#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define fi first
#define se second
ll N, M, S, T, U, V;
struct edge {
ll v, w, f;
edge() {
v = 0;
w = 0;
f = 0;
}
edge(ll v_, ll w_, ll f_) {
v = v_;
w = w_;
f = f_;
}
};
vector<edge> GR[100007];
ll dist[100007], visited[100007];
ll DP[100007][3], DPvisited[100007][3];
int main() {
ios_base :: sync_with_stdio(0);
cin.tie(0); cout.tie(0); cerr.tie(0);
if (fopen("test.inp", "r")) {
freopen("test.inp", "r", stdin);
freopen("test.out", "w", stdout);
}
cin >> N >> M >> S >> T >> U >> V;
for(int i = 1; i <= M; ++i) {
ll u, v, c;
cin >> u >> v >> c;
GR[u].push_back(edge(v, c, 0));
GR[v].push_back(edge(u, c, 0));
}
struct cmp {
bool operator () (ll x1, ll x2) {
return dist[x1] > dist[x2];
}
};
for(int i = 0; i <= N + 3; ++i) dist[i] = 1e18;
dist[S] = 0;
priority_queue<ll, vector<ll>, cmp> heap;
heap.push(S);
while(!heap.empty()) {
ll u = heap.top();
heap.pop();
if (visited[u]) continue;
visited[u] = 1;
for(auto tmp : GR[u]) {
ll v = tmp.v;
ll w = tmp.w;
if (dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
heap.push(v);
}
}
}
//for(int i = 1; i <= N; ++i) cerr << dist[i] << " "; cerr << '\n';
//coloring
set<pair<ll, ll>> chosen;
auto dfs = [&](auto&& self, ll u) -> void {
for(auto tmp : GR[u]) {
ll v = tmp.v;
ll w = tmp.w;
if (dist[v] == dist[u] - w) {
chosen.insert({u, v});
self(self, v);
}
}
};
dfs(dfs, T);
for(int i = 1; i <= N; ++i) {
for(auto& tmp : GR[i]) {
if (chosen.count({i, tmp.v}) || chosen.count({tmp.v, i})) {
tmp.f = 1;
}
if (tmp.f == 1) {
//cerr << "f1: " << i << " " << tmp.v << '\n';
}
}
}
//calc dp U to V
struct cmp2 {
bool operator () (pair<ll, ll>& x1, pair<ll, ll>& x2) {
return DP[x1.fi][x1.se] > DP[x2.fi][x2.se];
}
};
priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, cmp2> heap2;
for(int i = 0; i <= N + 2; ++i) DP[i][0] = DP[i][1] = DP[i][2] = 1e18;
DP[U][0] = 0;
heap2.push({U, 0});
while(!heap2.empty()) {
auto tmp = heap2.top();
heap2.pop();
ll u = tmp.fi;
ll s = tmp.se;
if (DPvisited[u][s]) continue;
DPvisited[u][s] = 1;
// cerr << u << " " << s << " " << DP[u][s] << '\n';
for(auto tmp2 : GR[u]) {
ll v = tmp2.v;
ll w = tmp2.w;
ll f = tmp2.f;
if (s == 0) {
if (DP[v][0] > DP[u][0] + w) {
DP[v][0] = DP[u][0] + w;
heap2.push({v, 0});
}
if (f == 1 && DP[v][1] > DP[u][0]) {
DP[v][1] = DP[u][0];
heap2.push({v, 1});
}
}
if (s == 1) {
if (f == 1 && dist[v] == dist[u] + w && DP[v][1] > DP[u][1]) {
DP[v][1] = DP[u][1];
heap2.push({v, 1});
}
if (DP[v][2] > DP[u][1] + w) {
DP[v][2] = DP[u][1] + w;
heap2.push({v, 2});
}
}
if (s == 2) {
if (DP[v][2] > DP[u][2] + w) {
DP[v][2] = DP[u][2] + w;
heap2.push({v, 2});
}
}
}
}
cout << min({DP[V][0], DP[V][1], DP[V][2]});
}
