#include <iostream>
#include <iomanip>
#include <vector>
#include <cmath>
#include <algorithm>
#include <set>
#include <queue>
#include <map>
#include <stack>
#include <bitset>
#include <string>
#include <cstring>
#include <iterator>
#include <random>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef long double ld;
const ll dim = 5*1e6+7;
//const ll mod = 1e9 + 7;
const ll inf = 1e18 + 77;
#define endl "\n"
#define fi first
#define pb push_back
#define se second
#define vll vector<ll>
ll n, m;
vector<pll> a[dim];
ll dst1[dim], dst2[dim], dst3[dim], dst11[dim], dst22[dim];
int main() {
ll k, s, t, u0, v0;
cin>>n>>m;
cin>>s>>t;
cin>>u0>>v0;
for(int i=1; i<=m; i++){
ll x, y, w;
cin>>x>>y>>w;
a[x].pb({y, w});
a[y].pb({x, w});
}
priority_queue<pll, vector<pll>, greater<pll>> q;
for(int i=1; i<=n; i++){
dst1[i]=inf;
dst2[i]=inf;
dst3[i]=inf;
dst11[i]=inf;
dst22[i]=inf;
}
dst1[u0]=0;
q.push({0, u0});
while(q.size()>0){
ll v=q.top().se;
// cout<<v<<endl;
q.pop();
for(auto x: a[v]){
if(dst1[x.fi]>dst1[v]+x.se){
dst1[x.fi]=dst1[v]+x.se;
q.push({dst1[x.fi], x.fi});
}
}
}
// cout<<dst1[6]<<endl;
q.push({0, v0});
dst2[v0]=0;
while(q.size()>0){
ll v=q.top().se;
q.pop();
for(auto x: a[v]){
if(dst2[x.fi]>dst2[v]+x.se){
dst2[x.fi]=dst2[v]+x.se;
q.push({dst2[x.fi], x.fi});
}
}
}
// cout<<dst2[1]<<endl;
q.push({0, s});
dst3[s]=0;
dst11[s]=dst1[s];
dst22[s]=dst2[s];
while(q.size()>0){
ll v=q.top().se;
q.pop();
for(auto x: a[v]){
ll w=x.se;
if(dst3[x.fi]==dst3[v]+w){
if(dst22[x.fi] + dst11[x.fi]>=min(dst1[x.fi], dst11[v])+ min(dst2[x.fi], dst22[v])) {
dst11[x.fi] = min(dst1[x.fi], dst11[v]);
dst22[x.fi] = min(dst2[x.fi], dst22[v]);
}
}
else if(dst3[x.fi]>dst3[v]+w){
dst3[x.fi]=dst3[v]+w;
q.push({dst3[x.fi], x.fi});
dst11[x.fi]=min(dst1[x.fi], dst11[v]);
dst22[x.fi]=min(dst2[x.fi], dst22[v]);
}
}
}
cout<<min(dst11[t]+dst22[t], dst1[v0])<<endl;
return 0;
}
