#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops,02,no-stack-protector")
#include <iostream>
#include <string>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <vector>
#include <set>
#include <map>
#include <deque>
#include <stack>
#include <queue>
#include <algorithm>
#include <cassert>
#include <random>
#include <chrono>
#include <iomanip>
#include <cmath>
#include <bitset>
#include <functional>
#include <numeric>
#define int long long
#define double long double
#define ii pair<int,int>
#define iii pair<int, ii >
#define fi first
#define se second
#define getbit(x,y) (((x)>>(y))&1ll)
#define turnon(x,y) ((x)|(1ll<<y))
#define turnof(x,y) ((x)^(1ll<<y))
#define oo 1e18
#define pb push_back
#define all(x) x.begin(),x.end()
#define con(mask) mask=(mask-1)&mask
#define Unique(val) val.erase(unique(val.begin(),val.end()),val.end())
#define ll long long
const int mod = 1e9 + 7;
const int base = 11;
using namespace std;
int n, m, S, T, U, V;
int dp_s[100005];
int dp_t[100005];
vector<ii> e[100005];
int dp[100005][3];
void solve() {
cin >> n >> m >> S >> T >> U >> V;
for(int i = 1; i <= n; i++) {
dp_s[i] = oo;
dp_t[i] = oo;
}
for(int i = 1; i <= m; i++) {
int u, v, w;
cin >> u >> v >> w;
e[u].pb(make_pair(v, w));
e[v].pb(make_pair(u, w));
}
priority_queue<ii, vector<ii>, greater<ii>> pq;
dp_s[S] = 0;
pq.push(make_pair(0, S));
while(!pq.empty()) {
ii top = pq.top();
pq.pop();
int u = top.se;
if(dp_s[u] < top.fi) continue;
for(auto it : e[u]) {
int v = it.fi, w = it.se;
if(dp_s[v] > dp_s[u] + w) {
dp_s[v] = dp_s[u] + w;
pq.push(make_pair(dp_s[v], v));
}
}
}
pq.push(make_pair(0, T));
dp_t[T] = 0;
while(!pq.empty()) {
ii top = pq.top();
pq.pop();
int u = top.se;
if(dp_t[u] < top.fi) continue;
for(auto it : e[u]) {
int v = it.fi, w = it.se;
if(dp_t[v] > dp_t[u] + w) {
dp_t[v] = dp_t[u] + w;
pq.push(make_pair(dp_t[v], v));
}
}
}
priority_queue<pair<int, ii>, vector<pair<int, ii>>, greater<pair<int, ii>>> pq2;
for(int i = 1; i <= n; i++) {
dp[i][0] = oo;
dp[i][1] = oo;
dp[i][2] = oo;
}
dp[U][0] = 0;
pq2.push(make_pair(0, make_pair(U, 0)));
while(!pq2.empty()) {
int u = pq2.top().se.fi;
int t = pq2.top().se.se;
int cost = pq2.top().fi;
pq2.pop();
if(dp[u][t] < cost) continue;
// 0 -> 1 phải đi qua 1 cạnh được cải tạo
// 1 -> 1 vậy cạnh đó cũng phải được cải tạo luôn
// 1 -> 2 nghĩa là hết cải tạo -> không cần đi qua cạnh
// 2 -> 2 bình thường
if(t == 0) {
for(auto it: e[u]) {
int v = it.fi, w = it.se;
if(dp[v][0] > dp[u][0] + w) {
dp[v][0] = dp[u][0] + w;
pq2.push(make_pair(dp[v][0], make_pair(v, 0)));
}
if(dp_s[u] + w + dp_t[v] == dp_s[T] && dp[v][1] > dp[u][0]) {
dp[v][1] = dp[u][0];
pq2.push(make_pair(dp[v][1], make_pair(v, 1)));
}
}
}
else if(t == 1) {
if(dp[u][2] > dp[u][1]) {
dp[u][2] = dp[u][1];
pq2.push(make_pair(dp[u][2], make_pair(u, 2)));
}
for(auto it: e[u]) {
int v = it.fi, w = it.se;
if(dp_s[u] + w + dp_t[v] == dp_s[T] && dp[v][1] > dp[u][1]) {
dp[v][1] = dp[u][1];
pq2.push(make_pair(dp[v][1], make_pair(v, 1)));
}
}
}
else if(t == 2) {
for(auto it: e[u]) {
int v = it.fi, w = it.se;
if(dp[v][2] > dp[u][2] + w) {
dp[v][2] = dp[u][2] + w;
pq2.push(make_pair(dp[v][2], make_pair(v, 2)));
}
}
}
}
int res = dp[V][0];
res = min(res, dp[V][1]);
res = min(res, dp[V][2]);
cout << res;
}
signed main() {
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
int t = 1;
//cin >> t;
while(t--) {
solve();
}
}
// ProTeam
//(¯`·.·´¯) (¯`·.·´¯)
//`·.¸(¯`·.·´¯)¸ .·
//×°× ` ·.¸.·´ ×°×
