/*
* @Author: MaxPhast
* @File: test.cpp
* @Date: 2025-11-05 14:31:40
*/
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ii pair <int , int>
#define iii pair <int , ii>
#define iiii pair <ii , ii>
#define FOR(i , l , r) for(int i = (l) , _r = (r) ; i <= _r ; ++ i)
#define FORD(i , r , l) for(int i = (r) , _l = (l) ; i >= _l ; -- i)
#define ALL(vec) vec.begin() , vec.end()
#define UNI(vec) sort(ALL(vec)) , vec.erase(unique(ALL(vec)) , vec.end())
#define pb push_back
#define MASK(i) (1ll << i)
#define BIT(mask , i) ((mask >> i) & 1ll)
#define ON(mask , i) (mask | MASK(i))
#define OFF(mask , i) (mask & (~MASK(i)))
#define TURN(mask , i) (mask ^ MASK(i))
#define BP(mask) __builtin_popcountll(mask)
#define sqr(x) (1ll * (x) * (x))
#define fi first
#define se second
#define oo 1e18
#define time() cerr << " \n " << "Time : " << 1000.0 * clock() / CLOCKS_PER_SEC << "ms."
#define IO(TASK) if(fopen(#TASK".INP" , "r")){freopen(#TASK".INP" , "r" , stdin); freopen(#TASK".OUT" , "w" , stdout);}
template <class X , class Y>
bool maxz(X &a , const Y b)
{
if(a < b)
{
a = b;
return true;
}
return false;
}
template <class X , class Y>
bool minz(X &a , const Y b)
{
if(a > b)
{
a = b;
return true;
}
return false;
}
namespace MaxPhast
{
const int N = 1e5 + 5;
int n , m , S , T , U , V;
int dist[N][2] , d[N][4];
vector <ii> g[N];
priority_queue <ii , vector <ii> , greater <ii>> pq;
priority_queue <iii , vector <iii> , greater <iii>> q;
void dijk(int s , int t)
{
FOR(i , 1 , n) dist[i][t] = oo;
dist[s][t] = 0;
pq.push({dist[s][t] , s});
while(!pq.empty())
{
ii tmp = pq.top();
pq.pop();
if(tmp.fi > dist[tmp.se][t])
continue;
for(ii &v : g[tmp.se])
if(minz(dist[v.fi][t] , dist[tmp.se][t] + v.se))
pq.push({dist[v.fi][t] , v.fi});
}
}
void solve()
{
cin >> n >> m >> S >> T >> U >> V;
FOR(i , 1 , m)
{
int u , v , w; cin >> u >> v >> w;
g[u].pb({v , w});
g[v].pb({u , w});
}
dijk(S , 0);
dijk(T , 1);
FOR(i , 1 , n)
FOR(j , 0 , 3)
d[i][j] = oo;
d[U][0] = 0;
q.push({d[U][0] , {U , 0}});
while(!q.empty())
{
iii tmp = q.top();
q.pop();
if(tmp.fi > d[tmp.se.fi][tmp.se.se])
continue;
for(ii &v : g[tmp.se.fi])
{
if(tmp.se.se == 0)
{
if(minz(d[v.fi][0] , d[tmp.se.fi][0] + v.se))
q.push({d[v.fi][0] , {v.fi , 0}});
if(dist[v.fi][0] + dist[tmp.se.fi][1] + v.se == dist[T][0])
{
if(minz(d[v.fi][1] , d[tmp.se.fi][0]))
q.push({d[v.fi][1] , {v.fi , 1}});
}
if(dist[v.fi][1] + dist[tmp.se.fi][0] + v.se == dist[T][0])
{
if(minz(d[v.fi][2] , d[tmp.se.fi][0]))
q.push({d[v.fi][2] , {v.fi , 2}});
}
}
if(tmp.se.se == 1)
{
if(dist[v.fi][0] + dist[tmp.se.fi][1] + v.se == dist[T][0])
{
if(minz(d[v.fi][1] , d[tmp.se.fi][1]))
q.push({d[v.fi][1] , {v.fi , 1}});
}
else
{
if(minz(d[v.fi][3] , d[tmp.se.fi][1] + v.se))
q.push({d[v.fi][3] , {v.fi , 3}});
}
}
if(tmp.se.se == 2)
{
if(dist[v.fi][1] + dist[tmp.se.fi][0] + v.se == dist[T][0])
{
if(minz(d[v.fi][2] , d[tmp.se.fi][2]))
q.push({d[v.fi][2] , {v.fi , 2}});
}
else
{
if(minz(d[v.fi][3] , d[tmp.se.fi][2] + v.se))
q.push({d[v.fi][3] , {v.fi , 3}});
}
}
if(tmp.se.se == 3)
{
if(minz(d[v.fi][3] , d[tmp.se.fi][3] + v.se))
q.push({d[v.fi][3] , {v.fi , 3}});
}
}
}
cout << min({d[V][0] , d[V][1] , d[V][2] , d[V][3]});
}
}
signed main()
{
ios_base :: sync_with_stdio(false) ; cin.tie(nullptr) ; cout.tie(nullptr);
IO(test);
MaxPhast :: solve();
time();
}
/*
*/
