#include <stdio.h>
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#include <random>
#include <chrono>
#include <queue>
#include <functional>
#include <iostream>
#include <queue>
//#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define mp make_pair
#define f first
#define s second
#define ld long double
const ll maxn = 1e5 + 1, maxm = 1e7 + 1;
const ll mod = 1e9 + 7, mod2 = 998244353, inf = 1e9, block = 550, hb = 31, base = 1000050017;
const ld eps = 1e-9;
int n, m;
int s, t;
int ss, tt;
bool is[maxn];
int go[maxn];
ll ans = inf * inf, dp[maxn], dp2[maxn], dp3[maxn], was[maxn];
ll pd[maxn][2];
vector<pair<int, int>> g[maxn];
vector<int> g2[maxn], g3[maxn];
void dfsis(int v){
if (v == t){
is[v] = 1;
}
for (auto to : g2[v]){
dfsis(to);
is[v] |= is[to];
}
}
void dijkstra(){
for (int i = 1; i <= n; ++i){
dp[i] = inf * inf;
}
dp[s] = 0;
set<pair<ll, int>> setik;
setik.insert(mp(0, s));
while (setik.size() > 0){
pair<ll, int> cur = *setik.begin();
setik.erase(cur);
ll cost = cur.f, v = cur.s;
if (dp[v] < cost){
continue;
}
for (auto to : g[v]){
int nv = to.f, w = to.s;
if (dp[nv] > cost + w){
dp[nv] = cost + w;
setik.insert(mp(dp[nv], nv));
}
}
}
for (int i = 1; i <= n; ++i){
for (auto to : g[i]){
int nv = to.f, w = to.s;
if (dp[i] > dp[nv]){
continue;
}
if (dp[nv] == w + dp[i] && dp[i] < dp[nv]){
g2[i].pb(nv);
}
}
}
dfsis(s);
for (int i = 1; i <= n; ++i){
g2[i].clear();
for (auto to : g[i]){
int nv = to.f, w = to.s;
if (dp[i] > dp[nv]){
continue;
}
if (dp[nv] == w + dp[i] && is[nv] == 1){
g2[i].pb(nv);
}
}
}
}
void dijkstra2(){
for (int i = 1; i <= n; ++i){
dp2[i] = inf * inf;
}
dp2[ss] = 0;
set<pair<ll, int>> setik;
setik.insert(mp(0, ss));
while (setik.size() > 0){
pair<ll, int> cur = *setik.begin();
setik.erase(cur);
ll cost = cur.f, v = cur.s;
if (dp2[v] < cost){
continue;
}
for (auto to : g[v]){
int nv = to.f, w = to.s;
if (dp2[nv] > cost + w){
dp2[nv] = cost + w;
setik.insert(mp(dp2[nv], nv));
}
}
}
}
void dijkstra3(){
for (int i = 1; i <= n; ++i){
dp3[i] = inf * inf;
}
dp3[tt] = 0;
set<pair<ll, int>> setik;
setik.insert(mp(0, tt));
while (setik.size() > 0){
pair<ll, int> cur = *setik.begin();
setik.erase(cur);
ll cost = cur.f, v = cur.s;
if (dp3[v] < cost){
continue;
}
for (auto to : g[v]){
int nv = to.f, w = to.s;
if (dp3[nv] > cost + w){
dp3[nv] = cost + w;
setik.insert(mp(dp3[nv], nv));
}
}
}
}
void backdfs(int v){
for (int i = 1; i <= n; ++i){
for (auto to : g2[i]){
go[i] += 1;
g3[to].pb(i);
}
pd[i][0] = inf * inf;
pd[i][1] = inf * inf;
}
queue<int> q;
q.push(v);
while (q.size() > 0){
int u = q.front();
q.pop();
pd[u][0] = min(pd[u][0], dp3[u]);
pd[u][1] = min(pd[u][1], dp2[u]);
ans = min(ans, pd[u][0] + dp2[u]);
ans = min(ans, pd[u][1] + dp3[u]);
for (auto to : g3[u]){
go[to] -= 1;
pd[to][0] = min(pd[to][0], pd[u][0]);
pd[to][1] = min(pd[to][1], pd[u][1]);
if (go[to] == 0){
q.push(to);
}
}
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cin >> n >> m;
cin >> s >> t;
cin >> ss >> tt;
for (int i = 1; i <= m; ++i){
int a, b, c;
cin >> a >> b >> c;
g[a].pb(mp(b, c));
g[b].pb(mp(a, c));
}
dijkstra();
dijkstra2();
dijkstra3();
backdfs(t);
ans = min(ans, dp2[tt]);
cout << ans << '\n';
}
