//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC optimize("Ofast,unroll-loops,fast-math,O3")
#include <map>
#include <set>
#include <list>
#include <cmath>
#include <ctime>
#include <deque>
#include <queue>
#include <stack>
#include <string>
#include <bitset>
#include <cstdio>
#include <limits>
#include <vector>
#include <climits>
#include <cstring>
#include <cstdlib>
#include <fstream>
#include <numeric>
#include <sstream>
#include <cassert>
#include <iomanip>
#include <iostream>
#include <algorithm>
#include <stdio.h>
#include <fstream>
#include <unordered_map>
#define ll long long
#define int long long
#define all(v) v.begin(), v.end()
#define nl '\n'
#define pb push_back
#define sz(s) (int)(s).size()
#define f first
#define s second
using namespace std;
const ll N = 1e5 + 50, MX = 1e18;
bool was[N], grd[N], use[N], had[N];
ll du[N], dv[N], ds[N], dt[N];
vector <pair <int, int> > g[N], Q[N];
vector <int> top;
ll dp[N][2];
ll n;
ll s, t, u, v;
void dfs(ll curv){
use[curv]=1;
for(auto [x,w]:g[curv]){
if(!use[x])dfs(x);
}
if(grd[curv])top.pb(curv);
}
void filv(){
for (int i = 1; i <= n; i++) {
was[i]=0;
//dv[i]=MX;
}
dv[v]=0;
priority_queue< pair<long long, int> > st;
st.push({0, v});
while(st.size() != 0) {
int curv = st.top().second;
st.pop();
if(was[curv]) continue;
was[curv] = 1;
for(auto [to, w]: g[curv]) {
if(dv[to] > dv[curv] + w) {
//s.erase({d[to], to});
dv[to] = dv[curv] + w;
st.push({-dv[to], to});
}
}
}
}
void filu(){
for (int i = 1; i <= n; i++) {
was[i]=0;
//du[i]=MX;
}
du[u]=0;
priority_queue< pair<long long, int> > st;
st.push({0, u});
while(st.size() != 0) {
int curv = st.top().second;
st.pop();
if(was[curv]) continue;
was[curv] = 1;
for(auto [to, w]: g[curv]) {
if(du[to] > du[curv] + w) {
//s.erase({d[to], to});
du[to] = du[curv] + w;
st.push({-du[to], to});
}
}
}
}
void fils(){
for (int i = 1; i <= n; i++) {
was[i]=0;
//ds[i]=MX;
}
ds[s]=0;
priority_queue< pair<long long, int> > st;
st.push({0, s});
while(st.size() != 0) {
int curv = st.top().second;
st.pop();
if(was[curv]) continue;
was[curv] = 1;
for(auto [to, w]: g[curv]) {
if(ds[to] > ds[curv] + w) {
//s.erase({d[to], to});
ds[to] = ds[curv] + w;
st.push({-ds[to], to});
}
}
}
}
void filt(){
for (int i = 1; i <= n; i++) {
was[i]=0;
dp[i][0]=dp[i][1]=MX;
//dt[i]=MX;
}
dt[t]=0;
priority_queue< pair<long long, int> > st;
st.push({0, t});
while(st.size() != 0) {
int curv = st.top().second;
st.pop();
if(was[curv]) continue;
was[curv] = 1;
for(auto [to, w]: g[curv]) {
if(dt[to] > dt[curv] + w) {
//s.erase({d[to], to});
dt[to] = dt[curv] + w;
st.push({-dt[to], to});
}
}
}
}
void solve(){
ll m;
cin >> n >> m;
cin >> s >> t >> u >> v;
for(int i = 1; i <= m; i++){
ll a, b, x;
cin >> a >> b >> x;
g[a].pb({b,x});
g[b].pb({a, x});
}
for(int i = 1; i <= n; i++){
dt[i] = ds[i] = du[i] = dv[i] = MX;
}
filt(), filu(), filv(), fils();
for(int i = 1; i <= n; i++){
if(ds[i] + dt[i] == ds[t]){
grd[i]=1;
//cout << i << nl;
}
}
for(int i = 1; i <= n; i++){
if(grd[i]) {
for (auto [x,w]: g[i]) {
if (dt[x] + w + ds[i] == ds[t]) {
Q[i].pb({x, w});
}
}
}
}
for(int i = 1; i <= n; i++){
g[i].clear();
}
for(int i = 1; i <= n; i++){
for(auto [x, w]: Q[i]){
g[i].pb({x, 0});
}
}
for(int i = 1; i <= n; i++){
for(auto [x, w]: g[i]){
//cout << i << " " << x << " " << w << nl;
}
}
for(int i = 1; i <= n; i++){
if(!use[i] && grd[i])dfs(i);
}
for(auto x:top){
dp[x][0] = du[x];
dp[x][1] = dv[x];
for (auto [to, w]: g[x]) {
dp[x][0] = min(dp[x][0], dp[to][0]);
dp[x][1] = min(dp[x][1], dp[to][1]);
}
}
ll mn = du[v];
for(auto x: top){
mn = min(mn, dp[x][0] + dv[x]);
mn = min(mn, dp[x][1] + du[x]);
}
cout << mn;
}
signed main(){
//freopen("lca.in", "r", stdin);
//freopen("lca.out", "w", stdout);
ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
ll ql=1;
//cin >> ql;
//tst++;
while(ql--){
solve();
}
}
