#include <bits/stdc++.h>
using namespace std;
#define endl "\n"
#define ms(arr, v) memset(arr, v, sizeof(arr))
#define mp make_pair
#define pb push_back
#define fix(prec) {cout << setprecision(prec) << fixed;}
#define fastio ios_base::sync_with_stdio(false);cin.tie(NULL); cout.tie(NULL);
#define ins insert
#define f first
#define s second
#define all(v) v.begin(), v.end()
#define sz(v) (ll)v.size()
#define readgraph(list, edges) for (ll i = 0; i < edges; i++) {ll a, b; cin >> a >> b; a--; b--; list[a].pb(b); list[b].pb(a);}
typedef long long ll;
typedef unsigned long long ull;
typedef long double lld;
typedef vector<ll> vi;
typedef pair<ll, ll> pii;
#define F_OR(i, a, b, s) for (ll i=(a); (s)>0?i<(b):i>(b); i+=(s))
#define F_OR1(e) F_OR(i, 0, e, 1)
#define F_OR2(i, e) F_OR(i, 0, e, 1)
#define F_OR3(i, b, e) F_OR(i, b, e, 1)
#define F_OR4(i, b, e, s) F_OR(i, b, e, s)
#define GET5(a, b, c, d, e, ...) e
#define F_ORC(...) GET5(__VA_ARGS__, F_OR4, F_OR3, F_OR2, F_OR1)
#define FOR(...) F_ORC(__VA_ARGS__)(__VA_ARGS__)
#define EACH(x, a) for (auto& x: a)
ll FIRSTTRUE(function<bool(ll)> f, ll lb, ll rb) {
while (lb < rb) {
ll mb = (lb + rb) / 2;
f(mb) ? rb = mb : lb = mb + 1;
}
return lb;
}
ll LASTTRUE(function<bool(ll)> f, ll lb, ll rb) {
while (lb < rb) {
ll mb = (lb + rb + 1) / 2;
f(mb) ? lb = mb : rb = mb - 1;
}
return lb;
}
void yn(bool t) {
if (t)cout << "YES" << endl;
else cout << "NO" << endl;
}
ll getmax(ll l, ll r, ll (*check)(ll)) {
ll lo = l, hi = r;
while (lo < hi) {
ll mid = (hi + lo) >> 1;
if (check(mid) > check(mid + 1))
hi = mid;
else
lo = mid + 1;
}
return check(hi);
}// returns maximum//returns maximum
ll getmin(ll l, ll r, ll (*check)(ll)) {
ll lo = l, hi = r;
while (lo < hi) {
ll mid = (hi + lo) >> 1;
if (check(mid) < check(mid + 1))
hi = mid;
else
lo = mid + 1;
}
return check(hi);
}// returns minimum//returns minimum
#ifndef DEBUG_TEMPLATE_CPP
#define DEBUG_TEMPLATE_CPP
#include <bits/stdc++.h>
// #define cerr cout
namespace __DEBUG_UTIL__
{
using namespace std;
/* Primitive Datatypes Print */
void print(const char *x) { cerr << x; }
void print(bool x) { cerr << (x ? "T" : "F"); }
void print(char x) { cerr << '\'' << x << '\''; }
void print(signed short int x) { cerr << x; }
void print(unsigned short int x) { cerr << x; }
void print(signed int x) { cerr << x; }
void print(unsigned int x) { cerr << x; }
void print(signed long int x) { cerr << x; }
void print(unsigned long int x) { cerr << x; }
void print(signed long long int x) { cerr << x; }
void print(unsigned long long int x) { cerr << x; }
void print(float x) { cerr << x; }
void print(double x) { cerr << x; }
void print(long double x) { cerr << x; }
void print(string x) { cerr << '\"' << x << '\"'; }
template <size_t N>
void print(bitset<N> x) { cerr << x; }
void print(vector<bool> v)
{ /* Overloaded this because stl optimizes vector<bool> by using
_Bit_reference instead of bool to conserve space. */
int f = 0;
cerr << '{';
for (auto && i : v)
cerr << (f++ ? "," : "") << (i ? "T" : "F");
cerr << "}";
}
/* Templates Declarations to support nested datatypes */
template <typename T>
void print(T &&x);
template <typename T>
void print(vector<vector<T>> mat);
template <typename T, size_t N, size_t M>
void print(T (&mat)[N][M]);
template <typename F, typename S>
void print(pair<F, S> x);
template <typename T, size_t N>
struct Tuple;
template <typename T>
struct Tuple<T, 1>;
template <typename... Args>
void print(tuple<Args...> t);
template <typename... T>
void print(priority_queue<T...> pq);
template <typename T>
void print(stack<T> st);
template <typename T>
void print(queue<T> q);
/* Template Datatypes Definitions */
template <typename T>
void print(T &&x)
{
/* This works for every container that supports range-based loop
i.e. vector, set, map, oset, omap, dequeue */
int f = 0;
cerr << '{';
for (auto && i : x)
cerr << (f++ ? "," : ""), print(i);
cerr << "}";
}
