#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
typedef long long ll;
using namespace __gnu_pbds;
using namespace std;
template <typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
ll M = 100'010;
vector<vector<vector<pair<pair<ll, ll>, ll>>>> g(4, vector<vector<pair<pair<ll, ll>, ll>>>(M));
vector<pair<pair<ll, ll>, ll>> edges;
ll inf = 3e15;
vector<vector<ll>> dijkstra(ll s) {
vector<vector<ll>> dist(4, vector<ll>(M, inf));
dist[0][s] = 0;
priority_queue<pair<ll, pair<ll, ll>>> pq;
pq.push({0, {s, 0}});
while(pq.size()) {
auto[dv, stat] = pq.top(); pq.pop();
auto[v, msk] = stat;
dv *= -1;
if(dist[msk][v]!=dv) continue;
for(auto[sr, w] : g[msk][v]) {
auto[u, msk2] = sr;
if(dist[msk2][u] > dv + w) {
dist[msk2][u] = dv + w;
pq.push({-dv-w, {u, msk2}});
}
}
}
return dist;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
ll n, m;
cin >> n >> m;
ll s, t, u, v;
cin >> s >> t >> u >> v;
for(ll i=0; i<m; ++i) {
ll a, b, c;
cin >> a >> b >> c;
edges.push_back({{a, b}, c});
g[0][a].push_back({{b, 0}, c});
g[0][b].push_back({{a, 0}, c});
}
vector<ll> distS = dijkstra(s)[0];
vector<ll> distT = dijkstra(t)[0];
ll ans = distS[t];
for(auto[e, d] : edges) {
auto[a, b] = e;
if(distS[a] + d + distT[b] == ans) {
g[0][a].push_back({{b, 1}, 0});
g[1][a].push_back({{b, 1}, 0});
g[0][b].push_back({{a, 2}, 0});
g[2][b].push_back({{a, 2}, 0});
} else if(distS[b] + d + distT[a] == ans) {
g[0][b].push_back({{a, 1}, 0});
g[1][b].push_back({{a, 1}, 0});
g[0][a].push_back({{b, 2}, 0});
g[2][a].push_back({{b, 2}, 0});
}
g[3][a].push_back({{b, 3}, d});
g[3][b].push_back({{a, 3}, d});
g[1][a].push_back({{b, 3}, d});
g[1][b].push_back({{a, 3}, d});
g[2][a].push_back({{b, 3}, d});
g[2][b].push_back({{a, 3}, d});
}
for(ll msk=1; msk<3; ++msk) {
for(ll i=1; i<=n; ++i) {
g[msk][i].push_back({{i, 3}, 0});
}
}
vector<vector<ll>> dist = dijkstra(u);
ans = inf;
for(ll i=0; i<4; ++i) ans = min(ans, dist[i][v]);
cout << ans << "\n";
return 0;
}
