#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pi;
#ifdef DEBUG
#define D(x...) printf(x);
#else
#define D(x...)
#endif
const ll MAXN = 1e5 + 5;
const ll INF = 1ll<<62;
ll N,M,S,T,U,V,D[MAXN],vis[MAXN];
vector<pi> edge[MAXN];
vector<ll> succ[MAXN], pred[MAXN];
void dfs(int i){
vis[i] = 1;
if(i == S) return;
for(auto e : edge[i]){
if(D[e.first] + e.second == D[i]){
succ[e.first].push_back(i);
pred[i].push_back(e.first);
if(!vis[e.first]) dfs(e.first);
}
}
}
int main(){
cin >> N >> M >> S >> T >> U >> V;
for(int i = 0; i < M; i++){
ll ai, bi, ci;
cin >> ai >> bi >> ci;
edge[bi].push_back({ai, ci});
edge[ai].push_back({bi, ci});
}
priority_queue<pi, vector<pi>, greater<pi>> pq;
fill(begin(D), end(D), INF);
D[S] = 0;
pq.push({0, S});
while(!pq.empty()){
pi t = pq.top(); pq.pop();
if(t.first != D[t.second]) continue;
if(t.second == T) break;
for(auto e : edge[t.second]){
if(D[t.second] + e.second < D[e.first]){
pq.push({D[e.first] = D[t.second] + e.second, e.first});
}
}
}
dfs(T);
using ti = tuple<ll,ll,ll>;
priority_queue<ti, vector<ti>, greater<ti>> pq2;
fill(begin(D), end(D), INF);
D[U] = 0;
pq2.push({0, U, 0});
while(!pq2.empty()){
ti t = pq2.top(); pq2.pop();
ll dist = get<0>(t), curr = get<1>(t), state = get<2>(t);
D("%d %d %d\n", dist, curr, state);
if(dist != D[curr]) continue;
if(curr == V) break;
if(state != -1){
for(auto e : succ[curr]){
if(dist < D[e]){
pq2.push({D[e] = dist, e, 1});
}
}
for(auto e : edge[curr]){
if(dist + e.second < D[e.first]){
pq2.push({D[e.first] = dist + e.second, e.first, -state});
}
}
}else{
for(auto e : edge[curr]){
if(dist + e.second < D[e.first]){
pq2.push({D[e.first] = dist + e.second, e.first, -1});
}
}
}
}
ll ans = D[V];
pq2 = priority_queue<ti, vector<ti>, greater<ti>>();
fill(begin(D), end(D), INF);
D[U] = 0;
pq2.push({0, U, 0});
while(!pq2.empty()){
ti t = pq2.top(); pq2.pop();
ll dist = get<0>(t), curr = get<1>(t), state = get<2>(t);
if(dist != D[curr]) continue;
if(curr == V) break;
if(state != -1){
for(auto e : pred[curr]){
if(dist < D[e]){
pq2.push({D[e] = dist, e, 1});
}
}
for(auto e : edge[curr]){
if(dist + e.second < D[e.first]){
pq2.push({D[e.first] = dist + e.second, e.first, -state});
}
}
}else{
for(auto e : edge[curr]){
if(dist + e.second < D[e.first]){
pq2.push({D[e.first] = dist + e.second, e.first, -1});
}
}
}
}
cout << min(ans, D[V]) << "\n";
}
