#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#include <iostream>
#include <vector>
#include <queue>
#include <tuple>
using namespace std;
#define ll long long
#define INF 1e17
#define X first
#define Y second
vector<pair<int, int>> stage[100005];
vector<ll> sdist, udist, vdist;
bool status[100005];
int in[100005];
ll udp[100005], vdp[100005];
vector<int> graph[100005];
queue<int> q;
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
void dijkstra(vector<ll>& dist, int s)
{
fill(dist.begin(), dist.end(), INF);
dist[s] = 0;
pq.push({0, s});
while(!pq.empty())
{
ll d; int cur;
tie(d, cur) = pq.top(); pq.pop();
if(dist[cur] != d)
continue;
for(auto& nxt : stage[cur])
if(dist[nxt.X] > d + nxt.Y)
{
dist[nxt.X] = d + nxt.Y;
pq.push({dist[nxt.X], nxt.X});
}
}
}
void dfs(int cur, ll& ans)
{
udp[cur] = udist[cur];
vdp[cur] = vdist[cur];
ans = min(ans, udp[cur] + vdp[cur]);
for(auto& nxt : stage[cur])
if(sdist[nxt.X] + nxt.Y == sdist[cur])
{
in[nxt.X]++;
graph[cur].push_back(nxt.X);
if(!status[nxt.X])
{
status[nxt.X] = 1;
dfs(nxt.X, ans);
}
}
}
int main()
{
ios::sync_with_stdio(0);
cin.tie(0);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
while(m--)
{
int a, b, c;
cin >> a >> b >> c;
stage[a].push_back({b, c});
stage[b].push_back({a, c});
}
sdist.resize(n+1); udist.resize(n+1); vdist.resize(n+1);
dijkstra(sdist, s);
dijkstra(udist, u);
dijkstra(vdist, v);
ll ans = udist[v];
status[t] = 1;
dfs(t, ans);
q.push(t);
while(!q.empty())
{
int cur = q.front(); q.pop();
for(int& nxt : graph[cur])
{
udp[nxt] = min(udp[nxt], udp[cur]);
vdp[nxt] = min(vdp[nxt], vdp[cur]);
ans = min(ans, min(udist[nxt]+vdp[cur], udp[cur]+vdist[nxt]));
in[nxt]--;
if(in[nxt] == 0)
q.push(nxt);
}
}
cout << ans << '\n';
}
