#include <bits/stdc++.h>
using namespace std;
const int N = (int)1e5+20;
const int inf = (int)1e9+7;
const long long INF = (long long)1e18+7;
const int MOD = 42043;
int sum(int x, int y) {
x += y;
if(x >= MOD) {
x -= MOD;
}
return x;
}
int mult(int x, int y) {
return 1ll*x*y%MOD;
}
struct Edge {
int u, v, w;
};
int n, m, s1, t1, s2, t2;
vector<pair<int, int> > g[N];
vector<int> g2[N];
long long d[4][N];
void dijkstra(int tp, int s) {
fill(d[tp], d[tp]+1+n, INF);
d[tp][s] = 0;
priority_queue<pair<long long, int> > q;
q.push({0, s});
while(!q.empty()) {
long long cur_d = -q.top().first;
int v = q.top().second;
q.pop();
if(cur_d>d[tp][v]) {
continue;
}
for(auto [to, w] : g[v]) {
if(d[tp][v]+w < d[tp][to]) {
d[tp][to] = d[tp][v]+w;
q.push({-d[tp][to], to});
}
}
}
}
bool used[N];
long long ans, mn1[N], mn2[N];
void dfs(int v) {
used[v] = 1;
mn1[v] = d[2][v];
mn2[v] = d[3][v];
for(auto to : g2[v]) {
if(!used[to]) {
dfs(to);
}
mn1[v] = min(mn1[v], mn1[to]);
mn2[v] = min(mn2[v], mn2[to]);
}
ans = min(ans, d[2][v]+mn2[v]);
ans = min(ans, d[3][v]+mn1[v]);
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cin >> n >> m >> s1 >> t1 >> s2 >> t2;
vector<Edge> e;
for(int i = 1; i <= m; ++i) {
int u, v, w;
cin >> u >> v >> w;
e.push_back({u, v, w});
g[u].push_back({v, w});
g[v].push_back({u, w});
}
dijkstra(0, s1);
dijkstra(1, t1);
dijkstra(2, s2);
dijkstra(3, t2);
ans = d[2][t2];
for(auto [u, v, w] : e) {
if(d[0][u]+w+d[1][v]==d[0][t1]) {
g2[u].push_back(v);
}
if(d[1][u]+w+d[0][v]==d[0][t1]) {
g2[v].push_back(u);
}
}
for(int i = 1; i <= n; ++i) {
if(!used[i]) {
dfs(i);
}
}
cout << ans;
return 0;
}
