#include <iostream>
#include <bits/stdc++.h>
#include <cmath>
#include <algorithm>
#include <vector>
#include <deque>
#include <set>
#include <stack>
#include <string>
#include <map>
#include <queue>
#define int long long
using namespace std;
const long long oo = 1000000000000000000;
long long sum, ans = 0, mx = 0, mn = 1000000000, num, pos;
/*
ViHHiPuh
(( `'-""``""-'` ))
)-__-_.._-__-(
/ --- (o _ o) --- \
\ .-* ( .0. ) *-. /
_'-. ,_ '=' _, .-'_
/ `;#'#'# - #'#'#;` \
\_)) -----'#'----- ((_/
# --------- #
'# ------- ------ #'
/..-'# ------- #'-.\
_\...-\'# -- #'/-.../_
((____)- '#' -(____))
cout << fixed << setprecision(6) << x;
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
freopen ( "sum.in", "r", stdin )
*/
vector <pair<int, int> > v[ 100001 ], vv[ 100001 ];
set <pair<int, int> > st;
int d[ 100001 ], p[ 100001 ], dd[ 100001 ], d1[ 100001 ], d2[ 301 ][ 301 ];
map <pair<int, int>, bool> mp;
main () {
int n, m;
cin >> n >> m;
int s, t;
cin >> s >> t;
int ss, tt;
cin >> ss >> tt;
int x[ m + 1 ], y[ m + 1 ], z[ m + 1 ];
for ( int i = 1; i <= n; i ++ )
d[ i ] = dd[ i ] = d1[ i ] = oo;
for ( int i = 1; i <= m; i ++ ) {
cin >> x[ i ] >> y[ i ] >> z[ i ];
v[ x[ i ] ].push_back( { y[ i ], z[ i ] } );
v[ y[ i ] ].push_back( { x[ i ], z[ i ] } );
}
if ( s == ss ) {
d[ t ] = 0;
st.insert( { d[ t ], t } );
while ( st.size() ) {
num = st.begin()->second;
st.erase( st.begin() );
for ( auto to : v[ num ] ) {
if ( d[ to.first ] > d[ num ] + to.second ) {
st.erase( { d[ to.first ], to.first } );
d[ to.first ] = d[ num ] + to.second;
st.insert( { d[ to.first ], to.first } );
}
}
}
dd[ tt ] = 0;
st.insert( { dd[ tt ], tt } );
while ( st.size() ) {
num = st.begin()->second;
st.erase( st.begin() );
for ( auto to : v[ num ] ) {
if ( dd[ to.first ] > dd[ num ] + to.second ) {
st.erase( { dd[ to.first ], to.first } );
dd[ to.first ] = dd[ num ] + to.second;
st.insert( { dd[ to.first ], to.first } );
}
}
}
d1[ s ] = 0;
st.insert( { d1[ s ], s } );
while ( st.size() ) {
num = st.begin()->second;
st.erase( st.begin() );
for ( auto to : v[ num ] ) {
if ( d1[ to.first ] > d1[ num ] + to.second ) {
st.erase( { d1[ to.first ], to.first } );
d1[ to.first ] = d1[ num ] + to.second;
st.insert( { d1[ to.first ], to.first } );
}
}
}
mn = oo;
for ( int i = 1; i <= n; i ++ ) {
if ( d[ i ] + d1[ i ] == d1[ t ] ) {
// cout << i << " - " << dd[ i ] << "\n";
mn = min( mn, dd[ i ] );
}
}
cout << mn;
}
else if ( n > 300 ) {
d[ s ] = 0;
st.insert( { d[ s ], s } );
p[ s ] = -1;
while ( st.size() ) {
num = st.begin()->second;
st.erase( st.begin() );
for ( auto to : v[ num ] ) {
if ( d[ to.first ] > to.second + d[ num ] ) {
st.erase( { d[ to.first ], to.first } );
d[ to.first ] = d[ num ] + to.second;
p[ to.first ] = num;
st.insert( { d[ to.first ], to.first } );
}
}
}
for ( int i = t; i != s; i = p[ i ] ) {
mp[ { i, p[ i ] } ] = mp[ { p[ i ], i } ] = 1;
}
for ( int i = 1; i <= m; i ++ ) {
if ( mp[ { x[ i ], y[ i ] } ] )
z[ i ] = 0;
vv[ x[ i ] ].push_back( { y[ i ], z[ i ] } );
vv[ y[ i ] ].push_back( { x[ i ], z[ i ] } );
}
for ( int i = 1; i <= n; i ++ )
dd[ i ] = oo;
dd[ ss ] = 0;
st.insert( { dd[ ss ], ss } );
while ( st.size() ) {
num = st.begin()->second;
st.erase( st.begin() );
for ( auto to : vv[ num ] ) {
if ( dd[ to.first ] > to.second + dd[ num ] ) {
st.erase( { dd[ to.first ], to.first } );
dd[ to.first ] = to.second + dd[ num ];
st.insert( { dd[ to.first ], to.first } );
}
}
}
cout << dd[ tt ];
}
else {
for ( int i = 1; i <= n; i ++ ) {
for ( int j = 1; j <= n; j ++ )
d2[ i ][ j ] = oo;
}
for ( int i = 1; i <= n; i ++ ) {
d2[ i ][ i ] = 0;
st.insert( { d2[ i ][ i ], i } );
while ( st.size() ) {
num = st.begin()->second;
st.erase( st.begin() );
for ( auto to : v[ num ] ) {
if ( d2[ i ][ to.first ] > d2[ i ][ num ] + to.second ) {
st.erase( { d2[ i ][ to.first ], to.first } );
d2[ i ][ to.first ] = d2[ i ][ num ] + to.second;
st.insert( { d2[ i ][ to.first ], to.first } );
}
}
}
}
mn = d2[ ss ][ tt ];
for ( int i = 1; i <= n; i ++ ) {
for ( int j = 1; j <= n; j ++ ) {
if ( d2[ s ][ i ] + d2[ j ][ t ] + d2[ i ][ j ] == d2[ s ][ t ] ) {
// cout << i << " " << j << "\n";
mn = min( mn, d2[ ss ][ i ] + d2[ j ][ tt ] );
mn = min( mn, d2[ ss ][ j ] + d2[ i ][ tt ] );
}
}
}
cout << mn;
}
}
