#include <bits/stdc++.h>
// #include <ext/rope>
// #include <ext/pb_ds/assoc_container.hpp>
// using namespace __gnu_pbds;
// using namespace __gnu_cxx;
using namespace std;
// #define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
#define ll long long
#define ull unsigned long long
#define ld long double
#define pb push_back
#define bit(mask, i) ((mask >> i) & 1)
#define el '\n'
#define F first
#define S second
template <class X, class Y> bool maximize(X &x, const Y &y) { return (x < y ? x = y, 1 : 0); }
template <class X, class Y> bool minimize(X &x, const Y &y) { return (x > y ? x = y, 1 : 0); }
const int INF = 1e9;
const ll LINF = 1e18;
const int MOD = 1e9 + 7;
const int MULTI = 0;
const ld eps = 1e-9;
const int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0}; // R D L U
const int ddx[4] = {-1, 1, 1, -1}, ddy[4] = {1, 1, -1, -1}; // UR DR DL UL
const char cx[4] = {'R', 'D', 'L', 'U'};
const ll base = 31;
const int nMOD = 2;
const ll mods[] = {(ll)1e9 + 10777, (ll)1e9 + 19777, (ll)1e9 + 3, (ll)1e9 + 3777};
const int maxn = 1e5 + 5;
int n, m, s, t, u, v;
ll dp[2][maxn], distS[maxn], res;
vector<ll> distU, distV;
vector<pair<int, int>> adj[maxn];
void dijkstra1(int s, vector<ll> &dist) {
dist.assign(n + 1, LINF);
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
dist[s] = 0; pq.push(make_pair(0, s));
while (!pq.empty()) {
auto top = pq.top(); pq.pop();
ll d = top.F;
int u = top.S;
if (dist[u] != d) continue;
for (auto g: adj[u]) {
int v = g.F, w = g.S;
if (minimize(dist[v], dist[u] + w))
pq.push(make_pair(dist[v], v));
}
}
}
void dijkstra2(int s, int t) {
fill(dp[0] + 1, dp[0] + 1 + n, LINF);
fill(dp[1] + 1, dp[1] + 1 + n, LINF);
fill(distS + 1, distS + 1 + n, LINF);
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
pq.push(make_pair(0, s)); distS[s] = 0;
dp[0][s] = distU[s];
dp[1][s] = distV[s];
while (!pq.empty()) {
auto top = pq.top(); pq.pop();
ll d = top.F;
int u = top.S;
if (distS[u] != d) continue;
for (auto g: adj[u]) {
int v = g.F, w = g.S;
if (distS[v] > d + w) {
distS[v] = d + w;
pq.push(make_pair(distS[v], v));
dp[0][v] = min(distU[v], dp[0][u]);
dp[1][v] = min(distV[v], dp[1][u]);
} else if (distS[v] == d + w) {
if (min(distU[v], dp[0][u]) + min(distV[v], dp[1][u]) <= dp[0][v] + dp[1][v]) {
dp[0][v] = min(distU[v], dp[0][u]);
dp[1][v] = min(distV[v], dp[1][u]);
}
}
}
}
minimize(res, dp[0][t] + dp[1][t]);
}
void solve() {
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1, u, v, w; i <= m; ++i) {
cin >> u >> v >> w;
adj[u].push_back(make_pair(v, w));
adj[v].push_back(make_pair(u, w));
}
dijkstra1(u, distU);
dijkstra1(v, distV);
res = distU[v];
dijkstra2(s, t);
dijkstra2(t, s);
cout << res;
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
if (!MULTI) solve();
else {
int test; cin >> test;
while (test--) solve();
}
return 0;
}
