#include <bits/stdc++.h>
#define ll long long
#define fi first
#define se second
using namespace std;
namespace std {
// https://judge.yosupo.jp/submission/193613
struct IOPre {
static constexpr int TEN = 10, SZ = TEN * TEN * TEN * TEN;
std::array<char, 4 * SZ> num;
constexpr IOPre() : num{} {
for (int i = 0; i < SZ; i++) for (int n = i, j = 3; j >= 0; j--) num[i * 4 + j] = n % TEN + '0', n /= TEN;
}
};
struct IO {
#if !HAVE_DECL_FREAD_UNLOCKED
#define fread_unlocked fread
#endif
#if !HAVE_DECL_FWRITE_UNLOCKED
#define fwrite_unlocked fwrite
#endif
static constexpr int SZ = 1 << 17, LEN = 32, TEN = 10, HUNDRED = TEN * TEN,
THOUSAND = HUNDRED * TEN, TENTHOUSAND = THOUSAND * TEN,
MAGIC_MULTIPLY = 205, MAGIC_SHIFT = 11, MASK = 15,
TWELVE = 12, SIXTEEN = 16;
static constexpr IOPre io_pre = {};
std::array<char, SZ> input_buffer, output_buffer;
int input_ptr_left, input_ptr_right, output_ptr_right;
IO() : input_buffer{}, output_buffer{}, input_ptr_left{}, input_ptr_right{}, output_ptr_right{} {}
IO(const IO&) = delete;
IO(IO&&) = delete;
IO& operator=(const IO&) = delete;
IO& operator=(IO&&) = delete;
~IO() { flush(); }
template<typename T> static constexpr bool is_char_v = std::is_same_v<T, char>;
template<typename T> static constexpr bool is_bool_v = std::is_same_v<T, bool>;
template<typename T> static constexpr bool is_string_v =
std::is_same_v<T, std::string> || std::is_same_v<T, const char*> ||
std::is_same_v<T, char*> || std::is_same_v< std::decay_t<T>, char*>;
template<typename T> static constexpr bool is_default_v =
is_char_v<T> || is_bool_v<T> || is_string_v<T> || std::is_integral_v<T>;
inline void load() {
memmove(std::begin(input_buffer),
std::begin(input_buffer) + input_ptr_left,
input_ptr_right - input_ptr_left);
input_ptr_right =
input_ptr_right - input_ptr_left +
fread_unlocked(
std::begin(input_buffer) + input_ptr_right - input_ptr_left, 1,
SZ - input_ptr_right + input_ptr_left, stdin);
input_ptr_left = 0;
}
inline void read_char(char& c) {
if (input_ptr_left + LEN > input_ptr_right) load();
c = input_buffer[input_ptr_left++];
}
inline void read_string(std::string& x) {
char c;
while (read_char(c), c < '!') continue;
x = c;
while (read_char(c), c >= '!') x += c;
}
template<typename T>
inline std::enable_if_t<std::is_integral_v<T>, void> read_int(T& x) {
if (input_ptr_left + LEN > input_ptr_right) load();
char c = 0;
do c = input_buffer[input_ptr_left++];
while (c < '-');
[[maybe_unused]] bool minus = false;
if constexpr (std::is_signed<T>::value == true)
if (c == '-') minus = true, c = input_buffer[input_ptr_left++];
x = 0;
while (c >= '0')
x = x * TEN + (c & MASK), c = input_buffer[input_ptr_left++];
if constexpr (std::is_signed<T>::value == true)
if (minus) x = -x;
}
inline void skip_space() {
if (input_ptr_left + LEN > input_ptr_right) load();
while (input_buffer[input_ptr_left] <= ' ') input_ptr_left++;
}
inline void flush() {
fwrite_unlocked(std::begin(output_buffer), 1, output_ptr_right, stdout);
output_ptr_right = 0;
}
inline void write_char(char c) {
if (output_ptr_right > SZ - LEN) flush();
output_buffer[output_ptr_right++] = c;
}
inline void write_bool(bool b) {
if (output_ptr_right > SZ - LEN) flush();
output_buffer[output_ptr_right++] = b ? '1' : '0';
}
inline void write_string(const std::string& s) {
for (auto x : s) write_char(x);
}
inline void write_string(const char* s) {
while (*s) write_char(*s++);
}
inline void write_string(char* s) {
while (*s) write_char(*s++);
}
template <typename T>
inline std::enable_if_t< std::is_integral_v<T>, void> write_int(T x) {
if (output_ptr_right > SZ - LEN) flush();
if (!x) {
output_buffer[output_ptr_right++] = '0';
return;
}
if constexpr (std::is_signed_v<T>) if (x < 0) output_buffer[output_ptr_right++] = '-', x = -x;
int i = TWELVE;
std::array<char, SIXTEEN> buf{};
for (; x >= TENTHOUSAND; x /= TENTHOUSAND, i -= 4)
memcpy(std::begin(buf) + i, std::begin(io_pre.num) + (x % TENTHOUSAND) * 4, 4);
if (x < HUNDRED) {
if (x < TEN) output_buffer[output_ptr_right++] = '0' + x;
else {
