#include<bits/stdc++.h>
#include<fstream>
using namespace std;
ifstream fin("WINTER.inp");
ofstream fout("WINTER.out");
#define ll long long
#define pb push_back
#define forr(i, a, b) for(int i = a; i < b; i++)
#define dorr(i, a, b) for(int i = a; i >= b; i--)
#define ld long double
#define vt vector
#include<fstream>
#define fi first
#define se second
#define pll pair<ll, ll>
#define pii pair<int, int>
const int x[4] = {1, -1, 0, 0};
const int y[4] = {0, 0, 1, -1};
const ld PI = 3.14159265359;
const ll mod = 1e9 + 7;
const int mxn = 8e5 + 5;
vt<pll>adj[mxn + 1];
int n, m, s, t, u, v;
struct D{
int s;
ll d[mxn + 1];
void go(int _s){
forr(i, 1, n + 1){
d[i] = 1e18;
}
s = _s;
priority_queue<pll, vt<pll>, greater<pll>>pq;
d[s] = 0; pq.push({d[s], s});
while(!pq.empty()){
auto [dd, u] = pq.top(); pq.pop();
if(d[u] != dd)continue;
for(auto [v, w]: adj[u]){
if(d[v] > d[u] + w){
d[v] = d[u] + w;
pq.push({d[v], v});
}
} }
}
};
D U, V;
ll res = 1e18;
struct D2{
int s;
ll d[mxn + 1], dp[2][mxn + 1];
void go(int _s, int t){
for(int i = 1; i <= n; i++){
d[i] = dp[0][i] = dp[1][i] = 1e18;
}
s = _s;
priority_queue<pll, vt<pll>, greater<pll>>pq;
d[s] = 0; pq.push({d[s], s});
dp[0][s] = U.d[s]; dp[1][s] = V.d[s];
while(!pq.empty()){
auto [dd, u] = pq.top(); pq.pop();
if(d[u] != dd)continue;
for(auto [v, w]: adj[u]){
if(d[v] > d[u] + w){
dp[0][v] = min(dp[0][u], U.d[v]); dp[1][v] = min(dp[1][u], V.d[v]);
d[v] = d[u] + w;
pq.push({d[v], v});
}else if(d[v] == d[u] + w){
if(min(dp[0][u], U.d[v]) + min(dp[1][u], V.d[v]) < dp[0][v] + dp[1][v]){
dp[0][v] = min(dp[0][u], U.d[v]); dp[1][v] = min(dp[1][u], V.d[v]);
}
}
}
}
res = min(res, dp[0][t] + dp[1][t]);
}
};
D2 S, T;
signed main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> n >> m >> s >> t >> u >> v;
forr(i, 0, m){
int a, b, w; cin >> a >> b >> w;
adj[a].pb(make_pair(b, w));
adj[b].pb(make_pair(a, w));
}
U.go(u); V.go(v);
res = U.d[v];
S.go(s, t); T.go(t, s);
cout << res;
return(0);
}
