#include <bits/stdc++.h>
#define int long long
#define NOT_DONE 1
#define DONE 2
using namespace std;
void open(){
if(fopen("input.inp", "r")){
freopen("input.inp", "r", stdin);
//freopen("output.out", "w", stdout);
}
}
const int maxn = 1e5 + 5;
const int inf = 3e18;
const int oo = 1e9 + 7;
int n, m;
vector<pair<int, int>> G[maxn];
int S, T;
int U, V;
int min_cost;
int d_s[maxn], d_t[maxn], d_u[maxn], d_v[maxn];
bool in_road[maxn];
int state[maxn];
pair<int, int> dp[maxn]; // trollge
struct Node{
int index, len;
Node(){}
Node(int _index, int _len) : index(_index), len(_len) {}
bool operator>(const Node &other) const{
if(len != other.len) return len > other.len;
return index > other.index;
}
};
bool check_if_in_road(int u, int v, int w){ // u(S) -> v(T)
return d_s[u] + w + d_t[v] == min_cost;
}
pair<int, int> custom_min(const pair<int, int> &A, const pair<int, int> &B){
pair<int, int> result = make_pair(min(A.first, B.first), min(A.second, B.second));
return result;
}
pair<int, int> custom_cmp(const pair<int, int> &A, const pair<int, int> &B, const pair<int, int> &C){ // compare A < B
pair<int, int> r1 = custom_min(A, C);
pair<int, int> r2 = custom_min(B, C);
if(r1.first + r1.second < r2.first + r2.second) return A;
else return B;
}
pair<int, int> dfs(int u){
state[u] = NOT_DONE;
pair<int, int> result = make_pair(d_u[u], d_v[u]);
pair<int, int> temp = make_pair(inf, inf);
for(pair<int, int> node : G[u]){
int v = node.first;
int w = node.second;
if(state[v] == NOT_DONE || !check_if_in_road(u, v, w)) continue;
if(state[v] == DONE){
temp = custom_cmp(temp, dp[v], result);
continue;
}
temp = custom_cmp(temp, dfs(v), result);
}
state[u] = DONE;
result = custom_min(result, temp);
return dp[u] = result;
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
open();
cin >> n >> m;
cin >> S >> T;
cin >> U >> V;
for(int i = 1; i <= m; i++){
int a, b, c;
cin >> a >> b >> c;
G[a].push_back({b, c});
G[b].push_back({a, c});
}
// From s:
priority_queue<Node, vector<Node>, greater<Node>> pq;
memset(d_s, oo, sizeof(d_s));
d_s[S] = 0;
pq.push({S, 0});
while(!pq.empty()){
Node first = pq.top();
pq.pop();
int u = first.index;
if(d_s[u] < first.len) continue;
for(pair<int, int> node : G[u]){
int v = node.first;
int w = node.second;
if(d_s[v] > d_s[u] + w){
d_s[v] = d_s[u] + w;
pq.push({v, d_s[v]});
}
}
}
// From t:
memset(d_t, oo, sizeof(d_t));
d_t[T] = 0;
pq.push({T, 0});
while(!pq.empty()){
Node first = pq.top();
pq.pop();
int u = first.index;
if(d_t[u] < first.len) continue;
for(pair<int, int> node : G[u]){
int v = node.first;
int w = node.second;
if(d_t[v] > d_t[u] + w){
d_t[v] = d_t[u] + w;
pq.push({v, d_t[v]});
}
}
}
// First handle:
assert(d_s[T] == d_t[S]);
min_cost = d_s[T];
for(int i = 1; i <= n; i++){
if(d_s[i] + d_t[i] == min_cost){
in_road[i] = true;
}
}
// From u:
memset(d_u, oo, sizeof(d_u));
d_u[U] = 0;
pq.push({U, 0});
while(!pq.empty()){
Node first = pq.top();
pq.pop();
int u = first.index;
if(d_u[u] < first.len) continue;
for(pair<int, int> node : G[u]){
int v = node.first;
int w = node.second;
if(d_u[v] > d_u[u] + w){
d_u[v] = d_u[u] + w;
pq.push({v, d_u[v]});
}
}
}
// From v:
memset(d_v, oo, sizeof(d_v));
d_v[V] = 0;
pq.push({V, 0});
while(!pq.empty()){
Node first = pq.top();
pq.pop();
int u = first.index;
if(d_v[u] < first.len) continue;
for(pair<int, int> node : G[u]){
int v = node.first;
int w = node.second;
if(d_v[v] > d_v[u] + w){
d_v[v] = d_v[u] + w;
pq.push({v, d_v[v]});
}
}
}
// Last handle:
// Handle the vertex is in the route:
pair<int, int> smallest = dfs(S);
int result = smallest.first + smallest.second;
for(int i = 1; i <= n; i++){
if(!in_road[i]){
result = min(result, d_u[i] + d_v[i]);
}
}
cout << result << endl;
return 0;
}
