#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define fi first
#define se second
#define p(x,y) pair<ll,ll>(x,y)
#define BIT(i,x) ((x>>i)&1)
#define MASK(x) (1<<x)
#define ld long double
#define __builtin_popcount __builtin_popcountll
#define pll pair<ll,ll>
template<class T1,class T2>
bool maximize(T1 &x,const T2 &y)
{
if(x<y)
{
x=y;
return 1;
}
return 0;
}
template<class T1,class T2>
bool minimize(T1 &x,const T2 &y)
{
if(x>y)
{
x=y;
return 1;
}
return 0;
}
void online()
{
std::ios_base::sync_with_stdio(0);
cin.tie(0);
#ifndef ONLINE_JUDGE
freopen("input.inp", "r", stdin);
freopen("output.out","w", stdout);
#else
#endif
}
const ll N=1e5+10;
vector<pll> gr[N];
ll f[N],n,m,s,t,x,y,U[2*N],V[2*N],C[2*N],f1[N];
int main()
{
online();
cin>>n>>m>>s>>t>>x>>y;
for(int i=1;i<=m;i++)
{
ll u,v,c;
cin>>u>>v>>c;
U[i]=u;
V[i]=v;
C[i]=c;
gr[u].emplace_back(v,c);
gr[v].emplace_back(u,c);
}
memset(f,0x3f,sizeof f);
f[s]=0;
priority_queue<pll,vector<pll>,greater<pll> > qq;
qq.emplace(0,s);
while(!qq.empty())
{
auto [d,u]=qq.top();
qq.pop();
if(f[u]!=d) continue;
for(auto [v,c]:gr[u])
{
if(minimize(f[v],d+c)) qq.emplace(f[v],v);
}
}
memset(f1,0x3f,sizeof f1);
f1[t]=0;
qq.emplace(0,t);
while(!qq.empty())
{
auto [d,u]=qq.top();
qq.pop();
if(f1[u]!=d) continue;
for(auto [v,c]:gr[u])
{
if(minimize(f1[v],d+c)) qq.emplace(f1[v],v);
}
}
for(int i=1;i<=m;i++)
{
if(f[U[i]]+C[i]+f1[V[i]]==f[t])
{
if(f[U[i]]<f[V[i]])
gr[U[i]].emplace_back(V[i],0);
else
gr[V[i]].emplace_back(U[i],0);
}
}
memset(f,0x3f,sizeof f);
f[x]=0;
qq.emplace(0,x);
while(!qq.empty())
{
auto [d,u]=qq.top();
qq.pop();
if(f[u]!=d) continue;
for(auto [v,c]:gr[u])
{
if(minimize(f[v],d+c)) qq.emplace(f[v],v);
}
}
ll ans=f[y];
memset(f,0x3f,sizeof f);
f[y]=0;
qq.emplace(0,y);
while(!qq.empty())
{
auto [d,u]=qq.top();
qq.pop();
if(f[u]!=d) continue;
for(auto [v,c]:gr[u])
{
if(minimize(f[v],d+c)) qq.emplace(f[v],v);
}
}
minimize(ans,f[x]);
cout<<ans;
}
