#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define MAXN 100100
#define RNG(i, n) for(int i=0;i<n;i++)
struct Edge{
int u, w;
Edge() : u(0), w(0) {}
Edge(int u, int w) : u(u), w(w) {}
};
struct Edge2 {
int u, j, w;
Edge2() : u(0), j(0), w(0) {}
Edge2(int u, int j, int w) : u(u), j(j), w(w) {}
};
ll du[MAXN];
ll dv[MAXN];
vector<Edge> adj[MAXN];
bool visited[MAXN];
bool v2[MAXN][4];
ll dist[MAXN];
vector<Edge2> adj2[MAXN][4];
ll d2[MAXN][4];
vector<ll> opt[MAXN];
int n;
void basicDjikstra(int u, ll *d) {
RNG(i, n) d[i]=LONG_LONG_MAX;
memset(visited, 0, sizeof(visited));
d[u]=0;
priority_queue<pair<ll, int>> pq;
pq.push({0, u});
while(!pq.empty()) {
pair<ll, int> pr=pq.top();
pq.pop();
int v=pr.second;
if(visited[v]) continue;
visited[v]=true;
ll curd=d[v];
for(auto e : adj[v]) {
int u=e.u;
int w=e.w;
ll newd=curd+w;
if(newd<d[u]) {
d[u]=newd;
pq.push({-newd, u});
}
}
}
}
int main() {
int m, s, t, u, v;
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
s--;
t--;
u--;
v--;
RNG(i, m) {
int a, b, c;
cin >> a >> b >> c;
a--;
b--;
adj[a].push_back(Edge(b, c));
adj[b].push_back(Edge(a, c));
}
basicDjikstra(u, du);
RNG(i, n) dist[i]=LONG_LONG_MAX;
memset(visited, 0, sizeof(visited));
priority_queue<pair<ll, int>> pq;
pq.push({0, s});
dist[s]=0;
while(!pq.empty()) {
pair<ll, int> pr=pq.top();
pq.pop();
int v=pr.second;
if(visited[v]) continue;
visited[v]=true;
ll curd=dist[v];
for(auto e : adj[v]) {
int to=e.u;
int w=e.w;
ll newd=curd+w;
if(newd<dist[to]) {
dist[to]=newd;
pq.push({-newd, to});
opt[to].clear();
}
if(newd<=dist[to]) {
opt[to].push_back(v);
}
}
}
RNG(i, n) {
for(auto e : adj[i]) {
adj2[i][0].push_back(Edge2(e.u, 0, e.w));
adj2[i][3].push_back(Edge2(e.u, 3, e.w));
}
RNG(j, 3) {
for(int k=j+1;k<4;k++) {
if(j==1&&k==2) continue;
adj2[i][j].push_back(Edge2(i, k, 0));
}
}
}
memset(visited, 0, sizeof(visited));
stack<int> st;
st.push(t);
visited[t]=true;
while(!st.empty()) {
int v=st.top();
st.pop();
for(auto u : opt[v]) {
adj2[u][1].push_back(Edge2(v, 1, 0));
adj2[v][2].push_back(Edge2(u, 2, 0));
if(visited[u]) continue;
visited[u]=true;
st.push(u);
}
}
priority_queue<pair<ll, pair<int, int>>> pq2;
pq2.push({0, {u, 0}});
memset(v2, 0, sizeof(v2));
RNG(i, n) RNG(j, 4) d2[i][j]=LONG_LONG_MAX;
d2[u][0]=0;
while(!pq2.empty()) {
pair<ll, pair<int, int>> pr = pq2.top();
pq2.pop();
int v=pr.second.first;
int j=pr.second.second;
if(v2[v][j]) continue;
ll d=d2[v][j];
v2[v][j]=true;
for(auto e : adj2[v][j]) {
ll newd=d+e.w;
ll &cur=d2[e.u][e.j];
if(newd<cur) {
cur=newd;
pq2.push({-newd, {e.u, e.j}});
}
}
}
cout << d2[v][3] << endl;
}
