#include <bits/stdc++.h>
#include <iostream>
#include <algorithm>
#include <stdio.h>
#include <climits>
#include <vector>
#include <queue>
#include <map>
#include <set>
#define int long long
using namespace std;
const int MAXN = 1e5 + 2;
int n, m;
int s, t, src, tar;
int dis[MAXN] = {0}, dis2[4][MAXN] = {0};
bool vis[MAXN] = {false};
vector <pair <int, int> > adj[MAXN];
vector <int> pp[MAXN], adj2[MAXN], radj[MAXN];
void Dijkstra() {
// reset:
memset(dis, 0x3f3f3f3f, sizeof(dis));
memset(dis2, 0x3f3f3f3f, sizeof(dis2));
// reset:
dis[s] = 0;
// main:
priority_queue <pair <int, int>, vector <pair <int, int> >, greater <pair <int, int> > > pq;
pq.push(make_pair(dis[s], s));
while(pq.empty() == false) {
pair <int, int> p = pq.top();
pq.pop();
int d = p.first;
int v = p.second;
if(d != dis[v]) {
continue;
}
for(int i = 0; i < (int)(adj[v].size()); i++) {
int u = adj[v][i].first;
int w = adj[v][i].second;
if(dis[u] > dis[v] + w) {
dis[u] = dis[v] + w;
pq.push(make_pair(dis[u], u));
pp[u] = {v};
} else if(dis[u] == dis[v] + w) {
pp[u].push_back(v);
}
}
}
return;
}
void Dijkstra2() {
// reset:
dis2[0][src] = 0;
// main:
priority_queue <pair <int, pair <int, int> >, vector <pair <int, pair <int, int> > >, greater <pair <int, pair <int, int> > > > pq2;
pq2.push(make_pair(dis2[0][src], make_pair(0, src)));
while(pq2.empty() == false) {
pair <int, pair <int, int> > p2 = pq2.top();
pq2.pop();
int d = p2.first;
int i = p2.second.first;
int v = p2.second.second;
// output:
if(v == tar) {
cout << d << "\n";
return;
}
if(d != dis2[i][v]) {
continue;
}
for(int j = 0; j < (int)(adj[v].size()); j++) {
int u = adj[v][j].first;
int w = adj[v][j].second;
int ni = 0;
if(i != 0) {
ni = 3;
}
if(dis2[ni][u] > dis2[i][v] + w) {
dis2[ni][u] = dis2[i][v] + w;
pq2.push(make_pair(dis2[ni][u], make_pair(ni, u)));
}
}
if(i == 0 || i == 1) {
for(int j = 0; j < (int)(adj2[v].size()); j++) {
int u = adj2[v][j];
if(dis2[1][u] > dis2[i][v]) {
dis2[1][u] = dis2[i][v];
pq2.push(make_pair(dis2[1][u], make_pair(1, u)));
}
}
}
if(i == 0 || i == 2) {
for(int j = 0; j < (int)(radj[v].size()); j++) {
int u = radj[v][j];
if(dis2[2][u] > dis2[i][v]) {
dis2[2][u] = dis2[i][v];
pq2.push(make_pair(dis2[2][u], make_pair(2, u)));
}
}
}
}
return;
}
void programme() {
// input:
cin >> n >> m >> s >> t >> src >> tar;
for(int i = 1; i <= m; i++) {
int a, b, w;
cin >> a >> b >> w;
adj[a].push_back(make_pair(b, w));
adj[b].push_back(make_pair(a, w));
}
// solve:
Dijkstra();
queue <int> q;
q.push(t);
vis[t] = true;
while(q.empty() == false) {
int v = q.front();
q.pop();
for(int i = 0; i < (int)(pp[v].size()); i++) {
int u = pp[v][i];
adj2[v].push_back(u);
radj[u].push_back(v);
if(vis[u] == false) {
vis[u] = true;
q.push(u);
}
}
}
// output:
Dijkstra2();
return;
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
// freopen("_mint.inp", "r", stdin);
// freopen("_mint.out", "w", stdout);
programme();
return 0;
}
