#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
#define ff first
#define ss second
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define lb lower_bound
#define ub upper_bound
#define setbits(x) __builtin_popcountll(x)
#define zrobits(x) __builtin_ctzll(x)
#define sz(v) (int)v.size()
#define ps(y) cout << fixed << setprecision(y)
#define ms(arr, v) memset(arr, v, sizeof(arr))
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define trav(x, v) for(auto &x: v)
#define w(t) int t; cin >> t; while(t--)
#define rep(i, a, b) for(int i = a; i <= b; i++)
#define rrep(i, a, b) for(int i = a; i >= b; i--)
#define rep0(i, n) rep(i, 0, n - 1)
#define rrep0(i, n) rrep(i, n - 1, 0)
#define rep1(i, n) rep(i, 1, n)
#define rrep1(i, n) rrep(i, n, 1)
#define inp(arr, n) rep0(i, n) cin >> arr[i];
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll, ll> pii;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<bool> vb;
typedef vector<string> vs;
typedef map<ll, ll> mii;
typedef map<char, ll> mci;
typedef priority_queue<ll> pq_mx;
typedef priority_queue<pii, vp, greater<>> pq_mn;
typedef tree<ll, null_type, less<>, rb_tree_tag, tree_order_statistics_node_update> pbds;
/*
* find_by_order(i) -> returns an iterator to the element at ith position (0 based)
* order_of_key(i) -> returns the position of element i (0 based)
*/
const int N = 2e5 + 5;
const int mod = 1e9 + 7;
//const int mod = 998244353;
const ll inf = 1e18;
const double eps = 1e-10;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
void fio() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
}
int n, m, S, T, U, V;
ll dp[2][N], res;
vi du, dv;
vp gr[N];
vi dijkstra(int src) {
vi dist(n + 1, inf);
dist[src] = 0;
set<pii> q;
q.emplace(0, src);
while (!q.empty()) {
auto[d, cur] = *q.begin();
q.erase(q.begin());
trav(neigh, gr[cur]) {
if (dist[neigh.ff] > d + neigh.ss) {
auto it = q.find({dist[neigh.ff], neigh.ff});
if (it != q.end()) q.erase(it);
dist[neigh.ff] = d + neigh.ss, q.emplace(dist[neigh.ff], neigh.ff);
}
}
}
return dist;
}
void f(ll s, ll e) {
rep0(i, 2) {
rep1(x, n) dp[i][x] = inf;
}
vi dist(n + 1, inf);
pq_mn q;
q.emplace(0, s), dist[s] = 0, dp[0][s] = du[s], dp[1][s] = dv[s];
while (!q.empty()) {
auto[d, cur] = q.top();
q.pop();
if (dist[cur] < d) continue;
trav(neigh, gr[cur]) {
if (dist[neigh.ff] > d + neigh.ss) {
dist[neigh.ff] = d + neigh.ss, q.emplace(dist[neigh.ff], neigh.ff);
dp[0][neigh.ff] = min(du[neigh.ff], dp[0][cur]);
dp[1][neigh.ff] = min(dv[neigh.ff], dp[1][cur]);
} else if (dist[neigh.ff] == d + neigh.ss and
min(du[neigh.ff], dp[0][cur]) + min(dv[neigh.ff], dp[1][cur]) <
dp[0][neigh.ff] + dp[1][neigh.ff]) {
dp[0][neigh.ff] = min(du[neigh.ff], dp[0][cur]);
dp[1][neigh.ff] = min(dv[neigh.ff], dp[1][cur]);
}
}
}
res = min(res, dp[0][e] + dp[1][e]);
}
int main() {
fio();
cin >> n >> m >> S >> T >> U >> V;
rep0(x, m) {
int u, v, w;
cin >> u >> v >> w;
gr[u].eb(v, w), gr[v].eb(u, w);
}
du = dijkstra(U), dv = dijkstra(V);
res = du[V];
f(S, T), f(T, S);
cout << res;
return 0;
}
