#include <iostream>
#include <vector>
#include <queue>
#include <set>
#include <algorithm>
using namespace std;
#define int long long
#define pii pair<ll, ll>
#define siz 100000
#define inf 1e18
#define ll long long
#define compSign >
int distFromB [siz];
int distFromA [siz];
int distFromDest [siz][4];
struct cdfb { bool operator()(int a, int b) { return (distFromB[a] compSign distFromB[b]); } };
struct cdfa { bool operator()(int a, int b) { return (distFromA[a] compSign distFromA[b]); } };
struct cdfd { bool operator()(pii a, pii b) { return (distFromDest[a.first][a.second] compSign distFromDest[b.first][b.second]); } };
int32_t main() {
int nbNodes, nbEdges;
cin >> nbNodes >> nbEdges;
int passA, passB;
cin >> passA >> passB;
passA--;
passB--;
int origin, destination;
cin >> origin >> destination;
origin--;
destination--;
vector<vector<pii>> graph(nbNodes);
for (int i = 0; i < nbEdges; i++) {
int la, lb, lw;
cin >> la >> lb >> lw;
la--;
lb--;
graph[la].push_back(pii(lb, lw));
graph[lb].push_back(pii(la, lw));
}
bool proc [nbNodes];
for (int i = 0; i < nbNodes; i++) {
proc[i] = false;
distFromB[i] = inf;
}
priority_queue<int, vector<int>, cdfb> pq1;
distFromB[passB] = 0;
pq1.push(passB);
while (!pq1.empty()) {
int cn = pq1.top();
pq1.pop();
if (proc[cn]) continue;
proc[cn] = true;
for (pii ne : graph[cn]) {
int nn = ne.first;
int nd = distFromB[cn]+ne.second;
if (nd < distFromB[nn]) {
distFromB[nn] = nd;
pq1.push(nn);
}
}
}
for (int i = 0; i < nbNodes; i++) {
proc[i] = false;
distFromA[i] = inf;
}
priority_queue<int, vector<int>, cdfa> pq2;
distFromA[passA] = 0;
pq2.push(passA);
while (!pq2.empty()) {
int cn = pq2.top();
pq2.pop();
if (proc[cn]) continue;
proc[cn] = true;
for (pii ne : graph[cn]) {
int nn = ne.first;
int nd = distFromA[cn]+ne.second;
if (nd < distFromA[nn]) {
distFromA[nn] = nd;
pq2.push(nn);
}
}
}
set<pii> stbEdges;
for (int i = 0; i < nbNodes; i++) {
for (pii j : graph[i]) {
if (distFromB[i] < distFromB[j.first] and distFromB[i]+distFromA[j.first]+j.second == distFromB[passA]) {
stbEdges.insert(pii(i, j.first));
}
}
}
bool procState [nbNodes][4];
for (int i = 0; i < nbNodes; i++) for (int j = 0; j < 4; j++) {
procState[i][j] = false;
distFromDest[i][j] = inf;
}
priority_queue<pii, vector<pii>, cdfd> q;
distFromDest[origin][0] = 0;
q.push(pii(origin, 0));
while (!q.empty()) {
int cn = q.top().first;
int cs = q.top().second;
q.pop();
if (procState[cn][cs]) continue;
proc[cn] = true;
for (pii ne : graph[cn]) {
int nn = ne.first;
if (cs != 3 and cs != 2 and stbEdges.find(pii(cn, nn)) != stbEdges.end()) {
int nd = distFromDest[cn][cs];
int ns = 1;
if (nd < distFromDest[nn][ns]) {
distFromDest[nn][ns] = nd;
q.push(pii(nn, ns));
}
}
else if (cs != 3 and cs != 1 and stbEdges.find(pii(nn, cn)) != stbEdges.end()) {
int nd = distFromDest[cn][cs];
int ns = 2;
if (nd < distFromDest[nn][ns]) {
distFromDest[nn][ns] = nd;
q.push(pii(nn, ns));
}
}
int nd = distFromDest[cn][cs]+ne.second;
int ns = 0;
if (cs != 0) ns = 3;
if (nd < distFromDest[nn][ns]) {
distFromDest[nn][ns] = nd;
q.push(pii(nn, ns));
}
}
}
int minD = inf;
for (int i = 0; i < 4; i++) minD = min(minD, distFromDest[destination][i]);
cout << minD;
int d = 0;
d++;
}
