#include <bits/stdc++.h>
using namespace std;
int a,b;
int s,t;
int u,v;
vector <pair<int,int>> z[1000000];
int cnt1[1000000];
int cnt2[1000000];
int cnt[1000000][3];
int bruh=1e18;
struct node{
int nxt,val,fri;
};
vector <node> z1[200005];
vector <node> z2[200005];
struct node1{
int val1,pos1,type;
};
struct compare{
bool operator()(node1 a,node1 b){
return a.val1<b.val1;
}
};
void dijkstras(){
for (int i=1;i<=a;i++){
cnt1[i]=bruh;
}
priority_queue<pair<int,int> , vector<pair<int,int> > , greater<pair<int,int> > > q;
q.push({0,s});
cnt1[s]=0;
while (q.size()){
pair<int,int> pos=q.top();
q.pop();
int val=pos.first;
int pos1=pos.second;
if (val>cnt1[pos1]){
continue;
}
for (auto p:z[pos1]){
if (cnt1[p.first]>val+p.second){
cnt1[p.first]=val+p.second;
q.push({cnt1[p.first],p.first});
}
}
}
}
void dijkstrat(){
for (int i=1;i<=a;i++){
cnt2[i]=bruh;
}
priority_queue<pair<int,int> , vector<pair<int,int> > , greater<pair<int,int> > > q;
q.push({0,t});
cnt2[t]=0;
while (q.size()){
pair<int,int> pos=q.top();
q.pop();
int val=pos.first;
int pos1=pos.second;
if (val>cnt2[pos1]){
continue;
}
for (auto p:z[pos1]){
if (cnt2[p.first]>val+p.second){
cnt2[p.first]=val+p.second;
q.push({cnt2[p.first],p.first});
}
}
}
}
void dijkstra(){
for (int i=1;i<=a;i++){
for (int j=0;j<=2;j++){
cnt[i][j]=bruh;
}
}
priority_queue< node1 , vector <node1> , compare > q;
q.push({0,u,0});
cnt[u][0]=0;
while (q.size()){
node1 pos=q.top();
q.pop();
int val=pos.val1;
int pos1=pos.pos1;
int type=pos.type;
if (val>cnt[pos1][type]){
continue;
}
for (auto p:z1[pos1]){
if (type==0){
if (cnt[p.nxt][type]>val+p.val){
cnt[p.nxt][type]=val+p.val;
q.push({cnt[p.nxt][type],p.nxt,type});
}
if (p.fri==0){
if (cnt[p.nxt][1]>val){
cnt[p.nxt][1]=val;
q.push({cnt[p.nxt][1],p.nxt,1});
}
}
}else if (type==1){
if (p.fri==0){
if (cnt[p.nxt][1]>val){
cnt[p.nxt][1]=val;
q.push({cnt[p.nxt][1],p.nxt,1});
}
}
if (cnt[p.nxt][2]>val+p.val){
cnt[p.nxt][2]=val+p.val;
q.push({cnt[p.nxt][2],p.nxt,2});
}
}else{
if (cnt[p.nxt][type]>val+p.val){
cnt[p.nxt][type]=val+p.val;
q.push({cnt[p.nxt][type],p.nxt,type});
}
}
}
}
}
void dijkstra1(){
for (int i=1;i<=a;i++){
for (int j=0;j<=2;j++){
cnt[i][j]=bruh;
}
}
priority_queue< node1 , vector <node1> , compare > q;
q.push({0,u,0});
cnt[u][0]=0;
while (q.size()){
node1 pos=q.top();
q.pop();
int val=pos.val1;
int pos1=pos.pos1;
int type=pos.type;
if (val>cnt[pos1][type]){
continue;
}
for (auto p:z2[pos1]){
if (type==0){
if (cnt[p.nxt][type]>val+p.val){
cnt[p.nxt][type]=val+p.val;
q.push({cnt[p.nxt][type],p.nxt,type});
}
if (p.fri==0){
if (cnt[p.nxt][1]>val){
cnt[p.nxt][1]=val;
q.push({cnt[p.nxt][1],p.nxt,1});
}
}
}else if (type==1){
if (p.fri==0){
if (cnt[p.nxt][1]>val){
cnt[p.nxt][1]=val;
q.push({cnt[p.nxt][1],p.nxt,1});
}
}
if (cnt[p.nxt][2]>val+p.val){
cnt[p.nxt][2]=val+p.val;
q.push({cnt[p.nxt][2],p.nxt,2});
}
}else{
if (cnt[p.nxt][type]>val+p.val){
cnt[p.nxt][type]=val+p.val;
q.push({cnt[p.nxt][type],p.nxt,type});
}
}
}
}
}
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin >> a >> b;
cin >> s >> t;
cin >> u >> v;
for (int i=1;i<=b;i++){
int x,y,t;
cin >> x >> y >> t;
z[x].push_back({y,t});
z[y].push_back({x,t});
}
dijkstras();
dijkstrat();
//cout << cnt1[t] << "\n";
for (int i=1;i<=a;i++){
for (auto p:z[i]){
int chisoan1=-1;
int chisoan=-1;
int y=p.first;
int val=p.second;
int x=i;
if (cnt1[x]+cnt2[y]+val==cnt1[t]){
chisoan=0;
}else if (cnt1[y]+cnt2[x]+val==cnt1[t]){
chisoan1=0;
}
z2[x].push_back({y,val,chisoan1});
z1[x].push_back({y,val,chisoan});
// if (chisoan==0){
// cout << x << " " << y << "\n";
// }
}
}
dijkstra();
//cout << cnt[4][1] << "\n";
int min1=min({cnt[v][0],cnt[v][1],cnt[v][2]});
dijkstra1();
min1=min({min1,cnt[v][0],cnt[v][1],cnt[v][2]});
cout << min1;
return 0;
}
