#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <functional>
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,
tree_order_statistics_node_update>
ordered_set;
//Dijkstra->set
//set.find_by_order(x) x-position value
//set.order_of_key(x) number of strictly less elements don't need *set.??
#define N 100005
#define wr cout << "Continue debugging\n";
#define all(x) (x).begin(), (x).end()
#define ll long long int
#define pii pair <ll, ll>
#define pb push_back
#define ff first
#define ss second
int n, m, s, t, u, v;
vector<pii> E[N];
void dijk(int x, vector<ll>&dis){
set<pii> s = {{0, x}};
dis[x] = 0;
while(!s.empty()){
int x = (*s.begin()).ss;
s.erase(s.begin());
for (auto i : E[x]){
if (dis[i.ff] > dis[x]+i.ss){
s.erase({dis[i.ff], i.ff});
dis[i.ff] = dis[x]+i.ss;
s.insert({dis[i.ff], i.ff});
}
}
}
}
int main ()
{
ios::sync_with_stdio(false);
cin.tie(0);
cin >> n >> m >> s >> t >> u >> v;
while(m--){
int x, y, w;
cin >> x >> y >> w;
E[x].pb({y, w});
E[y].pb({x, w});
}
vector<ll> disu(n+1, 1e17), disv(n+1, 1e17), diss(n+1, 1e17);
dijk(v, disv); dijk(u, disu);
vector<ll> dis(n+1, 1e17);
vector<ll> canu(n+1, 1e17), canv(n+1, 1e17);
priority_queue<pii, vector<pii>, greater<pii>> q;
q.push({0, s});
dis[s] = 0;
canu[s] = disu[s]; canv[s] = disv[s];
while(!q.empty()){
ll w = q.top().ff;
int x = q.top().ss;
q.pop();
if (w != dis[x]) continue;
for (auto i : E[x]){
if (dis[i.ff] > dis[x]+i.ss){
dis[i.ff] = dis[x]+i.ss;
canv[i.ff] = min(canv[x], disv[i.ff]);
canu[i.ff] = min(canu[x], disu[i.ff]);
q.push({dis[i.ff], i.ff});
}else if (dis[i.ff] == dis[x]+i.ss and canv[i.ff]+canu[i.ff] > min(canv[x], disv[i.ff])+min(canu[x], disu[i.ff])){
canv[i.ff] = min(canv[x], disv[i.ff]);
canu[i.ff] = min(canu[x], disu[i.ff]);
q.push({dis[i.ff], i.ff});
}
}
}
cout << min(canu[t]+canv[t], disv[u]);
}
