#include<bits/stdc++.h>
using namespace std;
// define
#define execute cerr << " Time: " << fixed << setprecision(6) << (1.0 * clock() / CLOCKS_PER_SEC) << "s\n";
#define ll long long
#define ii pair <ll , ll>
#define iii pair <ll , ii>
#define se second
#define fi first
#define all(v) (v).begin() , (v).end()
#define Unique(v) sort(all(v)) , v.resize(unique(all(v)) - v.begin())
#define bit(x,i) (((x) >> (i)) & 1LL)
#define flip(x,i) ((x) ^ (1LL << (i)))
#define ms(d,x) memset(d , x , sizeof(d))
#define exist __exist
#define ends __ends
#define visit visited
#define left __left
#define right __right
#define sitingfake 1
#define orz 1
//constant
const long long mod = 1e9 + 7;
const long long linf = 4557430888798830399LL;
const long long nlinf = -4485090715960753727LL;
const int inf = 1061109567;
const int ninf = -1044266559;
const int dx[] = {0 , -1 , 0 , 1};
const int dy[] = {-1 , 0 , 1 , 0};
template<typename T> bool maximize(T &a, const T &b)
{
if(a < b) {a = b; return 1;}
return 0;
}
template<typename T> bool minimize(T &a, const T &b)
{
if(a > b) {a = b; return 1;}
return 0;
}
void Plus(ll & a ,ll b)
{
b %= mod;
a += b;
if(a < 0) a += mod;
a %= mod;
return;
}
void Mul(ll & a, ll b)
{
(a *= (b % mod)) %= mod;
return;
}
//code
const int maxn = 1e5 + 7;
int S , T , U , V;
ll dist[maxn][3] , distS[maxn] , distT[maxn];
vector <ii> a[maxn];
int n , m;
void Dijkstra(int source , ll dist[])
{
for(int i = 1; i <= n; i++)
{
dist[i] = linf;
}
dist[source] = 0;
priority_queue <ii , vector <ii> , greater <ii>> pq;
pq.push({0 , source});
while(!pq.empty())
{
int u = pq.top().se;
ll cost = pq.top().fi;
pq.pop();
if(cost > dist[u]) continue;
for(ii i : a[u])
{
int v = i.fi;
ll w = i.se;
if(minimize(dist[v] , dist[u] + w))
{
pq.push({dist[v] , v});
}
}
}
}
bool check(int u , int v , ll w)
{
return distS[u] + distT[v] + w == distS[T];
}
void solve(void)
{
cin >> n >> m;
cin >> S >> T;
cin >> U >> V;
for(int i = 1; i <= m; i++)
{
int u , v , w;
cin >> u >> v >> w;
a[u].push_back(ii(v , w));
a[v].push_back(ii(u , w));
}
Dijkstra(S , distS);
Dijkstra(T , distT);
ms(dist , 0x3f);
dist[U][0] = 0;
priority_queue <iii , vector <iii> , greater <iii>> pq;
pq.push({0 , {U , 0}});
while(!pq.empty())
{
int u = pq.top().se.fi;
int d = pq.top().se.se;
ll cost = pq.top().fi;
pq.pop();
if(cost > dist[u][d]) continue;
if(d == 0 || d == 2)
{
for(ii i : a[u])
{
int v = i.fi;
ll w = i.se;
if(minimize(dist[v][d] , dist[u][d] + w))
{
pq.push({dist[v][d] , {v , d}});
}
}
}
if(d == 1)
{
for(ii i : a[u])
{
int v = i.fi;
int w = i.se;
if(check(u , v , w))
{
if(minimize(dist[v][d] , dist[u][d]))
{
pq.push({dist[v][d] , {v , d}});
}
}
if(minimize(dist[v][2] , dist[u][d] + w))
{
pq.push({dist[v][2] , {v , 2}});
}
}
}
if(d == 0)
{
for(ii i : a[u])
{
int v = i.fi;
ll w = i.se;
if(check(u , v , w))
{
if(minimize(dist[v][1] , dist[u][0]))
{
pq.push({dist[v][1] , {v , 1}});
}
}
}
}
}
ll ans = min({dist[V][0] , dist[V][1] , dist[V][2]});
ms(dist , 0x3f);
dist[V][0] = 0;
pq.push({0 , {V , 0}});
while(!pq.empty())
{
int u = pq.top().se.fi;
int d = pq.top().se.se;
ll cost = pq.top().fi;
pq.pop();
if(cost > dist[u][d]) continue;
if(d == 0 || d == 2)
{
for(ii i : a[u])
{
int v = i.fi;
ll w = i.se;
if(minimize(dist[v][d] , dist[u][d] + w))
{
pq.push({dist[v][d] , {v , d}});
}
}
}
if(d == 1)
{
for(ii i : a[u])
{
int v = i.fi;
int w = i.se;
if(check(u , v , w))
{
if(minimize(dist[v][d] , dist[u][d]))
{
pq.push({dist[v][d] , {v , d}});
}
}
if(minimize(dist[v][2] , dist[u][d] + w))
{
pq.push({dist[v][2] , {v , 2}});
}
}
}
if(d == 0)
{
for(ii i : a[u])
{
int v = i.fi;
ll w = i.se;
if(check(u , v , w))
{
if(minimize(dist[v][1] , dist[u][0]))
{
pq.push({dist[v][1] , {v , 1}});
}
}
}
}
}
cout << min({ans , dist[U][0] , dist[U][1] , dist[U][2]});
}
/**
**/
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
#define task ""
if(fopen(task".inp","r"))
{
freopen(task".inp","r",stdin);
freopen(task".out","w",stdout);
}
int tc = 1;
// cin >> tc;
while(tc--) solve();
// execute;
}
