#include <bits/stdc++.h>
//#include "factories.h"
//#include "wall.h"
#define f first
#define s second
#define int long long
using namespace std;
const int maxn = 1e5 + 69;
vector<pair<int, int>> g[maxn];
int n, m, s, t, u, v;
const int inf = 1e18;
vector<int> d(maxn, inf);
vector<int> ds(maxn, inf), dt(maxn, inf);
vector<int> du(maxn, inf), dv(maxn, inf);
vector<int> in(maxn, inf), out(maxn, inf);
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
int tt = 1;
//cin >> tt;
while(tt--) {
cin >> n >> m >> s >> t >> u >> v;
for(int i = 0;i < m;i++) {
int a, b, c;
cin >> a >> b >> c;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
ds[s] = du[u] = dv[v] = dt[t] = d[s] = 0;
priority_queue<pair<int, int>> pq;
pq.push({0, s});
while(!pq.empty()) {
auto u = pq.top();
pq.pop();
for(auto v : g[u.s]) {
if(ds[v.f] <= ds[u.s] + v.s)
continue;
ds[v.f] = ds[u.s] + v.s;
pq.push({-ds[v.f], v.f});
}
}
pq.push({0, t});
while(!pq.empty()) {
auto u = pq.top();
pq.pop();
for(auto v : g[u.s]) {
if(dt[v.f] <= dt[u.s] + v.s)
continue;
dt[v.f] = dt[u.s] + v.s;
pq.push({-dt[v.f], v.f});
}
}
pq.push({0, u});
while(!pq.empty()) {
auto u = pq.top();
pq.pop();
for(auto v : g[u.s]) {
if(du[v.f] <= du[u.s] + v.s)
continue;
du[v.f] = du[u.s] + v.s;
pq.push({-du[v.f], v.f});
}
}
pq.push({0, v});
while(!pq.empty()) {
auto u = pq.top();
pq.pop();
for(auto v : g[u.s]) {
if(dv[v.f] <= dv[u.s] + v.s)
continue;
dv[v.f] = dv[u.s] + v.s;
pq.push({-dv[v.f], v.f});
}
}
int ans = du[v];
for(int i = 1;i <= n;i++)
in[i] = out[i] = inf;
function<void(int)> dfs1 = [&](int v) {
if(in[v] != inf || ds[v] + dt[v] != ds[t])
return;
in[v] = du[v];
for(auto u : g[v]) {
if(ds[u.f] == ds[v] + u.s) {
dfs1(u.f);
in[v] = min(in[u.f], in[v]);
}
}
ans = min(ans, in[v] + dv[v]);
};
function<void(int)> dfs2 = [&](int v) {
if(in[v] != inf || ds[v] + dt[v] != ds[t])
return;
in[v] = du[v];
for(auto u : g[v]) {
if(dt[u.f] == dt[v] + u.s) {
dfs2(u.f);
in[v] = min(in[u.f], in[v]);
}
}
ans = min(ans, in[v] + dv[v]);
};
dfs1(s);
for(int i = 1;i <= n;i++)
in[i] = inf;
dfs2(t);
cout << ans;
}
return 0;
}
