/**
* Author: Lưu Diệp Thành (Save Diệp Thành)
* Le Hong Phong High School for the Gifted (i2528)
**/
#include<bits/stdc++.h>
using namespace std;
#define int long long
//#define ll long long
#define ushort unsigned short
#define FOR(i,l,r) for(int i = (l), _r = (r); i <= _r; i++)
#define FORN(i,r,l) for(int i = (r), _l = (l); i >= _l; i--)
#define endl '\n'
#define sz(x) (int)x.size()
#define fi first
#define se second
#define pb push_back
#define all(v) (v).begin(),(v).end()
#define MASK(x) (1LL << (x))
#define BIT(x,i) (((x) >> (i)) & 1)
#define ins insert
#define segleft (id<<1)
#define segright (id<<1|1)
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
const int MOD = 1e9+7;
const int INF = LLONG_MAX;
const int N = 1e5+5;
vector<pair<int,int>> edge[N];
vector<int> distU, distV;
int n, m, s, t, u, v;
vector<int> dijkstra(int st) {
vector<int> dist(n+5, INF);
dist[st] = 0;
priority_queue<
pair<int,int>,
vector<pair<int,int>>,
greater<pair<int,int>>
> q;
q.push({0, st});
while(!q.empty()) {
auto [du, u] = q.top();
q.pop();
if (du > dist[u]) continue;
for(auto [v,w] : edge[u]) {
if (dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
q.push({dist[v], v});
}
}
}
return dist;
}
struct State {
int d, u, par;
};
struct cmp {
bool operator()(const State &a, const State &b) const {
return a.d > b.d;
}
};
int getans(int st) {
vector<int> dist(n+5, LLONG_MAX);
vector<int> dp1(n+5, LLONG_MAX), dp2(n+5, LLONG_MAX);
priority_queue<State, vector<State>, cmp> q;
dist[st] = 0;
q.push({0, st, 0});
while(!q.empty()) {
auto [curdist, cur, par] = q.top(); q.pop();
if (curdist != dist[cur]) continue;
dp1[cur] = min({dp1[cur], distU[cur], dp1[par]});
dp2[cur] = min({dp2[cur], dp1[cur] + distV[cur], dp2[par]});
for(auto[v,w] : edge[cur]) {
if (dist[v] > dist[cur] + w) {
dist[v] = dist[cur] + w;
q.push({dist[v], v, cur});
} else if (dist[v] <= dist[cur] + w) {
dp1[v] = min(dp1[v], dp1[cur]);
dp2[v] = min(dp2[v], dp2[cur]);
}
}
}
return dp2[(st == s ? t : s)];
}
void Semicolon() {
cin >> n >> m >> s >> t >> u >> v;
FOR(i, 1, m) {
int u,v,w;
cin >> u >> v >> w;
edge[u].pb({v,w});
edge[v].pb({u,w});
}
vector<int> dist = dijkstra(u);
swap(dist, distU);
dist = dijkstra(v);
swap(dist, distV);
// cout << getans(s) << endl;
// cout << getans(t) << endl;
int ans1 = getans(s), ans2 = getans(t);
cout << min({ans1, ans2, distU[v], distV[u]}) << endl;
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
//freopen("", "r", stdin);
//freopen("", "w", stdout);
if (fopen("input.txt", "r")) freopen("input.txt", "r", stdin);
int t = 1;
//cin >> t;
while(t--) Semicolon();
cerr << endl;
cerr << "Time elapsed: " << TIME << " s.\n ";
return (0 ^ 0);
}
