#include <iostream>
#include <fstream>
#include <vector>
#include <set>
#include <bitset>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <list>
#include <cmath>
#include <algorithm>
#include <cassert>
#include <math.h>
using namespace std;
template <typename input_type>
inline input_type input() {
input_type inp;
cin >> inp;
return inp;
}
const int max_sz = 1e5 + 5;
const long long inf = 1e18;
long long ans[max_sz], dist[3][max_sz];
pair <int, int> sz, pnt, goal;
pair <long long, long long> dp[max_sz];
vector <int> dag, upd[max_sz];
vector <pair <int, int>> graph[max_sz];
void Dijkstra(int root, int idx) {
set <pair <long long, int>> vrtx_lst;
for (int i = 0; i < sz.first; i++) {
dist[idx][i] = (i == root) ? 0 : inf;
vrtx_lst.insert({dist[idx][i], i});
}
while (not vrtx_lst.empty()) {
int vrtx = (*vrtx_lst.begin()).second;
vrtx_lst.erase(vrtx_lst.begin());
for (auto ngh : graph[vrtx]) {
if (dist[idx][ngh.first] > dist[idx][vrtx] + ngh.second) {
vrtx_lst.erase({dist[idx][ngh.first], ngh.first});
dist[idx][ngh.first] = dist[idx][vrtx] + ngh.second, vrtx_lst.insert({dist[idx][ngh.first], ngh.first});
}
}
if (not idx) {
dag.push_back(vrtx);
}
}
}
int main() {
ios::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
sz = {input<int>(), input<int>()}, pnt = {input<int>() - 1, input<int>() - 1}, goal = {input<int>() - 1, input<int>() - 1};
for (int i = 0; i < sz.second; i++) {
pair <int, int> endpnt = {input<int>() - 1, input<int>() - 1};
int wght = input<int>();
graph[endpnt.first].push_back({endpnt.second, wght}), graph[endpnt.second].push_back({endpnt.first, wght});
}
Dijkstra(pnt.first, 0), Dijkstra(goal.first, 1), Dijkstra(goal.second, 2);
for (int i = 0; i < sz.first; i++) {
for (auto ngh : graph[i]) {
if (dist[0][i] == dist[0][ngh.first] + ngh.second) {
upd[i].push_back(ngh.first);
}
}
}
for (auto vrtx : dag) {
ans[vrtx] = dist[1][vrtx] + dist[2][vrtx], dp[vrtx] = {dist[1][vrtx], dist[2][vrtx]};
for (auto par : upd[vrtx]) {
dp[vrtx] = {min(dp[vrtx].first, dp[par].first), min(dp[vrtx].second, dp[par].second)};
ans[vrtx] = min(ans[vrtx], ans[par]);
}
ans[vrtx] = min(ans[vrtx], min(dist[2][vrtx] + dp[vrtx].first, dist[1][vrtx] + dp[vrtx].second));
}
cout << min(ans[pnt.second], dist[1][goal.second]);
return 0;
}
