#include <bits/stdc++.h>
#define pii pair<int,int>
#define pb push_back
#define ll long long
#define MOD 1000000007
#define all(x) x.begin(),x.end()
#define MOD2 998244353
using namespace std;
void solve(int cas){
int n,m; cin>>n>>m;
int s,t,u,v; cin>>s>>t>>u>>v;--s;--t;--u;--v;
vector<vector<pair<ll,ll>>> g(n);
for (int i = 0; i < m; i++){
ll a,b,c; cin>>a>>b>>c;
--a;--b;
g[a].emplace_back(make_pair(b,c));
g[b].emplace_back(make_pair(a,c));
}
vector<ll> ds(n, LLONG_MAX);
ds[s] = 0;
priority_queue<pair<ll,ll>, vector<pair<ll,ll>>, greater<pair<ll,ll>>> heap;
vector<set<ll>> par(n);
heap.push(make_pair(0,s));
while (!heap.empty()){
auto [weight, node] = heap.top(); heap.pop();
if (weight > ds[node]) continue;
for (auto [neighbor, w]: g[node]){
if (weight + w < ds[neighbor]){
ds[neighbor] = weight + w;
heap.push(make_pair(ds[neighbor], neighbor));
par[neighbor] = set<ll>{node};
}
else if (weight + w == ds[neighbor]){
par[neighbor].insert(node);
}
}
}
vector<ll> stk = {t};
vector<bool> vis(n);
vis[t] = true;
set<pair<ll,ll>> edges;
while (!stk.empty()){
ll node = stk.back();
stk.pop_back();
for (ll x: par[node]){
edges.insert(make_pair(x, node));
if (!vis[x]){
vis[x] = true;
stk.emplace_back(x);
}
}
}
set<pair<ll,ll>> rev;
for (auto& [a, b]: edges) rev.insert(make_pair(b,a));
vector<vector<vector<ll>>> dp(n, vector<vector<ll>> (3, vector<ll> (2, LLONG_MAX)));
//0 is not taken, 1 is taking, 2 is done taken
using tll = tuple<ll,ll,ll,ll>;
priority_queue<tll, vector<tll>, greater<tll>> heap1; // weight, state, node
heap1.push(make_tuple(0,0,u,0));
dp[u][0][0] = 0;
while (!heap1.empty()){
auto [weight, state, node, r] = heap1.top(); heap1.pop();
//cout << weight << " " << state << " " << node + 1 << '\n';
if (weight > dp[node][state][r]) continue;
if (node==v){
cout << weight << '\n';
return;
}
for (auto [neighbor, w]: g[node]){
if (state==2){
if (weight + w < dp[neighbor][2][r]){
dp[neighbor][2][r] = weight + w;
heap1.push(make_tuple(dp[neighbor][2][r], 2, neighbor, r));
}
}
else if (state==1){
if (weight + w < dp[neighbor][2][r]){
dp[neighbor][2][r] = weight + w;
heap1.push(make_tuple(dp[neighbor][2][r], 2, neighbor, r));
}
if (((!r && edges.count(make_pair(node, neighbor))) || (r && rev.count(make_pair(node, neighbor)))) && weight < dp[neighbor][1][r]){
dp[neighbor][1][r] = weight;
heap1.push(make_tuple(dp[neighbor][1][r], 1, neighbor, r));
}
}
else{
if (weight + w < dp[neighbor][0][r]){
dp[neighbor][0][r] = weight + w;
heap1.push(make_tuple(dp[neighbor][0][r], 0, neighbor, r));
}
if (edges.count(make_pair(node, neighbor)) && weight < dp[neighbor][1][0]){
dp[neighbor][1][0] = weight;
heap1.push(make_tuple(dp[neighbor][1][0], 1, neighbor, 0));
}
if (rev.count(make_pair(node, neighbor)) && weight < dp[neighbor][1][1]){
dp[neighbor][1][1] = weight;
heap1.push(make_tuple(dp[neighbor][1][1], 1, neighbor, 1));
}
}
}
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
int t = 1;
//cin>>t;
for (int i = 1; i <= t; i++){
solve(i);
}
return 0;
}
