/*
#pragma GCC optimize("Ofast")
#pragma GCC target("avx2")
#pragma GCC optimize("unroll-loops")
*/
#include <bits/stdc++.h>
#define taskname "bai3"
#define all(x) x.begin(), x.end()
#define ll long long
#define ull unsigned ll
#define ld long double
#define pb push_back
#define ff first
#define ss second
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vi vector<int>
using namespace std;
using cd = complex<double>;
const int mxN = 1e5 + 5;
const int mod = 1e9 + 7;
const ll oo = 1e18;
int n, m, s, t, u, v;
ll dp[mxN][2][2];
vector<ll> from_u, from_v;
vector<pair<int, ll>> G[mxN];
vector<ll> dijkstra(int v) {
vector<ll> res(n + 1, oo);
vector<bool> vis(n + 1);
res[v] = 0;
priority_queue<pair<ll, int>> pq;
pq.push({0, v});
while(pq.size()) {
pair<ll, int> top = pq.top(); pq.pop();
if(vis[top.ss])
continue;
vis[top.ss] = true;
for(auto [u, w] : G[top.ss]) {
if(res[u] > res[top.ss] + w) {
res[u] = res[top.ss] + w;
pq.push({-res[u], u});
}
}
}
return res;
}
void dijkstra1(int s, int t) {
vector<ll> res(n + 1, oo);
for(int i = 1; i <= n; ++i)
dp[i][0][0] = dp[i][0][1] = dp[i][1][0] = dp[i][1][1] = oo;
vector<bool> vis(n + 1);
priority_queue<pair<ll, int>> pq;
res[s] = 0;
dp[s][0][0] = 0;
dp[s][0][1] = from_v[s];
dp[s][1][0] = from_u[s];
dp[s][1][1] = from_v[s] + from_u[s];
pq.push({0, s});
while(pq.size()) {
pair<ll, int> top = pq.top(); pq.pop();
if(vis[top.ss])
continue;
vis[top.ss] = true;
for(auto [u, w] : G[top.ss]) {
if(res[u] > res[top.ss] + w) {
res[u] = res[top.ss] + w;
pq.push({-res[u], u});
dp[u][0][1] = min(dp[top.ss][0][1], from_v[u]);
dp[u][1][0] = min(dp[top.ss][1][0], from_u[u]);
dp[u][1][1] = min({dp[top.ss][1][1], dp[top.ss][0][1] + from_u[u], dp[top.ss][1][0] + from_v[u], from_v[u] + from_u[u]});
}
else if(res[u] == res[top.ss] + w) {
dp[u][0][1] = min({dp[u][0][1], dp[top.ss][0][1], from_v[u]});
dp[u][1][0] = min({dp[u][1][0], dp[top.ss][1][0], from_u[u]});
dp[u][1][1] = min({dp[u][1][1], dp[top.ss][1][1], dp[top.ss][0][1] + from_u[u], dp[top.ss][1][0] + from_v[u], from_v[u] + from_u[u]});
}
}
}
cout << min(from_u[v], dp[t][1][1]) << "\n";
}
void solve() {
cin >> n >> m;
cin >> 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});
}
from_u = dijkstra(u);
from_v = dijkstra(v);
dijkstra1(s, t);
}
signed main() {
#ifdef CDuongg
freopen("bai3.inp", "r", stdin);
freopen("bai3.out", "w", stdout);
auto start = chrono::high_resolution_clock::now();
#endif
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int t = 1; //cin >> t;
while(t--) solve();
#ifdef CDuongg
auto end = chrono::high_resolution_clock::now();
cout << "\n"; for(int i = 1; i <= 100; ++i) cout << '=';
cout << "\nExecution time: " << chrono::duration_cast<chrono::milliseconds> (end - start).count() << "[ms]" << endl;
#endif
}
