#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target ("avx2,bmi,bmi2,popcnt,lzcnt")
using namespace std;
const int N = 100005;
vector<pair<int, long long>> graph[N];
int mark[N]={0};
long long minU[N], minV[N];
long long dv[N], dt[N], ds[N], du[N];
vector<int> opt[N];
vector<pair<long long, int>> ve;
int main()
{
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int n, m, s, t, u, v; cin >> n >> m >> s >> t >> u >> v;
for(int i = 0; i < m; i++)
{
int a, b;
long long c;
cin >> a >> b >> c;
graph[a].push_back({b, c});
graph[b].push_back({a, c});
}
priority_queue <pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
for(int i = 0; i <= n; i++)ds[i]= 1e18;
int vis[N]={0};
ds[s]=0;
pq.push({0, s});
while(!pq.empty())
{
pair<long long,int> x = pq.top();
pq.pop();
if(vis[x.second]==1)continue;
vis[x.second]=1;
for(auto i: graph[x.second])
{
if(ds[i.first] > x.first+i.second)
{
pq.push({x.first+i.second, i.first});
ds[i.first]=x.first+i.second;
}
}
}
for(int i = 0; i <= n; i++)
{
dt[i]= 1e18;
vis[i]=0;
}
dt[t]=0;
pq.push({0, t});
while(!pq.empty())
{
pair<long long,int> x = pq.top();
pq.pop();
if(vis[x.second]==1)continue;
vis[x.second]=1;
for(auto i: graph[x.second])
{
if(dt[i.first] > x.first+i.second)
{
pq.push({x.first+i.second, i.first});
dt[i.first]=x.first+i.second;
}
}
}
for(int i = 0; i <= n; i++)
{
dv[i]= 1e18;
vis[i]=0;
}
dv[v]=0;
pq.push({0, v});
while(!pq.empty())
{
pair<long long,int> x = pq.top();
pq.pop();
if(vis[x.second]==1)continue;
vis[x.second]=1;
for(auto i: graph[x.second])
{
if(dv[i.first] > x.first+i.second)
{
pq.push({x.first+i.second, i.first});
dv[i.first]=x.first+i.second;
}
}
}
for(int i = 0; i <= n; i++)
{
du[i]= 1e18;
vis[i]=0;
}
du[u]=0;
pq.push({0, u});
while(!pq.empty())
{
pair<long long,int> x = pq.top();
pq.pop();
if(vis[x.second]==1)continue;
vis[x.second]=1;
for(auto i: graph[x.second])
{
if(du[i.first] > x.first+i.second)
{
pq.push({x.first+i.second, i.first});
du[i.first]=x.first+i.second;
}
}
}
// long long rezu=1e18, rezv= 1e18;
for(int i = 1; i <= n; i++)
{
if(dt[i]+ds[i]==ds[t])
{
mark[i]=1;
}
}
for(int i = 1; i <= n; i++)
{
if(!mark[i])continue;
for(auto j: graph[i])
{
if(mark[j.first] && (ds[j.first]==ds[i]+j.second))
{
opt[i].push_back(j.first);
}
}
ve.push_back({ds[i], i});
}
sort(ve.begin(), ve.end(), greater<pair<long long, int>>());
long long rez=1e18;
for(auto i: ve)
{
minU[i.second]=du[i.second];
minV[i.second]=dv[i.second];
for(auto j: opt[i.second])
{
minU[i.second]=min(minU[i.second], minU[j]);
minV[i.second]=min(minV[i.second], minV[j]);
}
rez = min(rez, min(du[i.second]+minV[i.second],dv[i.second]+minU[i.second]));
}
cout << min(dv[u], rez) << "\n";
return 0;
}
