#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <unordered_set>
#include <vector>
#include <climits>
#include <list>
using namespace std;
using ll = long long;
using db = long double; // or double, if TL is tight
using llu = unsigned long long;
using str = string; // yay python!
// pairs
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pdb = pair<db,db>;
#define mp make_pair
#define fr first
#define sc second
#define tcT template<class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>;
tcT, size_t SZ> using AR = array<T,SZ>;
using vi = V<int>;
using vb = V<bool>;
using vl = V<ll>;
using vd = V<db>;
using vs = V<str>;
using vpi = V<pii>;
using vpl = V<pll>;
using vpd = V<pdb>;
#define ms0(x) memset(x , 0, sizeof(x))
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()
#define lb lower_bound
#define ub upper_bound
tcT> int lwb(V<T>& a, const T& b) { return int(lb(all(a),b)-bg(a)); }
tcT> int upb(V<T>& a, const T& b) { return int(ub(all(a),b)-bg(a)); }
// loops
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define rep(a) F0R(_,a)
#define each(a,x) for (auto& a: x)
const int MOD = (int)1e9+7; // 998244353;
const int MX = (int)2e5+5;
const ll BIG = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4] = {0,1,0,-1};
const int dy[4] = {-1,0,1,0};
long long Commuter_Pass(int N, int M, int S, int T, int U, int V, vector<vector<pair<int,int>>>roads){
ll SPS[N + 1], SPU[N + 1], SPV[N + 1];
long long dp[N + 1];
for (int i = 0; i<=N; i++){
SPS[i] = SPU[i] = SPV[i] = 1e18;
dp[i] = 1e18;
}
SPS[S] = 0;
SPU[U] = 0;
SPV[V] = 0;
vector<int>parents[N + 1];
priority_queue<pair<ll,int>>q;
q.push(mp(0,S));
while(!q.empty()){
ll dst = -q.top().fr;
int node = q.top().sc;
q.pop();
if (SPS[node] != dst)continue;
for (auto edge : roads[node]){
int city = edge.fr;
int cost = edge.sc;
if (SPS[city] > dst + cost){
SPS[city] = dst + cost;
parents[city].clear();
parents[city].pb(node);
q.push(mp(-SPS[city], city));
}else if (SPS[city] == dst + cost){
parents[city].pb(node);
}
}
}
q.push(mp(0,U));
while(!q.empty()){
ll dst = -q.top().fr;
int node = q.top().sc;
q.pop();
if (SPU[node] != dst)continue;
for (auto edge : roads[node]){
int city = edge.fr;
int cost = edge.sc;
if (SPU[city] > dst + cost){
SPU[city] = dst + cost;
q.push(mp(-SPU[city], city));
}
}
}
q.push(mp(0,V));
while(!q.empty()){
ll dst = -q.top().fr;
int node = q.top().sc;
q.pop();
if (SPV[node] != dst)continue;
for (auto edge : roads[node]){
int city = edge.fr;
int cost = edge.sc;
if (SPV[city] > dst + cost){
SPV[city] = dst + cost;
q.push(mp(-SPV[city], city));
}
}
}
long long ans = SPU[V];
//fix a node p, ans = min(ans, min(SPU[parents of p]) + SPV[p])
//since we only know the parents of each node, this implies that we cannot use a bottom-up dynamic programming approach,
//we will have to use recursion
//keep track of calculated nodes to avoid time limit or overflow problems
int visited[N + 1];
memset(visited, 0, sizeof(visited));
function<void(int p, int from)>dinamicko = [&](int p, int from){
//cout<<p<<" "<<childs[p].size()<<endl;
if (visited[p] >= N)return;
visited[p]++;
dp[p] = min(dp[p], SPU[p]);
for (int parent : parents[p]){
dp[parent] = min(dp[parent], dp[p]);
dinamicko(parent, p);
dp[p] = min(dp[p], dp[parent]);
}
ans = min(ans, dp[p] + SPV[p]);
};
dinamicko(T, T);
return ans;
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int N, M, S, T, U, V;
cin >> N >> M >> S >> T >> U >> V;
vector<vector<pair<int,int>>>edges(N + 1);
for (int i = 0; i<M; i++){
int a,b,c;
cin >> a >> b >> c;
edges[a].pb(mp(b,c));
edges[b].pb(mp(a,c));
}
cout<<Commuter_Pass(N,M,S,T,U,V,edges);
return 0;
}
