#include <iostream>
#include <algorithm>
#include <cstring>
#include <iomanip>
#include <fstream>
#include <cmath>
#include <vector>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <map>
#include <stack>
#include <queue>
#include <assert.h>
#include <limits>
#include <cstdio>
#include <complex>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
#define mp make_pair
#define f first
#define s second
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353; // = (119<<23)+1
const int MX = 4e5+5;
const ll INF = 1e18;
const ld PI = 4*atan((ld)1);
const int dx[4] = {0,1,0,-1}, dy[4] = {1,0,-1,0};
namespace io {
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void setIO(string s = "") {
ios_base::sync_with_stdio(0); cin.tie(0); // fast I/O
// cin.exceptions(cin.failbit); // ex. throws exception when you try to read letter into int
if (sz(s)) {
setIn(s+".in");
setOut(s+".out");
} // for USACO
}
}
using namespace io;
namespace input {
template<class T> void re(complex<T>& x);
template<class T1, class T2> void re(pair<T1,T2>& p);
template<class T> void re(vector<T>& a);
template<class T, size_t SZ> void re(array<T,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(double& x) { string t; re(t); x = stod(t); }
void re(ld& x) { string t; re(t); x = stold(t); }
template<class Arg, class... Args> void re(Arg& first, Args&... rest) {
re(first); re(rest...);
}
template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}
namespace output {
template<class T1, class T2> void pr(const pair<T1,T2>& x);
template<class T, size_t SZ> void pr(const array<T,SZ>& x);
template<class T> void pr(const vector<T>& x);
template<class T> void pr(const set<T>& x);
template<class T1, class T2> void pr(const map<T1,T2>& x);
template<class T> void pr(const T& x) { cout << x; }
template<class Arg, class... Args> void pr(const Arg& first, const Args&... rest) {
pr(first); pr(rest...);
}
template<class T1, class T2> void pr(const pair<T1,T2>& x) {
pr("{",x.f,", ",x.s,"}");
}
template<class T> void prContain(const T& x) {
pr("{");
bool fst = 1; for (const auto& a: x) pr(!fst?", ":"",a), fst = 0; // const needed for vector<bool>
pr("}");
}
template<class T, size_t SZ> void pr(const array<T,SZ>& x) { prContain(x); }
template<class T> void pr(const vector<T>& x) { prContain(x); }
template<class T> void pr(const set<T>& x) { prContain(x); }
template<class T1, class T2> void pr(const map<T1,T2>& x) { prContain(x); }
void ps() { pr("\n"); }
template<class Arg> void ps(const Arg& first) {
pr(first); ps(); // no space at end of line
}
template<class Arg, class... Args> void ps(const Arg& first, const Args&... rest) {
pr(first," "); ps(rest...); // print w/ spaces
}
}
using namespace output;
using namespace input;
ll add(ll a, ll b) {
a += b;
if(a >= MOD) {
a -= MOD;
}
return a;
}
ll sub(ll a, ll b) {
a -= b;
if(a < 0) {
a += MOD;
}
return a;
}
ll mul(ll a, ll b) {
return (a * b)%MOD;
}
void add_self(ll& a, ll b) {
a = add(a, b);
}
void sub_self(ll& a, ll b) {
a = sub(a, b);
}
void mul_self(ll& a, ll b) {
a = mul(a, b);
}
