// Src : Vux2Code
/* Note :
*/
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> pll;
typedef pair<ll, pll> lll;
#define fi first
#define se second
#define pusb push_back
#define popb pop_back
#define pusf push_front
#define popf pop_front
#define vec3d vector<vector<vector<ll>>>
#define vec2d vector<vector<ll>>
#define vec1d vector<ll>
vec3d set3 (ll x, ll y, ll z, ll val = 0) {return vec3d (x, vec2d (y, vec1d (z, val)));}
vec2d set2 (ll x, ll y, ll val = 0) {return vec2d (x, vec1d (y, val));}
// debug (+20)
#define debug(...) debug_impl(#__VA_ARGS__, __VA_ARGS__)
template<typename... Args>
void debug_impl(const char* names, Args&&... args) {
vector<string> _names;
{
istringstream ss(names);
string token;
while (getline(ss, token, ',')) {
auto l = token.find_first_not_of(" ");
auto r = token.find_last_not_of(" ");
if (l == string::npos) _names.push_back("");
else _names.push_back(token.substr(l, r - l + 1));
}
}
cerr << "(";
size_t _i = 0;
int _dummy[] = { 0, ((cerr << _names[_i] << " : " << args << (++_i < _names.size() ? ", " : "")), 0)... };
(void)_dummy;
cerr << ")" << endl;
}
// handy for loops
#define forinc(i, a, b) for (ll i = (a); i <= (b); ++i)
#define fordec(i, a, b) for (ll i = (a); i >= (b); --i)
#define foreach(i, j) for (ll i : (j))
#define all(a) (a).begin (), (a). end ()
#define uni(a) (a).erase(unique((a).begin(), (a). end ()), (a). end ())
const ll maxN = 1e6 + 5, maxLog = 20, inf64 = 1e18, inf32 = 1e9, mod = 1e9 + 7;
void maxi(ll &x, ll y) { x = max(x, y); }
void mini(ll &x, ll y) { x = min(x, y); }
/* ---------HASHING-------- */
// const base = 31, mod2 = 1e9 + 9;
/* ---------BITMASK-------- */
// ll count(ll x) { return __builtin_popcountll(x); }
// ll fst(ll x) { return 63 - __builtin_clzll(x); }
// ll last(ll x) { return __builtin_ctzll(x); }
// bool bit(ll x, ll y) { return ((x >> y) & 1); }
ll t = 1;
ll n, m, d1 [maxN], d2 [maxN] [3];
pll s1, s2;
vector <pll> adj [maxN];
vec1d trace [maxN];
priority_queue <pll, vector <pll>, greater <pll>> q;
priority_queue <lll, vector <lll>, greater <lll>> q3;
queue <ll> fq;
set <ll> mp1 [maxN], mp2 [maxN];
bool vst [maxN];
bool fin (set <ll> &x, ll y) {
return (x. find (y) == x. end ());
}
void up (ll x, ll y, ll v) {
if (d2 [x] [y] > v) {
d2 [x] [y] = v;
q3. push ({d2 [x] [y], {x, y}});
}
}
void solve() {
cin >> n >> m >> s1. fi >> s1. se >> s2. fi >> s2. se;
forinc (i, 1, m) {
ll a, b, c; cin >> a >> b >> c;
adj [a]. pusb ({b, c});
adj [b]. pusb ({a, c});
}
memset (d1, 0x3f, sizeof d1);
d1 [s1. fi] = 0;
q. push ({d1 [s1. fi], s1. fi});
while (!q. empty ()) {
pll tmp = q. top ();
q. pop ();
if (tmp. fi != d1 [tmp. se]) continue;
for (pll i : adj [tmp. se]) {
if (d1 [i. fi] > d1 [tmp. se] + i. se) {
d1 [i. fi] = d1 [tmp. se] + i. se;
q. push ({d1 [i. fi], i. fi});
trace [i. fi]. clear ();
}
if (d1 [i. fi] == d1 [tmp. se] + i. se) trace [i. fi]. pusb (tmp. se);
}
}
fq. push (s1. se);
vst [s1. se] = 1;
while (!fq. empty ()) {
ll tmp = fq. front ();
fq. pop ();
for (ll i : trace [tmp]) {
if (vst [i]) continue;
mp1 [i]. insert (tmp);
mp2 [tmp]. insert (i);
vst [i] = 1;
fq. push (i);
}
}
ll ans = inf64;
memset (d2, 0x3f, sizeof d2);
d2 [s2. fi] [0] = 0;
q3. push ({d2 [s2. fi] [0], {s2. fi, 0}});
while (!q3. empty ()) {
ll val = q3. top (). fi;
ll id = q3. top (). se. fi;
ll sta = q3. top (). se. se;
q3. pop ();
if (val != d2 [id] [sta]) continue;
for (pll i : adj [id]) {
switch (sta) {
case 0 : up (i. fi, 0, d2 [id] [sta] + i. se); break;
case 1 : up (i. fi, 2, d2 [id] [sta] + i. se); break;
case 2 : up (i. fi, 2, d2 [id] [sta] + i. se); break;
}
if (!fin (mp1 [id], i. fi)) {
switch (sta) {
case 0 : up (i. fi, 1, d2 [id] [sta]); break;
case 1 : up (i. fi, 1, d2 [id] [sta]); break;
}
}
}
}
forinc (i, 0, 2) mini (ans, d2 [s2. se] [i]);
memset (d2, 0x3f, sizeof d2);
d2 [s2. fi] [0] = 0;
q3. push ({d2 [s2. fi] [0], {s2. fi, 0}});
while (!q3. empty ()) {
ll val = q3. top (). fi;
ll id = q3. top (). se. fi;
ll sta = q3. top (). se. se;
q3. pop ();
if (val != d2 [id] [sta]) continue;
for (pll i : adj [id]) {
switch (sta) {
case 0 : up (i. fi, 0, d2 [id] [sta] + i. se); break;
case 1 : up (i. fi, 2, d2 [id] [sta] + i. se); break;
case 2 : up (i. fi, 2, d2 [id] [sta] + i. se); break;
}
if (!fin (mp2 [id], i. fi)) {
switch (sta) {
case 0 : up (i. fi, 1, d2 [id] [sta]); break;
case 1 : up (i. fi, 1, d2 [id] [sta]); break;
}
}
}
}
forinc (i, 0, 2) mini (ans, d2 [s2. se] [i]);
cout << ans;
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
// #define TASK "E:/Code/CP/task"
// if (fopen (TASK".inp", "r")) {
// freopen (TASK".inp", "r", stdin);
// freopen (TASK".out", "w", stdout);
// }
// cin >> t;
while (t--) solve();
}