template <typename T>
void print(vector<vector<T>> mat)
{
int f = 0;
cerr << "\n~~~~~\n";
for (auto && i : mat)
{
cerr << setw(2) << left << f++, print(i), cerr << "\n";
}
cerr << "~~~~~\n";
}
template <typename T, size_t N, size_t M>
void print(T (&mat)[N][M])
{
int f = 0;
cerr << "\n~~~~~\n";
for (auto && i : mat)
{
cerr << setw(2) << left << f++, print(i), cerr << "\n";
}
cerr << "~~~~~\n";
}
template <typename F, typename S>
void print(pair<F, S> x)
{
cerr << '(';
print(x.first);
cerr << ',';
print(x.second);
cerr << ')';
}
template <typename T, size_t N>
struct Tuple
{
static void printTuple(T t)
{
Tuple < T, N - 1 >::printTuple(t);
cerr << ",", print(get < N - 1 > (t));
}
};
template <typename T>
struct Tuple<T, 1>
{
static void printTuple(T t) { print(get<0>(t)); }
};
template <typename... Args>
void print(tuple<Args...> t)
{
cerr << "(";
Tuple<decltype(t), sizeof...(Args)>::printTuple(t);
cerr << ")";
}
template <typename... T>
void print(priority_queue<T...> pq)
{
int f = 0;
cerr << '{';
while (!pq.empty())
cerr << (f++ ? "," : ""), print(pq.top()), pq.pop();
cerr << "}";
}
template <typename T>
void print(stack<T> st)
{
int f = 0;
cerr << '{';
while (!st.empty())
cerr << (f++ ? "," : ""), print(st.top()), st.pop();
cerr << "}";
}
template <typename T>
void print(queue<T> q)
{
int f = 0;
cerr << '{';
while (!q.empty())
cerr << (f++ ? "," : ""), print(q.front()), q.pop();
cerr << "}";
}
/* Printer functions */
void printer(const char *) {} /* Base Recursive */
template <typename T, typename... V>
void printer(const char *names, T &&head, V &&...tail)
{
/* Using && to capture both lvalues and rvalues */
int i = 0;
for (size_t bracket = 0; names[i] != '\0' and (names[i] != ',' or bracket != 0); i++)
if (names[i] == '(' or names[i] == '<' or names[i] == '{')
bracket++;
else if (names[i] == ')' or names[i] == '>' or names[i] == '}')
bracket--;
cerr.write(names, i) << " = ";
print(head);
if (sizeof...(tail))
cerr << " ||", printer(names + i + 1, tail...);
else
cerr << "]\n";
}
/* PrinterArr */
void printerArr(const char *) {} /* Base Recursive */
template <typename T, typename... V>
void printerArr(const char *names, T arr[], size_t N, V... tail)
{
size_t ind = 0;
for (; names[ind] and names[ind] != ','; ind++)
cerr << names[ind];
for (ind++; names[ind] and names[ind] != ','; ind++)
;
cerr << " = {";
for (size_t i = 0; i < N; i++)
cerr << (i ? "," : ""), print(arr[i]);
cerr << "}";
if (sizeof...(tail))
cerr << " ||", printerArr(names + ind + 1, tail...);
else
cerr << "]\n";
}
}
#ifdef LOCAL
#define debug(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printer(#__VA_ARGS__, __VA_ARGS__);
#define debugArr(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printerArr(#__VA_ARGS__, __VA_ARGS__);
#else
#define debug(...)
#define debugArr(...)
#endif
#endif
mt19937 mt_rng(chrono::steady_clock::now().time_since_epoch().count());
ll randint(ll a, ll b) {
return uniform_int_distribution<ll>(a, b)(mt_rng);
}
/*--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
const lld pi = 3.14159265358979323846;
const ll mod = 1000000007;
// const ll mod = 998244353;
// ll mod;
const ll INF = 1e17;
const int d4i[4] = { -1, 0, 1, 0}, d4j[4] = {0, 1, 0, -1};
const int d8i[8] = { -1, -1, 0, 1, 1, 1, 0, -1}, d8j[8] = {0, 1, 1, 1, 0, -1, -1, -1};
const int kni[8] = { +2, +2, -2, -2, 1, -1, 1, -1}, knj[8] = {1, -1, 1, -1, 2, 2, -2, -2};
ll n, m, k, q, l, r, x, y, z , h, u, v;
const ll tas = 1e5 + 10;
ll a[tas];
ll vis[tas];
ll d1[tas];
ll d2[tas];
ll d3[tas];
ll d4[tas];
ll d5[tas];
ll p1[tas];
ll p2[tas];
ll p3[tas];
string s, t;
vector<pii> grid[tas];
// vector<pii> edges[tas];
ll ans = 0;
void get(ll c[], int x) {
FOR(n)vis[i] = 0;
priority_queue<pii> pq;
pq.push(mp(0, x));
FOR(n)c[i] = INF;
c[x] = 0;
while (!pq.empty()) {
auto cur = pq.top();
pq.pop();
if (!vis[cur.s])vis[cur.s] = 1;
for (auto val : grid[cur.s]) {
// debug("hi", x,c[val.])
