<pll, vector<pll>, greater<pll>> q;
q.push(mp(d[p], p));
while (!q.empty()) {
int u = q.top().Y, cost = q.top().X;
q.pop();
if (cost > d[u]) continue;
if (u == end) break;
for (const auto& x : g[u]) {
if (d[x.X] > d[u] + x.Y) {
d[x.X] = d[u] + x.Y;
q.push(mp(d[x.X], x.X));
edge[x.X].clear();
}
if (d[x.X] == d[u] + x.Y) edge[x.X].pb(u);
}
}
}
void Dijkstra2(int p, int end) {
fill(d, d + n + 1, LLONG_MAX);
d[p] = 0;
priority_queue<pll, vector<pll>, greater<pll>> q;
q.push(mp(d[p], p));
while (!q.empty()) {
int u = q.top().Y, cost = q.top().X;
q.pop();
if (cost > d[u]) continue;
if (u == end) break;
for (const auto& x : g[u]) {
ll val = check[{u, x.X}] ? 0 : x.Y;
if (d[x.X] > d[u] + val) {
d[x.X] = d[u] + val;
q.push(mp(d[x.X], x.X));
}
}
}
}
void DFS(int u, int end) {
if (u == end) {
Dijkstra2(x, y);
ans = min(ans, d[y]);
}
for (const int& v : edge[u]) {
check[{u, v}] = check[{v, u}] = true;
DFS(v, end);
check[{u, v}] = check[{v, u}] = false;
}
}
void solve() {
Dijkstra(s, t);
DFS(t, s);
cout << ans;
}
int main() {
fast;
if (fopen(name".inp", "r")) {
freopen(name".inp", "r", stdin);
freopen(name".out", "w", stdout);
}
cin >> n >> m >> s >> t >> x >> y;
FOR1(i, 1, m) {
int u, v, w;
cin >> u >> v >> w;
g[u].pb(mp(v, w));
g[v].pb(mp(u, w));
}
solve();
return 0;
}
