#include <bits/stdc++.h>
using namespace std;
#define piii pair<long long, long long>
using ll = long long;
const ll nmax = 2e5 + 5;
const ll mod = 1e9 + 7;
int n, m, u, v, s, t;
ll ans;
long long uu[nmax], vv[nmax], u1[nmax], v1[nmax], ss[nmax], tt[nmax], u2[nmax], v2[nmax];
vector<piii> edge[nmax];
void dijkstra(ll u)
{
memset(uu, 0x3f, sizeof(uu));
uu[u] = 0;
priority_queue<piii, vector<piii>, greater<piii>> Q;
Q.push({0, u});
while (!Q.empty())
{
piii top = Q.top();
Q.pop();
ll u = top.second;
ll kc = top.first;
if (kc > uu[u])
continue;
for (auto it : edge[u])
{
ll v = it.first;
ll w = it.second;
if (uu[v] > uu[u] + w)
{
uu[v] = uu[u] + w;
Q.push({uu[v], v});
}
}
}
}
void dijkstra2(ll u)
{
memset(vv, 0x3f, sizeof(vv));
vv[u] = 0;
priority_queue<piii, vector<piii>, greater<piii>> Q;
Q.push({0, u});
while (!Q.empty())
{
piii top = Q.top();
Q.pop();
ll u = top.second;
ll kc = top.first;
if (kc > vv[u])
continue;
for (auto it : edge[u])
{
ll v = it.first;
ll w = it.second;
if (vv[v] > vv[u] + w)
{
vv[v] = vv[u] + w;
Q.push({vv[v], v});
}
}
}
}
void dijkstra3(ll u)
{
memset(ss, 0x3f, sizeof(ss));
memset(u1, 0x3f, sizeof(u1));
memset(v1, 0x3f, sizeof(v1));
ss[u] = 0;
u1[u] = uu[u];
v1[u] = vv[u];
priority_queue<piii, vector<piii>, greater<piii>> Q;
Q.push({0, u});
while (!Q.empty())
{
piii top = Q.top();
Q.pop();
ll u = top.second;
ll kc = top.first;
if (kc > ss[u])
continue;
for (auto it : edge[u])
{
ll v = it.first;
ll w = it.second;
if (ss[v] > ss[u] + w)
{
ss[v] = ss[u] + w;
u1[v] = min(u1[u], uu[v]);
v1[v] = min(v1[u], vv[v]);
Q.push({ss[v], v});
}
else if (ss[v] == ss[u] + w)
{
u1[v] = min(u1[u], u1[v]);
v1[v] = min(v1[u], v1[v]);
}
}
}
}
void dijkstra4(ll u)
{
memset(tt, 0x3f, sizeof(tt));
memset(u2, 0x3f, sizeof(u2));
memset(v2, 0x3f, sizeof(v2));
tt[u] = 0;
u2[u] = uu[u];
v2[u] = vv[u];
priority_queue<piii, vector<piii>, greater<piii>> Q;
Q.push({0, u});
while (!Q.empty())
{
piii top = Q.top();
Q.pop();
ll u = top.second;
ll kc = top.first;
if (kc > tt[u])
continue;
for (auto it : edge[u])
{
ll v = it.first;
ll w = it.second;
if (tt[v] > tt[u] + w)
{
tt[v] = tt[u] + w;
u2[v] = min(u2[u], uu[v]);
v2[v] = min(v2[u], vv[v]);
Q.push({tt[v], v});
}
else if (tt[v] == tt[u] + w)
{
u2[v] = min(u2[u], u2[v]);
v2[v] = min(v2[u], v2[v]);
}
}
}
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
for (ll i = 1; i <= m; ++i)
{
int a, b, c;
cin >> a >> b >> c;
edge[a].push_back({b, c});
edge[b].push_back({a, c});
}
dijkstra(u);
dijkstra2(v);
dijkstra3(s);
dijkstra4(t);
ans = uu[v];
for (int i = 1; i <= n; ++i)
if (ss[i] + tt[i] == ss[t])
ans = min({ans, u1[i] + v2[i], v1[i] + u2[i]});
cout << ans;
}
