#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<ll, ll>;
int n, m, s, t, uu, vv, x, y, z;
int main() {
scanf("%d %d %d %d %d %d", &n, &m, &s, &t, &uu, &vv);
vector<vector<pii>> v(n + 5, vector<pii>());
vector<ll> d(n + 5, 1e18), d2(n + 5, 1e18), d3(n + 5, 1e18);
vector<vector<ll>> dp(2, vector<ll>(n + 5));
vector<bool> f(n + 5);
ll ans = 1e18;
for (int i = 0; i < m; i++) {
scanf("%d %d %d", &x, &y, &z);
v[x].emplace_back(y, z);
v[y].emplace_back(x, z);
}
auto dijk = [&] (int st, vector<ll> &dist) {
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.emplace(dist[st] = 0, st);
while (!pq.empty()) {
auto [nd, nn] = pq.top(); pq.pop();
for (auto &[tn, td]: v[nn]) {
if (dist[tn] > dist[nn] + td) pq.emplace(dist[tn] = dist[nn] + td, tn);
}
}
};
auto dfs = [&] (auto &&dfs, int cur, int par) -> void {
if (f[cur]) return; f[cur] = 1;
dp[0][cur] = d[cur];
dp[1][cur] = d2[cur];
for (auto &[x, y]: v[cur]) {
if (par == x || d3[cur] != d3[x] + y) continue;
dfs(dfs, x, cur);
dp[0][cur] = min(dp[0][cur], dp[0][x]);
dp[1][cur] = min(dp[1][cur], dp[1][x]);
}
ans = min(ans, dp[0][cur] + d2[cur]);
ans = min(ans, dp[1][cur] + d[cur]);
};
dijk(uu, d);
dijk(vv, d2);
ans = min(ans, d[vv]);
dijk(s, d3);
dfs(dfs, t, 0);
printf("%lld", ans);
}
