#include <bits/stdc++.h>
#define int long long
using namespace std;
struct Vertice {
int end, weight;
};
struct compare {
bool operator() (Vertice a, Vertice b) {
return a.weight < b.weight;
}
};
vector<Vertice> graph[100001];
vector<int> before[100001];
vector<int> inverseBefore[100001];
int distMin[100001], distMinU[100001], distMinV[100001], mini = 1e18;
bool vu[100001], vu2[100001];
void dfs1(int pos) {
vu[pos] = true;
for(int loop = 0; loop < before[pos].size(); ++loop) {
if(!vu[before[pos][loop]]) {
dfs1(before[pos][loop]);
}
distMinU[pos] = min(distMinU[pos], distMinU[before[pos][loop]]);
}
}
void dfs2(int pos) {
vu2[pos] = true;
for(int loop = 0; loop < inverseBefore[pos].size(); ++loop) {
if(vu[inverseBefore[pos][loop]]) {
if(!vu2[inverseBefore[pos][loop]]) {
dfs2(inverseBefore[pos][loop]);
}
distMinU[pos] = min(distMinU[pos], distMinU[inverseBefore[pos][loop]]);
}
}
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
s--;t--;u--;v--;
for(int loop = 0; loop < m; ++loop) {
int a, b, c;
cin >> a >> b >> c;
graph[a-1].push_back({b-1, c});
graph[b-1].push_back({a-1, c});
}
for(int loop = 0; loop < n; ++loop) {
distMin[loop] = 1e18;
distMinU[loop] = 1e18;
distMinV[loop] = 1e18;
}
priority_queue<Vertice, vector<Vertice>, compare> q;
q.push({s, 0});
for(int loop = 0; loop < n; ++loop) {
vu[loop] = false;
}
while(q.size() > 0) {
Vertice enCours = q.top();
q.pop();
if(vu[enCours.end]) {
continue;
}
vu[enCours.end] = true;
for(int loop = 0; loop < graph[enCours.end].size(); ++loop) {
if(distMin[graph[enCours.end][loop].end] > enCours.weight + graph[enCours.end][loop].weight) {
q.push({graph[enCours.end][loop].end, graph[enCours.end][loop].weight + enCours.weight});
before[graph[enCours.end][loop].end].clear();
before[graph[enCours.end][loop].end].push_back(enCours.end);
distMin[graph[enCours.end][loop].end] = enCours.weight + graph[enCours.end][loop].weight;
}
else if(distMin[graph[enCours.end][loop].end] == enCours.weight + graph[enCours.end][loop].weight) {
before[graph[enCours.end][loop].end].push_back(enCours.end);
}
}
}
q.push({u, 0});
for(int loop = 0; loop < n; ++loop) {
vu[loop] = false;
}
while(q.size() > 0) {
Vertice enCours = q.top();
q.pop();
if(vu[enCours.end]) {
continue;
}
vu[enCours.end] = true;
for(int loop = 0; loop < graph[enCours.end].size(); ++loop) {
if(distMinU[graph[enCours.end][loop].end] > enCours.weight + graph[enCours.end][loop].weight) {
q.push({graph[enCours.end][loop].end, enCours.weight + graph[enCours.end][loop].weight});
distMinU[graph[enCours.end][loop].end] = enCours.weight + graph[enCours.end][loop].weight;
}
}
}
q.push({v, 0});
for(int loop = 0; loop < n; ++loop) {
vu[loop] = false;
}
while(q.size() > 0) {
Vertice enCours = q.top();
q.pop();
if(vu[enCours.end]) {
continue;
}
vu[enCours.end] = true;
for(int loop = 0; loop < graph[enCours.end].size(); ++loop) {
if(distMinV[graph[enCours.end][loop].end] > enCours.weight + graph[enCours.end][loop].weight) {
q.push({graph[enCours.end][loop].end, enCours.weight + graph[enCours.end][loop].weight});
distMinV[graph[enCours.end][loop].end] = enCours.weight + graph[enCours.end][loop].weight;
}
}
}
for(int loop = 0; loop < n; ++loop) {
for(int looping = 0; looping < before[loop].size(); ++looping) {
inverseBefore[before[loop][looping]].push_back(loop);
}
}
for(int loop = 0; loop < n; ++loop) {
vu[loop] = false;
}
dfs1(t);
for(int loop = 0; loop < n; ++loop) {
vu2[loop] = false;
}
dfs2(s);
for(int loop = 0; loop < n; ++loop) {
mini = min(mini, distMinU[loop] + distMinV[loop]);
}
cout << mini << '\n';
}
