#include <bits/stdc++.h>
#define fi first
#define se second
#define int long long
using namespace std;
const int MAXN = 100001;
typedef pair<int, int> II;
typedef pair<long long, int> LLI;
typedef pair<long long, II> LLII;
int n, m, s, t, u, v;
long long ds[MAXN], dt[MAXN];
vector<II> g[MAXN];
set<LLI> q;
void dijk(int start, long long *d)
{
for (int i = 1; i <= n; ++i)
d[i] = LLONG_MAX;
q.clear();
d[start] = 0;
q.insert(LLI(0, start));
while (!q.empty())
{
int a = q.begin()->se;
q.erase(q.begin());
for (II x : g[a])
{
int b = x.fi, w = x.se;
if (d[b] > d[a] + 1ll * w)
{
if (d[b] < LLONG_MAX)
q.erase(LLI(d[b], b));
d[b] = d[a] + 1ll * w;
q.insert(LLI(d[b], b));
}
}
}
}
set<LLII> sLII;
long long d[4][MAXN];
long long get(int start, int stop)
{
for (int j = 0; j < 4; ++j)
for (int i = 1; i <= n; ++i)
d[j][i] = LLONG_MAX;
sLII.clear();
d[0][start] = 0;
sLII.insert(LLII(0, II(0, start)));
while (!sLII.empty())
{
int a = sLII.begin()->se.se, type = sLII.begin()->se.fi;
sLII.erase(sLII.begin());
if (type < 3)
{
if (d[type + 1][a] > d[type][a] && (type == 2 || ds[a] + dt[a] == ds[t]))
{
if (d[type + 1][a] < LLONG_MAX)
sLII.erase(LLII(d[type + 1][a], II(type + 1, a)));
d[type + 1][a] = d[type][a];
sLII.insert(LLII(d[type + 1][a], II(type + 1, a)));
}
}
for (II x : g[a])
{
int b = x.fi, w = x.se;
if (d[type][b] > d[type][a] + 1ll * w && (type == 0 || (type == 1 && ds[b] + dt[b] == ds[t]) || (type == 2 && ds[a] + w + dt[b] == ds[t]) || type == 3))
{
if (d[type][b] < LLONG_MAX)
sLII.erase(LLII(d[type][b], II(type, b)));
d[type][b] = d[type][a] + 1ll * ((type == 2) ? 0 : w);
sLII.insert(LLII(d[type][b], II(type, b)));
}
}
}
long long ans = LLONG_MAX;
for (int j = 0; j < 4; ++j)
ans = min(ans, d[j][stop]);
return ans;
}
int32_t main()
{
if (fopen("inp.txt", "r"))
{
freopen("inp.txt", "r", stdin);
freopen("out.txt", "w", stdout);
}
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; ++i)
{
int a, b, c;
cin >> a >> b >> c;
g[a].push_back(II(b, c));
g[b].push_back(II(a, c));
}
dijk(s, ds);
dijk(t, dt);
cout << min(get(u, v), get(v, u));
}
