#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
#define II pair<int,int>
#define fi first
#define se second
#define III pair <ll, pair<ll, ll>>
vector<pair<ll, ll>> graph[100001]; // weight, node
ll du[100001], dv[100001], ds[100001], dp[2][100001], ans;
bool visited[100001];
void dijkstra1(ll start, ll arr[])
{
fill(visited, visited + 100001, false);
priority_queue<II, vector<II>, greater<II>> pq;
pq.push({0, start});
while (!pq.empty())
{
ll c, node;
tie(c, node) = pq.top();
pq.pop();
if (!visited[node])
{
arr[node] = c;
visited[node] = true;
for (auto &i : graph[node])
{
pq.push({c + i.first, i.second}); // i.first = weight, i.second = node
}
}
}
}
void dijkstra2(ll start, ll end)
{
fill(dp[0], dp[0] + 100001, LLONG_MAX / 2);
fill(dp[1], dp[1] + 100001, LLONG_MAX / 2);
fill(visited, visited + 100001, false);
priority_queue<III, vector<III>, greater<III>> pq;
pq.push({0, {start, 0}});
dp[0][0] = dp[1][0] = LLONG_MAX / 2;
while (!pq.empty())
{
ll c, node, par;
pair<ll, ll> p;
tie(c, p) = pq.top();
tie(node, par) = p;
pq.pop();
if (!visited[node])
{
visited[node] = true;
ds[node] = c;
dp[0][node] = min(du[node], dp[0][par]);
dp[1][node] = min(dv[node], dp[1][par]);
for (auto i : graph[node])
{
pq.push({c + i.first, {i.second, node}}); // i.first = weight, i.second = node
}
}
else if (c == ds[node])
{
if (min(du[node], dp[0][par]) + min(dv[node], dp[1][par]) <= dp[0][node] + dp[1][node])
{
dp[0][node] = min(du[node], dp[0][par]);
dp[1][node] = min(dv[node], dp[1][par]);
}
}
}
ans = min(ans, dp[0][end] + dp[1][end]);
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
if (fopen("_ab.inp", "r"))
{
freopen("_ab.inp", "r", stdin);
freopen("_ab.out", "w", stdout);
}
cin.tie(0);
ll n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
for (int i = 0; i < m; i++)
{
ll a, b, c;
cin >> a >> b >> c;
graph[a].push_back({c, b}); // store weight first
graph[b].push_back({c, a});
}
dijkstra1(u, du);
dijkstra1(v, dv);
ans = du[v];
// for (int i = 1; i<=n; i++) cout << du[i] << " ";
// cout << '\n';
// for (int i = 1; i <= n; i++) cout << dv[i] << " ";
// cout << '\n';
dijkstra2(s, t);
// cout << ans << '\n';
// dijkstra2(t, s);
cout << ans << '\n';
return 0;
}
