#include<bits/stdc++.h>
using namespace std;
vector<pair<int,int>> graf[100005];
vector<int> dag[100005];
bool odw[100005];
long long odl[100005][3];
bool czy[100005];
long long dp[100005];
long long dp1[100005];
int topo[100005];
void dij(long long x,long long y,long long n)
{
for(long long i = 1;i <= n;++i)
{
odl[i][y] = 1e18;
}
priority_queue<pair<long long,long long>> kol;
odl[x][y] = 0;
kol.push({0,x});
long long a,b;
while(kol.size())
{
a = -kol.top().first;
b = kol.top().second;
kol.pop();
if(odl[b][y] == a)
{
for(pair<long long,long long> i : graf[b])
{
if(odl[i.first][y] > a+i.second)
{
odl[i.first][y] = a+i.second;
kol.push({-(a+i.second),i.first});
}
}
}
}
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
long long n,m,u,t,s,v,a,b,c;
cin >> n >> m >> s >> t >> u >> v;
for(long long i = 0;i < m;++i)
{
cin >> a >> b >> c;
graf[a].push_back({b,c});
graf[b].push_back({a,c});
}
dij(s,0,n);
queue<long long> kol;
kol.push(t);
czy[t] = 1;
//set<pair<int,int>> cz;
while(kol.size())
{
a = kol.front();
kol.pop();
for(pair<long long,long long> i : graf[a])
{
if(odl[a][0]-i.second == odl[i.first][0])
{
dag[i.first].push_back(a);
//topo[a]++;
if(!czy[i.first])
{
czy[i.first]=true;
kol.push(i.first);
}
}
}
}
for(long long i = 1;i <= n;++i)
{
dp[i] = 1e18;
dp1[i] = 1e18;
for(int j : dag[i])
{
topo[j]++;
//cout << i << ' ' << j.first << endl;
}
}
dij(u,1,n);
dij(v,2,n);
kol.push(s);
long long wyn = 1e18;
while(kol.size())
{
a = kol.front();
kol.pop();
dp[a] = min(dp[a],odl[a][1]);
dp1[a] = min(dp1[a],odl[a][2]);
wyn = min(wyn,dp[a]+odl[a][2]);
wyn = min(wyn,dp1[a]+odl[a][1]);
for(int i : dag[a])
{
topo[i]--;
dp[i] = min(dp[i],dp[a]);
dp1[i] = min(dp1[i],dp1[a]);
if(topo[i] == 0)
{
kol.push(i);
}
}
}
/*for(long long i = 1;i <= n;++i)
{
cout << odl[i][1] << ' ';
}
cout << endl;
for(long long i = 1;i <= n;++i)
{
cout << odl[i][2] << ' ';
}cout << endl;
for(long long i = 1;i <= n;++i)
{
cout << dp[i] << ' ';
}cout << endl;*/
cout << min(wyn,odl[u][2]);
/*for(long long i = 1;i <= n;++i)
{
if(czy[i] == 1)
{
for(pair<long long,long long> j : graf[i])
{
if(czy[j.first] == 1)
{
dag[i].push_back(j);
dag[j.first].push_back({i,j.second});
}
}
}
}*/
}
