#include <iostream>
#include <vector>
#include <set>
#include <tuple>
using namespace std;
using ll = long long;
const ll INF = 1e15;
int n, m, s, t, x, y;
vector<vector<pair<int, ll>>> g;
vector<ll> sssp(int start) {
vector<ll> d(n, INF);
set<pair<ll, int>> q;
d[start] = 0;
q.insert({0, start});
while (not q.empty()) {
auto [dist, u] = *q.begin();
q.erase(q.begin());
for (auto [v, w] : g[u]) {
if (d[u] + w < d[v]) {
q.erase({d[v], v});
d[v] = d[u] + w;
q.insert({d[v], v});
}
}
}
return d;
}
ll solve(vector<ll> ds, vector<ll> dt, vector<ll> to_x, vector<ll> to_y) {
ll ans = to_x[y];
vector<tuple<ll, ll, ll>> dp(n);
for (int u = 0; u < n; u++) {
auto &[dist, from_x, from_y] = dp[u];
dist = (u == s ? 0 : INF);
from_x = to_x[u];
from_y = to_y[u];
}
set<tuple<ll, ll, ll, int>> q;
q.insert({0, to_x[s], to_y[s], s});
while (not q.empty()) {
auto [dist, from_x, from_y, u] = *q.begin();
q.erase(q.begin());
if (ds[t] == ds[u] + dt[u]) ans = min(ans, min(from_x + to_y[u], from_y + to_x[u]));
for (auto [v, w] : g[u]) {
auto &[dist_v, from_x_v, from_y_v] = dp[v];
if (dist + w < dist_v) {
q.erase({dist_v, from_x_v, from_y_v, v});
dist_v = dist + w;
from_x_v = min(to_x[v], from_x);
from_y_v = min(to_y[v], from_y);
q.insert({dist_v, from_x_v, from_y_v, v});
} else if (dist + w == dist_v) {
q.erase({dist_v, from_x_v, from_y_v, v});
from_x_v = min(from_x_v, from_x);
from_y_v = min(from_y_v, from_y);
q.insert({dist_v, from_x_v, from_y_v, v});
}
}
}
return ans;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin >> n >> m >> s >> t >> x >> y;
s--, t--, x--, y--;
g.resize(n);
while (m--) {
int a, b;
ll w;
cin >> a >> b >> w;
a--, b--;
g[a].push_back({b, w});
g[b].push_back({a, w});
}
cout << solve(sssp(s), sssp(t), sssp(x), sssp(y)) << '\n';
return 0;
}
