// Calm down.
// Think three times, code twice.
#include "bits/stdc++.h"
#define forr(_a,_b,_c) for(int _a = (_b); _a <= (_c); ++_a)
#define ford(_a,_b,_c) for(int _a = (_b) + 1; _a --> (_c);)
#define forf(_a,_b,_c) for(int _a = (_b); _a < (_c); ++_a)
#define st first
#define nd second
#define ll long long
#define ull unsigned long long
#define pii pair <ll,int>
#define pll pair <ll,ll>
#define piii pair <ll,pii>
#define vi vector <int>
#define pb push_back
#define mp make_pair
#define all(x) begin(x),end(x)
#define mask(i) (1LL << (i))
#define bit(x, i) (((x) >> (i)) & 1)
#define bp __builtin_popcountll
#define file "test"
using namespace std;
const int N = 2e5 + 5;
const int mod = 1e9 + 7; // 998244353
const ll oo = 1e18;
ll ans;
int n, m, s, t, u, v;
vector<pii> a[N];
ll du[N], dv[N];
void xuly(int bd, ll d[]) {
priority_queue<pii, vector<pii>, greater<pii>> q;
q.push({0, bd}); d[bd] = 0;
while(q.size()) {
int u = q.top().nd; ll du = q.top().st; q.pop();
if(du < d[u]) continue;
for(pii e: a[u]) {
int v = e.nd; ll dv = e.st;
if(du + dv < d[v]) {
d[v] = du + dv;
q.push({d[v], v});
}
}
}
}
void xuly2(int bd, int kt) {
vector<ll> d(n + 5, oo);
vector<vector<ll>> dp(2, vector<ll>(n+5, oo));
priority_queue<piii, vector<piii>, greater<piii>> q;
q.push({0, {bd, 0}}); d[bd] = 0;
dp[0][bd] = du[bd]; dp[1][bd] = dv[bd];
while(q.size()) {
int u = q.top().nd.st, par = q.top().nd.nd; ll dist = q.top().st; q.pop();
if(d[u] < dist) continue;
for(pii e: a[u]) {
int v = e.nd; ll distv = e.st;
if(dist + distv < d[v]) {
d[v] = dist + distv;
dp[0][v] = min(dp[0][u], du[v]);
dp[1][v] = min(dp[1][u], dv[v]);
q.push({d[v], {v, u}});
} else if(dist + distv == d[v]) {
if(min(dp[0][u], du[v]) + min(dp[1][u], dv[v]) <= dp[0][v] + dp[1][v]) {
dp[0][v] = min(dp[0][u], du[v]);
dp[1][v] = min(dp[1][u], dv[v]);
}
}
}
}
// cout << dp[0][kt] << " " << dp[1][kt] << "\n";
ans = min(ans, dp[0][kt] + dp[1][kt]);
}
void to_nho_cau() {
cin >> n >> m >> s >> t >> u >> v;
forr(i, 1, m) {
int u, v; ll val; cin >> u >> v >> val;
a[u].pb({val, v});
a[v].pb({val, u});
}
memset(du, 63, sizeof du);
memset(dv, 63, sizeof dv);
xuly(u, du); xuly(v, dv);
ans = du[v];
xuly2(s, t); xuly2(t, s);
cout << ans << "\n";
}
signed main(){
ios_base::sync_with_stdio(0);cin.tie(0);
#ifdef LOCAL
freopen(file".inp","r",stdin);
freopen(file".out","w",stdout);
#endif
int t = 1;
//cin >> t;
while(t--) to_nho_cau();
}
/*
1.self check:
2.long long
3.size of array
4.code for testing
5.initializing
6.modulo number
*/
/**
∧__∧
（｀•ω• )づ__∧
（つ /( •ω•。)
しーＪ (nnノ) pat pat
**/
/** /\_/\
* (= ._.)
* / >☕ \>💻
**/
