#include <bits/stdc++.h>
using namespace std;
#define NMAX 100000
#define f first
#define s second
int N, M, S, T, U, V;
vector<pair<long long, int> > E[NMAX + 5];
long long res;
class state {
public:
int u;
long long d;
bool t1, t2;
state() {
u = 0;
d = 0;
t1 = t2 = 0;
}
state(long long _d, int _u, bool _t1, bool _t2) {
d = _d;
u = _u;
t1 = _t1;
t2 = _t2;
}
bool operator < (const state &v) const {
return d < v.d;
}
bool operator == (const state &v) const {
return d == v.d;
}
bool operator > (const state &v) const {
return d > v.d;
}
};
long long d[NMAX + 5][2][2], len[2][NMAX + 5];
int start[2];
priority_queue<state, vector<state>, greater<state> > pq;
typedef pair<long long, int> pli;
priority_queue<pli, vector<pli>, greater<pli> > pq2;
void prepare(int t) {
pq2.push({0, start[t]});
len[t][start[t]] = 0;
while(pq2.size()) {
long long len_u = pq2.top().f;
int u = pq2.top().s;
pq2.pop();
if(len_u != len[t][u])
continue;
for(pair<long long, int> &x : E[u]) {
int v = x.s;
long long uv = x.f;
if(len[t][v] > len[t][u] + uv) {
len[t][v] = len[t][u] + uv;
pq2.push({len[t][v], v});
}
}
}
}
void solve() {
memset(d, 0x3f, sizeof d);
d[U][0][0] = 0;
pq.push(state(0, U, 0, 0));
while(pq.size()) {
int u = pq.top().u;
long long du = pq.top().d;
bool t1 = pq.top().t1;
bool t2 = pq.top().t2;
pq.pop();
if(du != d[u][t1][t2])
continue;
for(pair<long long, int> &x : E[u]) {
long long uv = x.f;
int v = x.s;
if(d[v][t1][0] > d[u][t1][t2] + uv) {
d[v][t1][0] = d[u][t1][t2] + uv;
pq.push(state(d[v][t1][0], v, t1, 0));
}
if(len[0][u] + uv + len[1][v] == len[0][T]) {
if(t1 == 1 && t2 == 0)
continue;
if(d[v][1][1] > d[u][t1][t2]) {
d[v][1][1] = d[u][t1][t2];
pq.push(state(d[v][1][1], v, 1, 1));
}
}
}
}
res = min(res, min(d[V][1][1], d[V][1][0]));
res = min(res, d[V][0][0]);
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
if(fopen("BUS.INP", "r")) {
freopen("BUS.INP", "r", stdin);
freopen("BUS.OUT", "w", stdout);
}
cin >> N >> M >> S >> T >> U >> V;
for(int i = 1; i <= M; i++) {
int u, v;
long long w;
cin >> u >> v >> w;
E[u].push_back({w, v});
E[v].push_back({w, u});
}
start[0] = S;
start[1] = T;
memset(len, 0x3f, sizeof len);
for(int i = 0; i < 2; i++)
prepare(i);
res = 1e18;
solve();
swap(U, V);
solve();
cout << res;
}
