#include <bits/stdc++.h>
using namespace std;
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC optimize("Ofast,unroll-loops,fast-math,O3")
#define pb push_back
#define ll long long
#define int long long
//#define sort(all(v)) sort(v.begin(),v.end())
int mod = 998244353;
const int N = 1e5 + 10;
const int inf = 1e9;
int fact[200001];
ll binpow(ll a, ll b){
if(b == 0) return 1;
else if(b % 2 == 1) return (a * binpow(a, b - 1)) % mod;
ll p = binpow(a,b / 2);
return (p * p) % mod;
}
vector<int> d(N,1e18),d1(N,1e18),d2(N,1e18),d3(N,1e18);
int was[N],dp[N][3];
vector <pair<int,int>> g[N];
vector <int> g1[N],top;
void dfs(int u){
was[u] = 1;
for(int to : g1[u]){
if(was[to] != 0) continue;
dfs(to);
}
top.pb(u);
}
signed main(){
//freopen("mootube.in", "r", stdin);
//freopen("mootube.out", "w", stdout);
int n,m,s,t,u,v;
cin >> n >> m >> s >> t >> u >> v;
vector <array<int,3>> q;
for(int i = 1; i <= m; i++){
int a,b,c;
cin >> a >> b >> c;
g[a].pb({b,c});
g[b].pb({a,c});
q.pb({a,b,c});
}
set <pair<int,int>> st;
st.insert({0,s});
d[s] = 0;
while(st.size() > 0){
int u1 = (*st.begin()).second;
st.erase(st.begin());
for(auto [to,w] : g[u1]){
if(d[to] > d[u1] + w){
st.erase({d[to],to});
d[to] = d[u1] + w;
st.insert({d[to],to});
}
}
}
st.insert({0,t});
d1[t] = 0;
while(st.size() > 0){
int u1 = (*st.begin()).second;
st.erase(st.begin());
for(auto [to,w] : g[u1]){
if(d1[to] > d1[u1] + w){
st.erase({d1[to],to});
d1[to] = d1[u1] + w;
st.insert({d1[to],to});
}
}
}
st.insert({0,u});
d2[u] = 0;
while(st.size() > 0){
int u1 = (*st.begin()).second;
st.erase(st.begin());
for(auto [to,w] : g[u1]){
if(d2[to] > d2[u1] + w){
st.erase({d2[to],to});
d2[to] = d2[u1] + w;
st.insert({d2[to],to});
}
}
}
st.insert({0,v});
d3[v] = 0;
while(st.size() > 0){
int u1 = (*st.begin()).second;
st.erase(st.begin());
for(auto [to,w] : g[u1]){
if(d3[to] > d3[u1] + w){
st.erase({d3[to],to});
d3[to] = d3[u1] + w;
st.insert({d3[to],to});
}
}
}
for(int i = 0; i < m; i++){
int a = q[i][0],b = q[i][1],c = q[i][2];
if(d[a] + d1[b] + c == d[t]){
g1[a].pb(b);
}
if(d[b] + d1[a] + c == d[t]){
g1[b].pb(a);
}
}
dfs(s);
for(int i = 0; i < top.size(); i++){
//cout << top[i] << ' ';
dp[top[i]][1] = d3[top[i]];
dp[top[i]][2] = d2[top[i]];
for(auto to : g1[top[i]]){
dp[top[i]][1] = min(dp[top[i]][1],dp[to][1]);
dp[top[i]][2] = min(dp[top[i]][2],dp[to][2]);
//cout << to << " ";
}
}
int ans = d2[v];
for(int i : top){
ans = min({ans,d2[i] + dp[i][1],d3[i] + dp[i][2]});
//cout << dp[i][1] << ' ' << dp[i][2] << " " << i << '\n';
}
cout << ans;
}