ll N, M, S, T, U, V;
vpl adj[MX];
ll usp[MX], vsp[MX];
pair<pl, ll> edgelist[MX];
ll good[MX];
ll sp[MX][2][2];
void dijkstra1(ll s) {
usp[s] = 0;
using pii = pair<ll, ll>;
priority_queue<pl, vector<pl>, greater<pl>> q;
q.push({0, s});
while (!q.empty()) {
ll v = q.top().second;
ll d_v = q.top().first;
q.pop();
if (d_v != usp[v]) {
continue;
}
for (auto edge : adj[v]) {
ll to = edge.first;
ll len = edgelist[edge.second].second;
if (usp[v] + len < usp[to]) {
usp[to] = usp[v] + len;
q.push({usp[to], to});
}
}
}
}
void dijkstra2(ll s) {
vsp[s] = 0;
priority_queue<pl, vector<pl>, greater<pl>> q;
q.push({0, s});
while (!q.empty()) {
ll v = q.top().second;
ll d_v = q.top().first;
q.pop();
if (d_v != vsp[v]) {
continue;
}
for (auto edge : adj[v]) {
ll to = edge.first;
ll len = edgelist[edge.second].second;
if (vsp[v] + len < vsp[to]) {
vsp[to] = vsp[v] + len;
q.push({vsp[to], to});
}
}
}
}
void dijkstra3(ll s) {
sp[s][0][0] = 0;
priority_queue<pair<pl, pl>, vector<pair<pl, pl>>, greater<pair<pl, pl>>> q;
q.push({{0, s}, {0, 0}});
while (!q.empty()) {
ll v = q.top().f.s;
ll d_v = q.top().f.f;
ll inChain = q.top().s.f;
ll doneChain = q.top().s.s;
q.pop();
if (d_v != sp[v][inChain][doneChain]) {
continue;
}
trav(edge, adj[v]) {
ll to = edge.f;
ll len = edgelist[edge.s].s;
if (inChain) {
if (good[edge.s]) {
if (sp[v][inChain][doneChain] < sp[to][inChain][doneChain]) {
sp[to][inChain][doneChain] = sp[v][inChain][doneChain];
q.push({{sp[to][inChain][doneChain], to}, {1, 0}});
}
} else {
if (sp[v][inChain][doneChain]+len < sp[to][0][1]) {
sp[to][0][1] = sp[v][inChain][doneChain]+len;
q.push({{sp[to][0][1], to}, {0, 1}});
}
}
} else if (doneChain) {
if (sp[v][inChain][doneChain]+len < sp[to][0][1]) {
sp[to][0][1] = sp[v][inChain][doneChain]+len;
q.push({{sp[to][0][1], to}, {0, 1}});
}
} else {
if (good[edge.s]) {
if (sp[v][inChain][doneChain] < sp[to][1][0]) {
sp[to][1][0] = sp[v][inChain][doneChain];
q.push({{sp[to][1][0], to}, {1, 0}});
}
}
if (sp[v][inChain][doneChain] + len < sp[to][0][0]) {
sp[to][0][0] = sp[v][inChain][doneChain] + len;
q.push({{sp[to][0][0], to}, {0, 0}});
}
}
}
}
}
int main() {
setIO();
re(N, M, S, T, U, V);
F0R (i, MX) {
usp[i] = 1e16;
vsp[i] = 1e16;
sp[i][0][0] = 1e16;
sp[i][0][1] = 1e16;
sp[i][1][0] = 1e16;
sp[i][1][1] = 1e16;
}
F0R (i, M) {
ll a, b, c;
re(a, b, c);
adj[a].pb({b, i});
adj[b].pb({a, i+M});
edgelist[i] = {{a, b}, c};
edgelist[i+M] = {{b, a}, c};
}
dijkstra1(S);
dijkstra2(T);
// FOR (i, 1, N+1) {
// pr(usp[i], " ");
//
// }
// ps();
// FOR (i, 1, N+1) {
// pr(vsp[i], " ");
//
// }
// ps();
F0R (i, M*2) {
if (usp[edgelist[i].f.f] + vsp[edgelist[i].f.s] + edgelist[i].s == usp[T]) {
// ps(edgelist[i].f.f, edgelist[i].f.s, edgelist[i].s, "is 'good'");
good[i] = true;
}
}
dijkstra3(U);
ll ret = min({sp[V][0][0], sp[V][0][1], sp[V][1][0]});
F0R (i, MX) {
sp[i][0][0] = 1e16;
sp[i][0][1] = 1e16;
sp[i][1][0] = 1e16;
sp[i][1][1] = 1e16;
}
dijkstra3(V);
ret = min({ret, sp[U][0][0], sp[U][0][1], sp[U][1][0]});
ps(ret);
// ps(min({sp[V][0][0], sp[V][0][1], sp[V][1][0]}));
return 0;
}
