#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <bits/stdc++.h>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<ld,ld> pdd;
#define ff(i,a,b) for(int i = a; i <= b; i++)
#define fb(i,b,a) for(int i = b; i >= a; i--)
#define trav(a,x) for (auto& a : x)
#define sz(a) (int)(a).size()
#define pb push_back
#define fi first
#define se second
#define lb lower_bound
#define ub upper_bound
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template<typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
// os.order_of_key(k) the number of elements in the os less than k
// *os.find_by_order(k) print the k-th smallest number in os(0-based)
const int mod = 1000000007;
const ll inf = 1e18 + 5;
const int mxN = 200005;
int n, m;
int S, T;
int A, B;
vector<pii> g[mxN];
ll dist_S[mxN];
ll dist_T[mxN];
ll dist_A[mxN];
ll dist_B[mxN];
void dij(int s, ll dist[]){
ff(i,1,n)dist[i] = inf;
priority_queue<pll, vector<pll>, greater<pll>> pq;
pq.push({dist[s] = 0, s});
while(sz(pq)){
pll v = pq.top(); pq.pop();
if(dist[v.se] < v.fi)continue;
for(auto c : g[v.se]){
int u = c.fi;
int w = c.se;
if(dist[u] > v.fi + w){
pq.push({dist[u] = v.fi + w, u});
}
}
}
}
ll rez = inf;
void dfs_S(int v, ll mn){
mn = min(mn, dist_A[v]);
rez = min(rez, mn + dist_B[v]);
for(auto c : g[v]){
int u = c.fi;
int w = c.se;
if(dist_T[v] == w + dist_T[u]){
dfs_S(u, mn);
}
}
}
void dfs_T(int v, ll mn){
mn = min(mn, dist_A[v]);
rez = min(rez, mn + dist_B[v]);
for(auto c : g[v]){
int u = c.fi;
int w = c.se;
if(dist_S[v] == w + dist_S[u]){
dfs_T(u, mn);
}
}
}
int main() {
cin.tie(0)->sync_with_stdio(0);
cin >> n >> m >> S >> T >> A >> B;
ff(i,1,m){
int u, v, w;
cin >> u >> v >> w;
g[u].pb({v, w});
g[v].pb({u, w});
}
dij(S, dist_S);
dij(T, dist_T);
dij(A, dist_A);
dij(B, dist_B);
rez = dist_A[B];
dfs_S(S, inf);
dfs_T(T, inf);
cout << rez << '\n';
return 0;
}
/*
6 6
1 6
1 4
1 2 1
2 3 1
3 5 1
2 4 3
4 5 2
5 6 1
6 5
1 2
3 6
1 2 1000000000
2 3 1000000000
3 4 1000000000
4 5 1000000000
5 6 1000000000
8 8
5 7
6 8
1 2 2
2 3 3
3 4 4
1 4 1
1 5 5
2 6 6
3 7 7
4 8 8
5 5
1 5
2 3
1 2 1
2 3 10
2 4 10
3 5 10
4 5 10
10 15
6 8
7 9
2 7 12
8 10 17
1 3 1
3 8 14
5 7 15
2 3 7
1 10 14
3 6 12
1 5 10
8 9 1
2 9 7
1 4 1
1 8 1
2 4 7
5 6 16
// probati bojenje sahovski
*/
