#include<bits/stdc++.h>
using namespace std;
#define int long long
#define F first
#define S second
#define all(x) x.begin(),x.end()
#define pii pair<int,int>
#define pb push_back
#define sz(x) (int)(x.size())
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
#define vi vector<int>
#define vp vector<pii>
#define vvi vector<vi>
#define ykh mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count())
void __print(int x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifdef local
void setio(){freopen("/Users/iantsai/Library/Mobile Documents/com~apple~CloudDocs/cpp/Empty.md","r",stdin);}
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
void setio(){}
#define debug(x...)
#endif
void setIO(string s) {
freopen((s + ".in").c_str(), "r", stdin);
freopen((s + ".out").c_str(), "w", stdout);
}
struct line{
int a,b;
int operator()(const int x)const{
return a*x+b;
}
};
bool check(line l1,line l2,line l3){
return (l3.b-l2.b)*(l1.a-l2.a)<=(l2.b-l1.b)*(l2.a-l3.a);
}
const int mxn=1e5+5;
vector<pii>adj[mxn];
int d[4][mxn];
int dp[2][mxn];
bool vis[mxn];
void dij(int st,int arr[]){
fill(vis,vis+mxn,false);
priority_queue<pii,vector<pii>,greater<pii>>pq;
pq.push({0,st});
while(sz(pq)){
auto [dis,v]=pq.top();
pq.pop();
if(!vis[v]){
arr[v]=dis;
vis[v]=1;
for(auto &u:adj[v]){
pq.push({dis+u.S,u.F});
}
}
}
}
int ans;
void dij2(int st,int ed,int arr[]){
fill(vis,vis+mxn,false);
fill(dp[0],dp[0]+mxn,1e18);
fill(dp[1],dp[1]+mxn,1e18);
priority_queue<pair<int,pii>,vector<pair<int,pii>>,greater<pair<int,pii>>>pq;
pq.push({0,{st,0}});
dp[0][0]=dp[1][0]=1e18;
while(sz(pq)){
int dis=pq.top().F;
int v=pq.top().S.F;
int pa=pq.top().S.S;
pq.pop();
if(!vis[v]){
vis[v]=1;
arr[v]=dis;
dp[0][v]=min(d[0][v],dp[0][pa]);
dp[1][v]=min(d[1][v],dp[1][pa]);
for(auto u:adj[v]){
pq.push({u.S+dis,{u.F,v}});
}
}
else if(dis==arr[v]){
if(min(d[0][v],dp[0][pa])+min(d[1][v],dp[1][pa])<=dp[0][v]+dp[1][v]){
dp[0][v]=min(d[0][v],dp[0][pa]);
dp[1][v]=min(d[1][v],dp[1][pa]);
}
}
debug(v,dp[0][v]+dp[1][v]);
}
chmin(ans,dp[0][ed]+dp[1][ed]);
}
signed main(){
setio();
ios::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
int n,m,s,t,u,v;
cin>>n>>m>>s>>t>>u>>v;
for(int i=0;i<m;i++){
int a,b,c;
cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
dij(u,d[0]);
dij(v,d[1]);
ans=d[0][v];
for(int i=1;i<=n;i++){
debug(d[0][i]);
}
dij2(s,t,d[2]);
dij2(t,s,d[3]);
cout<<ans<<'\n';
}
/*
input:
[node,dp[0][node]+dp[1][node]] = [6, 46]
[node,dp[0][node]+dp[1][node]] = [3, 22]
[node,dp[0][node]+dp[1][node]] = [1, 21]
[node,dp[0][node]+dp[1][node]] = [8, 20]
[node,dp[0][node]+dp[1][node]] = [4, 21]
[node,dp[0][node]+dp[1][node]] = [3, 22]
[node,dp[0][node]+dp[1][node]] = [9, 19]
[node,dp[0][node]+dp[1][node]] = [1, 21]
[node,dp[0][node]+dp[1][node]] = [1, 21]
[node,dp[0][node]+dp[1][node]] = [8, 20]
[node,dp[0][node]+dp[1][node]] = [5, 27]
[node,dp[0][node]+dp[1][node]] = [2, 15]
[node,dp[0][node]+dp[1][node]] = [2, 15]
[node,dp[0][node]+dp[1][node]] = [2, 15]
[node,dp[0][node]+dp[1][node]] = [5, 27]
[node,dp[0][node]+dp[1][node]] = [6, 46]
[node,dp[0][node]+dp[1][node]] = [9, 19]
[node,dp[0][node]+dp[1][node]] = [8, 20]
[node,dp[0][node]+dp[1][node]] = [4, 21]
[node,dp[0][node]+dp[1][node]] = [3, 22]
[node,dp[0][node]+dp[1][node]] = [1, 21]
[node,dp[0][node]+dp[1][node]] = [10, 21]
[node,dp[0][node]+dp[1][node]] = [3, 22]
[node,dp[0][node]+dp[1][node]] = [10, 21]
[node,dp[0][node]+dp[1][node]] = [7, 12]
[node,dp[0][node]+dp[1][node]] = [7, 3]
[node,dp[0][node]+dp[1][node]] = [6, 46]
[node,dp[0][node]+dp[1][node]] = [1, 21]
[node,dp[0][node]+dp[1][node]] = [2, 15]
[node,dp[0][node]+dp[1][node]] = [8, 20]
[node,dp[0][node]+dp[1][node]] = [5, 27]
[node,dp[0][node]+dp[1][node]] = [8, 21]
[node,dp[0][node]+dp[1][node]] = [9, 19]
[node,dp[0][node]+dp[1][node]] = [1, 21]
[node,dp[0][node]+dp[1][node]] = [8, 21]
[node,dp[0][node]+dp[1][node]] = [8, 21]
[node,dp[0][node]+dp[1][node]] = [4, 20]
[node,dp[0][node]+dp[1][node]] = [3, 20]
[node,dp[0][node]+dp[1][node]] = [1, 21]
[node,dp[0][node]+dp[1][node]] = [1, 21]
[node,dp[0][node]+dp[1][node]] = [2, 12]
[node,dp[0][node]+dp[1][node]] = [2, 12]
[node,dp[0][node]+dp[1][node]] = [2, 12]
[node,dp[0][node]+dp[1][node]] = [5, 16]
[node,dp[0][node]+dp[1][node]] = [6, 20]
[node,dp[0][node]+dp[1][node]] = [3, 20]
[node,dp[0][node]+dp[1][node]] = [10, 21]
[node,dp[0][node]+dp[1][node]] = [9, 19]
[node,dp[0][node]+dp[1][node]] = [4, 20]
[node,dp[0][node]+dp[1][node]] = [3, 20]
[node,dp[0][node]+dp[1][node]] = [8, 21]
[node,dp[0][node]+dp[1][node]] = [10, 21]
[node,dp[0][node]+dp[1][node]] = [7, 0]
[node,dp[0][node]+dp[1][node]] = [1, 21]
[node,dp[0][node]+dp[1][node]] = [7, 0]
[node,dp[0][node]+dp[1][node]] = [3, 20]
[node,dp[0][node]+dp[1][node]] = [6, 20]
[node,dp[0][node]+dp[1][node]] = [1, 21]
[node,dp[0][node]+dp[1][node]] = [5, 16]
[node,dp[0][node]+dp[1][node]] = [8, 21]
[node,dp[0][node]+dp[1][node]] = [2, 12]
[node,dp[0][node]+dp[1][node]] = [5, 16]
*/
