#include<bits/stdc++.h>
#define god dimasi5eks
#pragma GCC optimize("O3")
#define fi first
#define se second
#define pb push_back
#define pf push_front
#define mod 1000000007
#define dancila 3.14159265359
#define eps 1e-9
// #define fisier
using namespace std;
typedef long long ll;
int n, m;
int s, t;
int u, v;
vector<pair<int, int> >g[200002];
ll shp[2][100002];
bool viz[2][100002];
struct cmp
{
bool operator()(pair<ll, pair<int, int> > a,pair<ll, pair<int, int> > b)
{
return a.fi > b.fi;
}
};
priority_queue<pair<ll, pair<int, int> >, vector<pair<ll, pair<int, int> > >, cmp> q;
bool was[2][100002];
void djk(int wh, int st)
{
viz[wh][st] = 1;
q.push({0, {0, st}});
while(!q.empty())
{
pair<ll, pair<int, int> > nod = q.top();
q.pop();
if(was[wh][nod.se.se])
continue;
was[wh][nod.se.se] = 1;
for(int i = 0; i < g[nod.se.se].size(); ++i)
{
int vecin = g[nod.se.se][i].fi;
int cost = g[nod.se.se][i].se;
if(!viz[wh][vecin] || nod.fi + cost < shp[wh][vecin])
{
shp[wh][vecin] = nod.fi + cost;
viz[wh][vecin] = 1;
q.push({shp[wh][vecin], {0, vecin}});
}
}
}
while(!q.empty())
q.pop();
}
bool viz2[4][100002];
bool was2[4][100002];
ll cost[4][100002];
int main()
{
#ifdef fisier
ifstream f("input.in");
ofstream g("output.out");
#endif
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
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});
}
djk(0, s);
djk(1, t);
viz2[0][u] = 1;
q.push({0, {0, u}});
while(!q.empty())
{
pair<ll, pair<int, int> > nod = q.top();
q.pop();
if(was2[nod.se.fi][nod.se.se])
continue;
// cout << nod.fi << " " << nod.se.fi << " " << nod.se.se << '\n';
was2[nod.se.fi][nod.se.se] = 1;
for(int i = 0; i < g[nod.se.se].size(); ++i)
{
int vecin = g[nod.se.se][i].fi;
int cs = g[nod.se.se][i].se;
if(nod.se.fi == 3)
{
if(!viz2[3][vecin] || nod.fi + cs < cost[3][vecin])
{
cost[3][vecin] = nod.fi + cs;
viz2[3][vecin] = 1;
q.push({cost[3][vecin], {3, vecin}});
}
}
if(nod.se.fi == 2)
{
if(shp[0][t] == shp[0][vecin] + shp[1][vecin] && shp[0][t] == shp[0][nod.se.se] + shp[1][nod.se.se] && shp[0][vecin] > shp[0][nod.se.se])
{
if(!viz2[2][vecin] || nod.fi < cost[2][vecin])
{
cost[2][vecin] = nod.fi;
viz2[2][vecin] = 1;
q.push({cost[2][vecin], {2, vecin}});
}
}
else
{
if(!viz2[3][vecin] || nod.fi + cs < cost[3][vecin])
{
cost[3][vecin] = nod.fi + cs;
viz2[3][vecin] = 1;
q.push({cost[3][vecin], {3, vecin}});
}
}
}
if(nod.se.fi == 1)
{
if(shp[0][t] == shp[0][vecin] + shp[1][vecin] && shp[0][t] == shp[0][nod.se.se] + shp[1][nod.se.se] && shp[0][vecin] < shp[0][nod.se.se])
{
if(!viz2[1][vecin] || nod.fi < cost[1][vecin])
{
cost[1][vecin] = nod.fi;
viz2[1][vecin] = 1;
q.push({cost[1][vecin], {1, vecin}});
}
}
else
{
if(!viz2[3][vecin] || nod.fi + cs < cost[3][vecin])
{
cost[3][vecin] = nod.fi + cs;
viz2[3][vecin] = 1;
q.push({cost[3][vecin], {3, vecin}});
}
}
}
if(nod.se.fi == 0)
{
if(shp[0][t] == shp[0][vecin] + shp[1][vecin] && shp[0][t] == shp[0][nod.se.se] + shp[1][nod.se.se] && shp[0][vecin] > shp[0][nod.se.se])
{
if(!viz2[2][vecin] || nod.fi < cost[2][vecin])
{
cost[2][vecin] = nod.fi;
viz2[2][vecin] = 1;
q.push({cost[2][vecin], {2, vecin}});
}
}
else
if(shp[0][t] == shp[0][vecin] + shp[1][vecin] && shp[0][t] == shp[0][nod.se.se] + shp[1][nod.se.se] && shp[0][vecin] < shp[0][nod.se.se])
{
if(!viz2[1][vecin] || nod.fi < cost[1][vecin])
{
cost[1][vecin] = nod.fi;
viz2[1][vecin] = 1;
q.push({cost[1][vecin], {1, vecin}});
}
}
if(!viz2[0][vecin] || nod.fi + cs < cost[0][vecin])
{
cost[0][vecin] = nod.fi + cs;
viz2[0][vecin] = 1;
q.push({cost[0][vecin], {0, vecin}});
}
}
/*
int mult = 1;
if(shp[0][t] == shp[0][nod.se] + shp[1][nod.se] && shp[0][t] == shp[0][vecin] + shp[1][vecin])
mult = 0;
if(!viz2[vecin] || nod.fi + cs * mult < cost[vecin])
{
cost[vecin] = nod.fi + cs * mult;
viz2[vecin] = 1;
q.push({cost[vecin], vecin});
}
*/
}
}
ll ans = (1LL<<60);
for(int i = 0; i <= 3; ++i)
if(viz2[i][v])
ans = min(ans, cost[i][v]);
cout << ans << '\n';
return 0;
}
