#include<algorithm>
#include<iostream>
#include<vector>
#include<queue>
#include<set>
using namespace std;
#define ll long long
const ll maxn=100011;
const ll inf=999999999999999999;
ll n,m,s1,f1,s2,f2,ans[3][maxn],min_d[2][maxn];
vector<pair<int,int>> a[maxn];
vector<int> p[maxn],b[maxn];
void dj(ll v,ll ans_co){
priority_queue<pair<ll,int>> q;
q.push(make_pair(0,v));
while(!q.empty()){
ll cur_ans=-q.top().first;
int cur=q.top().second;
q.pop();
if(cur_ans!=ans[ans_co][cur])continue;
for(auto [to,cost] : a[cur]){
if(ans[ans_co][cur]+cost<=ans[ans_co][to]){
if(ans_co==0){
if(ans[ans_co][cur]+cost<ans[ans_co][to])p[to].clear();
if(to!=cur)p[to].push_back(cur);
}
ans[ans_co][to]=ans[ans_co][cur]+cost;
q.push(make_pair(-ans[ans_co][to],to));
}
}
}
}
void cl_ans(int v,int ans_co){
for(int i=1;i<=n;i++)ans[ans_co][i]=inf;
ans[ans_co][v]=0;
}
void go(int v,int ans_co){
cl_ans(v,ans_co);
dj(v,ans_co);
}
void build_b(int cur){
for(auto to : p[cur]){
b[to].push_back(cur);
build_b(to);
}
}
void go_b(int cur,int prev){
min_d[0][cur]=ans[0][cur];
min_d[1][cur]=ans[1][cur];
min_d[0][cur]=min(min_d[0][cur],min_d[0][prev]);
min_d[1][cur]=min(min_d[1][cur],min_d[1][prev]);
for(auto to : b[cur]){
go_b(to,cur);
}
}
ll get_ans(int cur){
ll cur_ans=min_d[0][cur]+min_d[1][cur];
//cout<<cur<<' '<<min_d[1][cur]<<'='<<min_d[2][cur]<<endl;
for(auto to : b[cur]){
cur_ans=min(cur_ans,get_ans(to));
}
return cur_ans;
}
int main(){
cin>>n>>m>>s1>>f1>>s2>>f2;
int st,ft,c;
for(int i=0;i<m;i++){
cin>>st>>ft>>c;
a[ft].push_back(make_pair(st,c));
a[st].push_back(make_pair(ft,c));
}
go(s1,0);
go(s2,1);
go(f2,2);
build_b(f1);
go_b(s1,s1);
ll final_ans=ans[1][f2];
cout<<min(get_ans(s1),final_ans)<<endl;
return 0;
}
