#include <iostream>
#include <vector>
#include <queue>
#include <climits>
// #include "debugging.h"
using std::cout;
using std::endl;
using std::vector;
vector<long long> origin_min_costs(int from, const vector<vector<std::pair<int, int>>>& neighbors) {
vector<long long> min_cost(neighbors.size(), LLONG_MAX);
min_cost[from] = 0;
auto cmp = [&] (const int& a, const int& b) { return min_cost[a] > min_cost[b]; };
std::priority_queue<int, vector<int>, decltype(cmp)> frontier(cmp);
frontier.push(from);
while (!frontier.empty()) {
int curr = frontier.top();
frontier.pop();
long long curr_cost = min_cost[curr];
for (auto [n, nc] : neighbors[curr]) {
if (curr_cost + nc <= min_cost[n]) {
min_cost[n] = curr_cost + nc;
frontier.push(n);
}
}
}
return min_cost;
}
// https://oj.uz/problem/view/JOI18_commuter_pass (input ommitted due to length)
int main() {
int station_num;
int railway_num;
std::cin >> station_num >> railway_num;
// i'll make all of these 0-indexed later in the code
int pass_start;
int pass_end;
std::cin >> pass_start >> pass_end;
int start;
int end;
std::cin >> start >> end;
vector<vector<std::pair<int, int>>> neighbors(station_num);
for (int r = 0; r < railway_num; r++) {
int from;
int to;
int cost;
std::cin >> from >> to >> cost;
neighbors[--from].push_back({--to, cost});
neighbors[to].push_back({from, cost});
}
vector<long long> start_min = origin_min_costs(--pass_start, neighbors);
vector<long long> end_min = origin_min_costs(--pass_end, neighbors);
int total_min = start_min[pass_end]; // or end_min[pass_start], doesn't matter
vector<long long> min_cost(station_num, LLONG_MAX);
min_cost[--start] = 0;
auto cmp = [&] (const int& a, const int& b) { return min_cost[a] > min_cost[b]; };
std::priority_queue<int, vector<int>, decltype(cmp)> frontier(cmp);
frontier.push(start);
end--;
while (!frontier.empty()) {
int curr = frontier.top();
frontier.pop();
if (curr == end) {
break;
}
long long curr_cost = min_cost[curr];
for (auto [n, nc] : neighbors[curr]) {
long long new_cost = curr_cost;
if (start_min[curr] + nc + end_min[n] > total_min && end_min[curr] + nc + start_min[n] > total_min) {
new_cost += nc;
}
// cout << vector<int>{curr, n, (int) curr_cost, (int) new_cost} << endl;
if (new_cost < min_cost[n]) {
min_cost[n] = new_cost;
frontier.push(n);
}
}
}
// cout << start_min << endl;
// cout << end_min << endl << endl;
// cout << min_cost << endl;
cout << min_cost[end] << endl;
}
