#include <iostream>
#include <iomanip>
#include <vector>
#include <cmath>
#include <algorithm>
#include <set>
#include <queue>
#include <map>
#include <unordered_map>
#include <stack>
#include <bitset>
#include <string>
#include <cstring>
#include <iterator>
#include <random>
#define ll long long
#define ld long double
#define inf (ll)(2*1e18)
#define sort(a) sort(a.begin(), a.end())
#define reverse(a) reverse(a.begin(), a.end())
#define pb push_back
#define endl "\n"
using namespace std;
void Dijkstra(ll start, vector<vector<pair<ll, ll>>>& a, vector<ll>& dis){
set<pair<ll, ll>> s;
dis[start] = 0;
s.insert({0, start});
while(!s.empty()){
auto [val, x] = *s.begin();
s.erase(s.begin());
for(auto [el, w]: a[x]){
if(dis[el] > val + w){
s.erase({dis[el], el});
dis[el] = val + w;
s.insert({dis[el], el});
}
}
}
}
void solve(){
ll n, m, i, start, finish, u, v, x, y, w;
cin>>n>>m;
cin>>start>>finish;
cin>>u>>v;
--start;
--finish;
--u;
--v;
vector<vector<pair<ll, ll>>> a(n);
vector<ll> b(n, inf);
vector<ll> b2(n, inf);
vector<ll> c(n, inf);
vector<ll> c2(n, inf);
vector<ll> dis(n, inf);
for(i=0;i<m;++i){
cin>>x>>y>>w;
--x;
--y;
a[x].pb({y, w});
a[y].pb({x, w});
}
Dijkstra(u, a, b);
Dijkstra(v, a, c);
set<pair<ll, ll>> s;
dis[start] = 0;
s.insert({0, start});
b2[start] = b[start];
c2[start] = c[start];
while(!s.empty()){
x = s.begin()->second;
s.erase(s.begin());
for(auto el: a[x]){
y = el.first;
w = el.second;
if(dis[y] > dis[x] + w){
b2[y] = min(b[y], b2[x]);
c2[y] = min(c[y], c2[x]);
s.erase({dis[y], y});
dis[y] = dis[x] + w;
s.insert({dis[y], y});
}else if(dis[y] == dis[x] + w){
if(b2[y] + c2[y] > min(b[y], b2[x]) + min(c[y], c2[x])){
b2[y] = min(b[y], b2[x]);
c2[y] = min(c[y], c2[x]);
}
}
}
}
cout<<min(b2[finish] + c2[finish], b[v])<<endl;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
srand(time(nullptr));
ll t=1;
// cin>>t;
for(;t>0;--t){
solve();
}
return 0;
}