uint32_t q = (uint32_t(x) * MAGIC_MULTIPLY) >> MAGIC_SHIFT;
uint32_t r = uint32_t(x) - q * TEN;
output_buffer[output_ptr_right++] = '0' + q;
output_buffer[output_ptr_right++] = '0' + r;
}
} else {
if (x < THOUSAND)
memcpy(std::begin(output_buffer) + output_ptr_right, std::begin(io_pre.num) + (x << 2) + 1, 3),
output_ptr_right += 3;
else
memcpy(std::begin(output_buffer) + output_ptr_right, std::begin(io_pre.num) + (x << 2), 4),
output_ptr_right += 4;
}
memcpy(std::begin(output_buffer) + output_ptr_right, std::begin(buf) + i + 4, TWELVE - i);
output_ptr_right += TWELVE - i;
}
template <typename T_>
std::enable_if_t<(is_default_v< std::remove_cv_t< std::remove_reference_t<T_> > >), IO&> operator<<(T_&& x) {
using T = std::remove_cv_t< std::remove_reference_t<T_> >;
if constexpr (is_bool_v<T>) write_bool(x);
else if constexpr (is_string_v<T>) write_string(x);
else if constexpr (is_char_v<T>) write_char(x);
else if constexpr (std::is_integral_v<T>) write_int(x);
return *this;
}
template<typename T>
std::enable_if_t<(is_default_v<T> && !is_bool_v<T>), IO&> operator>>(T& x) {
if constexpr (is_string_v<T>) read_string(x);
else if constexpr (is_char_v<T>) read_char(x);
else if constexpr (std::is_integral_v<T>) read_int(x);
return *this;
}
IO* tie(std::nullptr_t) { return this; }
void sync_with_stdio(bool) {}
} io;
} // namespace std
using std::io;
#define cin io
#define cout io
ll MAX = 1e18;
int N, M, S, T, U, V;
ll answer;
vector<vector<pair<int,ll>>> adj;
vector<bool> processed;
vector<ll> distS, distT, distU, distV;
vector<pair<ll,ll>> memo;
pair<ll, ll> res(int pos) {
if (pos == T) return {distU[T], distV[T]};
if (memo[pos].fi < MAX) return memo[pos];
processed[pos] = true;
pair<ll, ll> best = {MAX, MAX};
for (pair<int,ll> x : adj[pos]) {
if (!processed[x.fi]) {
if (distT[x.fi] + distS[x.fi] == distS[T] && distS[pos] + x.se == distS[x.fi]) {
pair<ll, ll> func = res(x.fi);
if (distU[pos] <= func.fi) { func.fi = distU[pos]; answer = min(answer, func.fi + func.se); }
if (distV[pos] <= func.se) { func.se = distV[pos]; answer = min(answer, func.fi + func.se); }
best.fi = min(best.fi, func.fi);
best.se = min(best.se, func.se);
}
}
}
processed[pos] = false;
return memo[pos] = best;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); //cout.tie(0);
cin >> N >> M >> S >> T >> U >> V;
S--; T--; U--; V--;
adj.resize(N); memo.resize(N, {MAX, MAX}); processed.resize(N, false);
for (int i = 0; i < M; i++) {
int a, b; ll c; cin >> a >> b >> c;
a--, b--;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
distS.resize(N, MAX); distT.resize(N, MAX); distU.resize(N, MAX); distV.resize(N, MAX);
priority_queue < pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll,int>>> q;
q.push({0, S}); distS[S] = 0;
while (!q.empty()) {
int x = q.top().se; q.pop();
if (processed[x]) continue;
processed[x] = true;
for (pair<int,ll> w : adj[x]) {
if (distS[w.fi] > distS[x] + w.se) {
distS[w.fi] = distS[x] + w.se;
q.push({distS[w.fi], w.fi});
}
}
}
processed.clear(); processed.resize(N, false);
q.push({0,T}); distT[T] = 0;
while (!q.empty()) {
int x = q.top().se; q.pop();
if (processed[x]) continue;
processed[x] = true;
for (pair<int,ll> w : adj[x]) {
if (distT[w.fi] > distT[x] + w.se) {
distT[w.fi] = distT[x] + w.se;
q.push({distT[w.fi], w.fi});
}
}
}
processed.clear(); processed.resize(N,false);
q.push({0,U}); distU[U] = 0;
while (!q.empty()) {
int x = q.top().se; q.pop();
if (processed[x]) continue;
processed[x] = true;
for (pair<int,ll> w : adj[x]) {
if (distU[w.fi] > distU[x] + w.se) {
distU[w.fi] = distU[x] + w.se;
q.push({distU[w.fi], w.fi});
}
}
}
processed.clear(); processed.resize(N, false);
q.push({0, V}); distV[V] = 0;
while (!q.empty()) {
int x = q.top().se; q.pop();
if (processed[x]) continue;
processed[x] = true;
for (pair<int,ll> w : adj[x]) {
if (distV[w.fi] > distV[x] + w.se) {
distV[w.fi] = distV[x] + w.se;
q.push({distV[w.fi], w.fi});
}
}
}
//cout << distS[11] + distT[11] << '\n';
processed.clear(); processed.resize(N, false);
answer = min(distU[T] + distV[T], distU[V]);
res(S);
cout << answer;
return 0;
}
