#include <bits/stdc++.h>
 
//    #include <boost/multiprecision/cpp_int.hpp>
 #define int long long
 #define inf  1000000007
 #define pa pair<int,int>
 #define ll long long
 #define pal pair<double,double>
 #define ppap pair<pa,int>
  #define PI 3.14159265358979323846
  #define paa pair<int,char>
  #define  mp make_pair
  #define  pb push_back
  #define EPS (1e-8)
                                          
    int dx[8]={0,1,0,-1,1,1,-1,-1};
    int dy[8]={1,0,-1,0,-1,1,1,-1};
                                            using namespace std;
                                   			class pa3{
                                            	public:
                                            	int x;
                                   				int y,z;
                                            	pa3(int x=0,int y=0,int z=0):x(x),y(y),z(z) {}
                                            	bool operator < (const pa3 &p) const{
                                            		if(x!=p.x) return x<p.x;
                                            		if(y!=p.y) return y<p.y;
                                            		 return z<p.z;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                   				bool operator > (const pa3 &p) const{
                                            		if(x!=p.x) return x>p.x;
                                            		if(y!=p.y) return y>p.y;
                                            		 return z>p.z;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa3 &p) const{
                                            		return x==p.x && y==p.y && z==p.z;
                                            	}
                                            		bool operator != (const pa3 &p) const{
                                            			return !( x==p.x && y==p.y && z==p.z);
                                            	}
                                            
                                            };
                                            
                                            class pa4{
                                            	public:
                                            	int x;
                                            	int y,z,w;
                                            	pa4(int x=0,int y=0,int z=0,int w=0):x(x),y(y),z(z),w(w) {}
                                            	bool operator < (const pa4 &p) const{
                                            		if(x!=p.x) return x<p.x;
                                            		if(y!=p.y) return y<p.y;
                                            		if(z!=p.z)return z<p.z;
                                            		return w<p.w;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator > (const pa4 &p) const{
                                            		if(x!=p.x) return x>p.x;
                                            		if(y!=p.y) return y>p.y;
                                            		if(z!=p.z)return z>p.z;
                                            		return w>p.w;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa4 &p) const{
                                            		return x==p.x && y==p.y && z==p.z &&w==p.w;
                                            	}
                                            		
                                            
                                            };
                                            class pa2{
                                            	public:
                                            	int x,y;
                                            	pa2(int x=0,int y=0):x(x),y(y) {}
                                            	pa2 operator + (pa2 p) {return pa2(x+p.x,y+p.y);}
                                            	pa2 operator - (pa2 p) {return pa2(x-p.x,y-p.y);}
                                            	bool operator < (const pa2 &p) const{
                                            		return y != p.y ? y<p.y: x<p.x;
                                            	}
                                            	bool operator > (const pa2 &p) const{
                                            		return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa2 &p) const{
                                            		return abs(x-p.x)==0 && abs(y-p.y)==0;
                                            	}
                                            	bool operator != (const pa2 &p) const{
                                            		return !(abs(x-p.x)==0 && abs(y-p.y)==0);
                                            	}
                                            		
                                            
                                            };
                                            
 
                      
                                string itos( int i ) {
                                ostringstream s ;
                                s << i ;
                                return s.str() ;
                                }
                                 
                                int gcd(int v,int b){
                                	if(v==0) return b;
                                	if(b==0) return v;
                                	if(v>b) return gcd(b,v);
                                	if(v==b) return b;
                                	if(b%v==0) return v;
                                	return gcd(v,b%v);
                                }
                 
                            
                                int mod;
int extgcd(int a, int b, int &x, int &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    int d = extgcd(b, a%b, y, x);
    y -= a/b * x;
    return d;
}
pa operator+(const pa & l,const pa & r) {   
    return {l.first+r.first,l.second+r.second};                                    
}    
pa operator-(const pa & l,const pa & r) {   
    return {l.first-r.first,l.second-r.second};                                    
}  
                                
                int pr[10000100];
                int inv[10000010];
                
                int beki(int wa,int rr,int warukazu){
                	if(rr==0) return 1%warukazu;
                	if(rr==1) return wa%warukazu;
                	wa%=warukazu;
                	if(rr%2==1) return ((ll)beki(wa,rr-1,warukazu)*(ll)wa)%warukazu;
                	ll zx=beki(wa,rr/2,warukazu);
                	return (zx*zx)%warukazu;
                }
 
