//#pragma GCC target ("avx2")
//#pragma GCC optimize ("Ofast")
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define F first
#define S second
#define pb push_back
const int N = 1e6, NN=10;
const int mod=1e9+7;
vector < pair < int, int > > vr[N], vr2[N];
vector < int > top;
bool was[N], was2[N];
int n, m, s, t, u, v;
int d1[N], d2[N], dp[3][N], d[N];
void dfs(int x){
was[x]=1;
for(auto to : vr2[x]){
if(was[to.F]) continue;
dfs(to.F);
}
top.pb(x);
}
void dfs2(int x){
was2[x]=1;
for(auto to : vr[x]){
if(was2[to.F]) continue;
if(d[to.F]+to.S==d[x]){
vr2[to.F].pb({x, 0});
dfs2(to.F);
}
}
}
void dj1(int x){
multiset < pair < int, int > > st;
st.insert({0, x});
for(int i=1;i<=n;i++){
d1[i]=1e18;
}
d1[x]=0;
while(st.size()>0){
int f1=(*st.begin()).F, s1=(*st.begin()).S;
st.erase(st.find({f1, s1}));
for(auto to : vr[s1]){
int f2=to.F, s2=to.S;
if(d1[f2]>d1[s1]+s2){
st.erase({d1[f2], f2});
d1[f2]=d1[s1]+s2;
st.insert({d1[f2], f2});
}
}
}
dfs2(t);
}
void dj2(int x){
multiset < pair < int, int > > st;
st.insert({0, x});
for(int i=1;i<=n;i++) d2[i]=1e18;
d2[x]=0;
while(st.size()>0){
int f1=(*st.begin()).F, s1=(*st.begin()).S;
st.erase(st.find({f1, s1}));
for(auto to : vr[s1]){
int f2=to.F, s2=to.S;
if(d2[f2]>d2[s1]+s2){
st.erase({d2[f2], f2});
d2[f2]=d2[s1]+s2;
st.insert({d2[f2], f2});
}
}
}
}
void dj(){
multiset < pair < int, int > > st;
st.insert({0, s});
for(int i=1;i<=n;i++){
d[i]=1e18;
}
d[s]=0;
while(st.size()>0){
int f1=(*st.begin()).F, s1=(*st.begin()).S;
st.erase(st.find({f1, s1}));
for(auto to : vr[s1]){
int f2=to.F, s2=to.S;
if(d[f2]>d[s1]+s2){
st.erase({d[f2], f2});
d[f2]=d[s1]+s2;
st.insert({d[f2], f2});
}
}
}
dfs2(t);
}
//int gcd(int a, int b) { if (b == 0) return a; else return gcd(b, a % b); }
//int lcm(int a, int b) { return a / gcd(a, b) * b; }
//int binpow(int a,int b){if(!b)return 1; if(b&1)return a*binpow(a,b-1)%mod; int x=binpow(a,b/2); return x*x%mod;}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
for(int i=1;i<=n;i++){
int a, b, c;
cin >> a >> b >> c;
vr[a].pb({b, c});
vr[b].pb({a, c});
}
dj1(u);
dj2(v);
dj();
dfs(s);
for(int i=1;i<=n;i++){
dp[1][i]=1e18;
dp[2][i]=1e18;
}
int ans=d1[v];
for(auto to : top){
ans=min(ans, d1[to]+d2[to]);
dp[1][to]=d2[to];
dp[2][to]=d1[to];
for(auto to2 : vr2[to]){
dp[1][to]=min(dp[1][to], dp[1][to2.F]);
dp[2][to]=min(dp[2][to], dp[2][to2.F]);
ans=min({ans, dp[1][to]+d1[to], dp[2][to]+d2[to]});
}
}
cout << ans;
}
