// ~~ icebear ~~
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
template<class T>
bool minimize(T &a, const T &b) {
if (a > b) return a = b, true;
return false;
}
template<class T>
bool maximize(T &a, const T &b) {
if (a < b) return a = b, true;
return false;
}
#define FOR(i,a,b) for(int i=(a); i<=(b); ++i)
#define FORR(i,a,b) for(int i=(a); i>=(b); --i)
#define REP(i, n) for(int i=0; i<(n); ++i)
#define RED(i, n) for(int i=(n)-1; i>=0; --i)
#define MASK(i) (1LL << (i))
#define BIT(S, i) (((S) >> (i)) & 1)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define all(x) x.begin(), x.end()
#define task "icebear"
const int MOD = 1e9 + 7;
const int inf = 1e9 + 27092008;
const ll INF = 1e18 + 27092008;
const int N = 2e5 + 5;
int n, m, S, T, U, V;
vector<ii> G[N];
ll dist[4][N], f[2][N];
void dijkstra(ll dist[], int src) {
FOR(i, 1, n) dist[i] = INF;
dist[src] = 0;
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> Q;
Q.push(mp(0, src));
while(!Q.empty()) {
ll du; int u;
tie(du, u) = Q.top(); Q.pop();
if (du != dist[u]) continue;
for(ii x : G[u]) {
int v, w; tie(v, w) = x;
if (minimize(dist[v], dist[u] + w))
Q.push(mp(dist[v], v));
}
}
}
ll dp(int src) {
FOR(i, 1, n) {
dist[2][i] = f[0][i] = f[1][i] = INF;
}
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> Q;
Q.push(mp(0, src));
dist[2][src] = 0;
f[0][src] = dist[0][src];
f[1][src] = dist[1][src];
while(!Q.empty()) {
ll du; int u;
tie(du, u) = Q.top(); Q.pop();
if (du != dist[2][u]) continue;
for(ii x : G[u]) {
int v, w; tie(v, w) = x;
if (minimize(dist[2][v], dist[2][u] + w)) {
f[0][v] = min(f[0][u], dist[0][v]);
f[1][v] = min(f[1][u], dist[1][v]);
Q.push(mp(dist[2][v], v));
} else if (dist[2][v] == dist[2][u] + w && f[0][v] + f[1][v] > min(dist[0][v], f[0][u]) + min(dist[1][v], f[1][u])) {
f[0][v] = min(dist[0][v], f[0][u]);
f[1][v] = min(dist[1][v], f[1][u]);
}
}
}
int dest = (src == S ? T : S);
return f[0][dest] + f[1][dest];
}
void init(void) {
cin >> n >> m >> S >> T >> U >> V;
FOR(i, 1, m) {
int u, v, w;
cin >> u >> v >> w;
G[u].pb(mp(v, w));
G[v].pb(mp(u, w));
}
}
void process(void) {
dijkstra(dist[0], U);
dijkstra(dist[1], V);
cout << min({dist[0][V], dp(S)});
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
if (fopen(task".inp", "r")) {
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
int tc = 1;
// cin >> tc;
while(tc--) {
init();
process();
}
return 0;
}
