#include <bits/stdc++.h>
#define ll long long
#define F first
#define S second
#define MAXN 100005
#define ii pair<ll,int>
#define bit(i,j) ((i>>j)&1)
#define sz(i) (int)i.size()
#define endl '\n'
using namespace std;
const ll INF = 1e18 + 7;
int n, m, S, T, U, V;
vector<ii>g[MAXN];
namespace sub1
{
ll d[4][MAXN], dp1[MAXN], dp2[MAXN];
void bfs(int k, int st)
{
for(int i = 1; i <= n; i++)
d[k][i] = INF;
priority_queue<ii, vector<ii>, greater<ii>>q;
q.push({0, st});
d[k][st] = 0;
while(q.empty() != 1)
{
ii top = q.top();
q.pop();
ll kc = top.F;
int u = top.S;
for(ii i : g[u])
{
int v = i.F, w = i.S;
if(d[k][v] > kc + w)
{
d[k][v] = kc + w;
q.push({d[k][v], v});
}
}
}
}
void calc1()
{
priority_queue<ii, vector<ii>, greater<ii>>q;
for(int i = 1; i <= n; i++)
{
dp1[i] = d[2][i];
q.push({dp1[i], i});
}
while(q.empty() != 1)
{
ii top = q.top();
q.pop();
ll kc = top.F;
int u = top.S;
for(ii i : g[u])
{
int v = i.F, w = i.S;
if(d[0][v] + d[1][v] == d[0][T] && d[0][v] == d[0][u] + w && dp1[v] > kc)
{
dp1[v] = kc;
q.push({kc, v});
}
}
}
}
void calc2()
{
priority_queue<ii, vector<ii>, greater<ii>>q;
for(int i = 1; i <= n; i++)
{
dp2[i] = d[2][i];
q.push({dp2[i], i});
}
while(q.empty() != 1)
{
ii top = q.top();
q.pop();
ll kc = top.F;
int u = top.S;
for(ii i : g[u])
{
int v = i.F, w = i.S;
if(d[0][v] + d[1][v] == d[0][T] && d[1][v] == d[1][u] + w && dp2[v] > kc)
{
dp2[v] = kc;
q.push({kc, v});
}
}
}
}
void solve()
{
bfs(0, S);
bfs(1, T);
bfs(2, U);
bfs(3, V);
calc1();
calc2();
ll res = d[2][V];
for(int i = 1; i <= n; i++)
res = min(res, d[3][i] + min(dp1[i], dp2[i]));
cout << res;
}
}
main()
{
if(fopen("TEST.inp", "r"))
{
freopen("TEST.inp", "r", stdin);
freopen("TEST.out", "w", stdout);
}
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m >> S >> T >> U >> V;
for(int i = 1; i <= m; i++)
{
int x, y, z;
cin >> x >> y >> z;
g[x].push_back({y, z});
g[y].push_back({x, z});
}
sub1::solve();
// cerr << "\nTIME: " << 1.0 * clock() / CLOCKS_PER_SEC << endl;
}