if (c[val.f] > c[cur.s] + val.s) {
c[val.f] = c[cur.s] + val.s;
pq.push(mp(-c[val.f], val.f));
}
}
}
}
void solve(int tc = 0) {
cin >> n >> m;
cin >> x >> y;
x--, y--;
cin >> u >> v;
u--, v--;
FOR(m) {
cin >> l >> r >> z;
l--, r--;
grid[l].pb(mp(r, z));
grid[r].pb(mp(l, z));
}
get(d1, x);
get(d2, u);
get(d3, y);
get(d4, v);
// FOR()
priority_queue<pii> pq;
pq.push(mp(0, x));
FOR(n)vis[i] = 0, d5[i] = INF, p1[i] = 0, p2[i] = INF, p3[i] = INF;
// debug()
vis[x] = 0, d5[x] = 0, p1[x] = 0, p2[x] = d2[x], p3[x] = d2[x] + d4[x];
// debug(d2)
while (!pq.empty()) {
auto cur = pq.top();
// debug(cur)
pq.pop();
// debug(cur.s)
if (!vis[cur.s])vis[cur.s] = 1;
for (auto val : grid[cur.s]) {
// debug()
// debug(cur.s, val.f)
if (d5[val.f] > d5[cur.s] + val.s) {
d5[val.f] = d5[cur.s] + val.s;
// debug(cur.s, val.f)
// debug(cur.s, p2[cur.s], d2[val.f])
p2[val.f] = min(p2[cur.s], d2[val.f]);
p3[val.f] = min({p3[cur.s], p2[cur.s] + d4[val.f], d2[val.f] + d4[val.f]});
pq.push(mp(-d5[val.f], val.f));
}
else if (d5[val.f] == d5[cur.s] + val.s) {
p2[val.f] = min({p2[val.f], p2[cur.s], d2[val.f]});
p3[val.f] = min({p3[val.f], p3[cur.s], p2[cur.s] + d4[val.f], d2[val.f] + d4[val.f]});
}
}
}
// debug(p2[2])
ll t1 = p3[y];
// priorpq;
pq.push(mp(0, x));
FOR(n)vis[i] = 0, d5[i] = INF, p1[i] = 0, p2[i] = INF, p3[i] = INF;
// debug()
vis[x] = 0, d5[x] = 0, p1[x] = 0, p2[x] = d4[x], p3[x] = d2[x] + d4[x];
// debug(d2)
while (!pq.empty()) {
auto cur = pq.top();
pq.pop();
// debug(cur.s)
if (!vis[cur.s])vis[cur.s] = 1;
for (auto val : grid[cur.s]) {
// debug()
if (d5[val.f] > d5[cur.s] + val.s) {
d5[val.f] = d5[cur.s] + val.s;
// debug(cur.s, val.f)
// debug(cur.s, p2[cur.s], d2[val.f])
p2[val.f] = min(p2[cur.s], d4[val.f]);
p3[val.f] = min({p3[cur.s], p2[cur.s] + d2[val.f], d4[val.f] + d2[val.f]});
pq.push(mp(-d5[val.f], val.f));
}
else if (d5[val.f] == d5[cur.s] + val.s) {
p2[val.f] = min({p2[val.f], p2[cur.s], d4[val.f]});
p3[val.f] = min({p3[val.f], p3[cur.s], p2[cur.s] + d2[val.f], d2[val.f] + d4[val.f]});
}
}
}
// FOR(n)debug(i, p2[i])
// debug(t1)
cout << min({d4[u], p3[y], t1}) << endl;
}
int main() {
fastio
#ifdef LOCAL
auto begin = std::chrono::high_resolution_clock::now();
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
freopen("error.txt", "w", stderr);
#endif
ll tc = 1;
// cin >> tc;
for (int t = 0; t < tc; t++) solve(t);
#ifdef LOCAL
auto end = std::chrono::high_resolution_clock::now();
auto elapsed = std::chrono::duration_cast<std::chrono::nanoseconds>(end - begin);
// cerr << "Time measured: " << elapsed.count() * 1e-9 << " seconds.\n";
#endif
}
