#include <iostream>
#include <algorithm>
#include <vector>
#include <random>
#include <chrono>
#include <set>
#include <map>
#include <stack>
#include <functional>
#include <iomanip>
#include <queue>
#include <cassert>
#include <complex>
#include <cstring>
#include <memory>
#include <bitset>
#include <sstream>
#include <cmath>
#include <numeric>
#include <numbers>
#include <fstream>
using namespace std;
#ifndef template
#ifndef define
#define ll long long
#define ld long double
#define pl pair<ll, ll>
#define pi pair<int, int>
#define nl cout << '\n';
#define x first
#define y second
#define cbit(x) __builtin_popcountll(x)
#define uid(a, b) uniform_int_distribution<ll>(a, b)(rng)
#define siz(x) (int)x.size()
#endif
#ifndef print
void print(size_t x) {cout << x << ' ';}
void print(int x) {cout << x << ' ';}
void print(long long x) {cout << x << ' ';}
void print(float x) {cout << x << ' ';}
void print(long double x) {cout << x << ' ';}
void print(char x) {cout << x << ' ';}
void print(const char* x) {cout << x << ' ';}
void print(bool x) {cout << x << ' ';}
void print(string &x) {cout << x << ' ';}
template<typename T, typename V>
void print(pair<T, V> &p) {print(p.x); print(p.y);}
template<typename T>
void print(vector<T> v) {for (int i = 0; i < v.size(); i++) print(v[i]);}
template<typename T>
void print(vector<vector<T>> v) {
for (int i = 0; i < v.size(); i++){
for (int j = 0; j < v[i].size(); j++)
print(v[i][j]);
nl;
}
}
template <typename T, typename... V>
void print(T t, V&&... v) {print(t); print(v...);}
#endif
#ifndef read
void read(int &x) {cin >> x;}
void read(long long &x) {cin >> x;}
void read(unsigned &x) {cin >> x;}
void read(unsigned long long &x) {cin >> x;}
void read(float &x) {cin >> x;}
void read(long double &x) {cin >> x;}
void read(char &x) {cin >> x;}
void read(string &x) {cin >> x;}
void read(bool &x) {cin >> x;}
template<typename T>
void read(vector<T> &v) {
for (int i = 0; i < v.size(); i++)
read(v[i]);
}
template <typename T, typename... V>
void read(T &t, V&... v) {read(t); read(v...);}
#endif
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template<class T> bool maxi(T& a, const T& b) {
return a < b ? a = b, 1 : 0;
}
template<class T> bool mini(T& a, const T& b) {
return a > b ? a = b, 1 : 0;
}
template<class... Args>
auto vec(size_t n, Args&&... args) {
if constexpr(sizeof...(args) == 1)
return vector(n, args...);
else
return vector(n, vec(args...));
}
#endif
using namespace std;
const ll inf = 1e15;
const ll def = 2e5+1;
const ll mod = 998244353;
vector<ll> dijkstra(vector<vector<pi>> &edg, int s){
int n = edg.size();
priority_queue<pl, vector<pl>, greater<pl>> pq;
auto dp = vec(n, inf);
dp[s] = 0;
pq.push({0, s});
while (pq.size()){
auto [dis, u] = pq.top();
pq.pop();
for (auto [v, w] : edg[u]){
ll ndis = w + dis;
if (ndis < dp[v]){
dp[v] = ndis;
pq.push({ndis, v});
}
}
}
return dp;
}
void solve(){
int n, m;
read(n, m);
int s, t, U, V;
read(s, t, U, V);
s--; t--; U--; V--;
vector<vector<pi>> edg(n);
for (int i = 0; i < m; i++){
int u, v, w;
read(u, v, w);
u--; v--;
edg[u].push_back({v, w});
edg[v].push_back({u, w});
}
auto dps = dijkstra(edg, s);
auto dpt = dijkstra(edg, t);
auto dp1 = vec(n, 3, inf);
auto dp2 = dp1;
priority_queue<pair<ll, pi>, vector<pair<ll, pi>>, greater<pair<ll, pi>>> pq;
pq.push({0, {U, 0}});
ll good = dps[t];
dp1[U][0] = dp2[U][0] = 0;
while (pq.size()){
ll dis = pq.top().x;
auto [u, has] = pq.top().y; pq.pop();
for (auto [v, w] : edg[u]){
for (int o = 0; o < 1; o++){
ll ndis = dis;
ll val = dps[u] + dpt[v] + w;
ll nhas = has;
if (o == 0 && val == good && has != 2){
if (!has)
nhas = 1;
}
else{
ndis += w;
if (nhas == 1)
nhas = 2;
}
if (ndis < dp1[v][nhas]){
dp1[v][nhas] = ndis;
pq.push({ndis, {v, nhas}});
}
}
}
}
pq.push({0, {U, 0}});
while (pq.size()){
ll dis = pq.top().x;
auto [u, has] = pq.top().y; pq.pop();
for (auto [v, w] : edg[u]){
for (int o = 0; o < 1; o++){
ll ndis = dis;
ll val = dps[u] + dpt[v] + w;
ll nhas = has;
if (o == 0 && val == good && has != 2){
if (!has)
nhas = 1;
}
else{
ndis += w;
if (nhas == 1)
nhas = 2;
}
if (ndis < dp2[v][nhas]){
dp2[v][nhas] = ndis;
pq.push({ndis, {v, nhas}});
}
}
}
}
ll res = inf;
for (int i = 0; i < 3; i++)
mini(res, min(dp1[V][i], dp2[V][i]));
print(res);
}
/*
4 5
a s k A
d s D t
O R i A
a X b Y
b a k A -
u s k J
6
*/
int32_t main(){
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
if (ifstream("input.txt").good()){
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
}
int t;
t = 1;
while (t--){
solve();
nl;
}
}