                
    			int comb(int nn,int rr){
    				if(rr<0 || rr>nn || nn<0) return 0;
    				int r=pr[nn]*inv[rr];
    				r%=mod;
    				r*=inv[nn-rr];
    				r%=mod;
    				return r;
    			}
               
                void gya(int ert){
                	pr[0]=1;
                	for(int i=1;i<=ert;i++){
                		pr[i]=(pr[i-1]*i)%mod;
                	}
                		inv[ert]=beki(pr[ert],mod-2,mod);
                	for(int i=ert-1;i>=0;i--){
                		inv[i]=inv[i+1]*(i+1)%mod;
                	}
                }
                
              //   cin.tie(0);
    		//	ios::sync_with_stdio(false);
    			//priority_queue<pa3,vector<pa3>,greater<pa3>> pq;            
                 //sort(ve.begin(),ve.end(),greater<int>());
 //   mt19937(clock_per_sec);
  //  mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()) ;
      
       



vector<pa> G[100020];

int dis[100020][4];

int n;
void dij(int r,int po){
	for(int i=1;i<=n;i++)dis[i][po]=-1;
	priority_queue<pa,vector<pa>,greater<pa>> pq;   
	pq.push(mp(0,r));
	while(pq.size()){
		pa z=pq.top();
		pq.pop();
		if(dis[z.second][po]>=0) continue;
		dis[z.second][po]=z.first;
		for(auto v:G[z.second])pq.push(mp(z.first+v.second,v.first));
	}
}



vector<int> G1[100020];
vector<int> G2[100020];

int nyu[100020]={};
int use[100020]={};

int ue[100020][2];
int si[100020][2];
signed main(){
	
	
   cin.tie(0);
	ios::sync_with_stdio(false);
	int m;
cin>>n>>m;
	int S,T,U,V;
	cin>>S>>T>>U>>V;
	
	for(int i=0;i<m;i++){
		int y,yy,yyy;
		cin>>y>>yy>>yyy;
		G[y].pb(mp(yy,yyy));
		G[yy].pb(mp(y,yyy));
		
	}
	dij(S,0);
	dij(T,1);
	dij(U,2);
	dij(V,3);
	
	int ST=dis[T][0];
	
	for(int i=1;i<=n;i++)for(auto v:G[i]){
		int s=i,t=v.first,val=v.second;
		if(dis[s][0]+dis[t][1]+val==ST){
			G1[s].pb(t);
			G2[t].pb(s);
			nyu[t]++;
			use[s]=1,use[t]=1;
			
		}
	}
	queue<int> qu;
	for(int i=1;i<=n;i++)if(use[i])if(nyu[i]==0)qu.push(i);
	vector<int> topo;
	while(qu.size()){
		int y=qu.front();
		qu.pop();
		topo.pb(y);
		for(auto v:G1[y]){
			nyu[v]--;
			if(nyu[v]==0)qu.push(v);
		}
	}
	
	for(auto v:topo){
		ue[v][0]=dis[v][2];
		ue[v][1]=dis[v][3];
		
		for(auto r:G2[v]){
			ue[v][0]=min(ue[v][0],ue[r][0]);
			ue[v][1]=min(ue[v][1],ue[r][1]);
			
		}
	}
	reverse(topo.begin(),topo.end());
	for(auto v:topo){
		si[v][0]=dis[v][2];
		si[v][1]=dis[v][3];
		
		for(auto r:G1[v]){
			si[v][0]=min(si[v][0],si[r][0]);
			si[v][1]=min(si[v][1],si[r][1]);
			
		}
	}
	int ans=dis[U][3];
	for(int i=1;i<=n;i++)if(use[i]==1){
		ans=min({ans,ue[i][0]+si[i][1],si[i][0]+ue[i][1]});
	
	}
	cout<<ans<<endl;
	return 0;
	

 
 }



Measured memory_bytes: 36588