#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#define vi vector<int>
#define ve vector
#define ll long long
#define vl vector<ll>
#define vll vector<pair<ll,ll>>
#define onbit __builtin_popcount
#define ii pair<int,int>
#define vvi vector<vi>
#define vii vector<ii>
#define gii greater<ii>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define INF 1e18
#define eps 1e-7
#define eps1 1e-2
#define optimise ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define MAX_A 1e5+5
using namespace std;
using namespace __gnu_pbds;
template <class T>
using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const int MOD = 1e9+7;
const int nax = 1e5+5;
const int MAX_VAL = 1e6;
double PI=3.14159265359;
int arx[8]={1,1,0,-1,-1,-1, 0, 1};
int ary[8]={0,1,1, 1, 0,-1,-1,-1};
typedef complex<int> Point;
#define X real()
#define Y imag()
void setIO(string s) {
freopen((s + ".in").c_str(), "r", stdin);
freopen((s + ".out").c_str(), "w", stdout);
}
vector<pair<int,int>> adj[nax];
bool vis[nax];
ll dis[nax];
vector<set<int>> cyc(nax);
vector<set<int>> cyc2(nax);
bool bahma[nax];
int s,t,u,v;
void sp(int k)
{
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<>> pq;
pq.push({0,k});
dis[k]=0;
while(!pq.empty())
{
int x=pq.top().fi;
int y=pq.top().se;
pq.pop();
for(auto i:adj[y])
{
int d=i.se;
int node=i.fi;
if (dis[node]<dis[y]+d) continue;
else if(dis[node]==dis[y]+d){
cyc[node].insert(y);
continue;
}else{
dis[node]=dis[y]+d;
pq.push({dis[node],node});
cyc[node].clear();
cyc[node].insert(y);
}
}
}return;
}
bool dfs(int x)
{
//cout << x<<endl;
if (x==s) {
return true;
}
bool test=false;
for(auto i:cyc[x])
{
if (vis[i]) continue;
vis[i]=true;
if (dfs(i)){
//cout << i<<endl;
cyc2[x].insert(i);
cyc2[i].insert(x);
test=true;
bahma[i]=true;
}
}return test;
}
int bfs(int x)
{
if(x==t||x==s) return 1;
int res=0;
for(auto i:adj[x])
{
if (cyc[i.fi].count(x)) continue;
if (vis[i.fi])continue;
vis[i.fi]=1;
res+=bfs(i.fi);
}
return res;
}
int main(){
optimise;
/*#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif*/
//setIO("pump");
int n,m;
cin>>n>>m;
for (int i = 0; i < n; ++i)
{
dis[i]=1e18;
}
cin>>s>>t>>u>>v;
s--;t--;u--;v--;
for (int i = 0; i < m; ++i)
{
int x,y,z;
cin>>x>>y>>z;
x--;y--;
adj[x].pb({y,z});
adj[y].pb({x,z});
}
bahma[t]=1;
sp(s);
dfs(t);
bool sum=false;
if (bahma[u]||bahma[v]) sum=true;
memset(vis,0,sizeof vis);
int k=bfs(s);
if (k==1)sum=true;
for (int i = 0; i < n; ++i)
{
dis[i]=1e18;
}
if (sum)
{
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<>> pq;
pq.push({0,u});
dis[u]=0;
while(!pq.empty())
{
int x=pq.top().fi;
int y=pq.top().se;
//cout << y<<endl;
pq.pop();
for(auto i:adj[y])
{
int d=i.se;
int node=i.fi;
if(cyc2[node].count(y)){
d=0;
}
//cout <<y<<" "<<node<<" "<<dis[node]<<" "<<dis[y]+d<<endl;
if(dis[node]<=dis[y]+d)continue;
dis[node]=dis[y]+d;
pq.push({dis[node],node});
}
}
//cout << v<<endl;
cout << dis[v]<<endl;
}else{
}
}
