This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) 42
#endif
/*
refs:
edi
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
void solve(int test_case)
{
ll n,m; cin >> n >> m;
vector<pll> a(m+5);
rep1(i,m){
ll l,r,c; cin >> l >> r >> c;
if(l > r) swap(l,r);
a[i] = {l,r};
}
vector<ll> enter[n+5];
vector<ll> diff(n+5);
rep1(i,m){
auto [l,r] = a[i];
diff[l]++, diff[r]--;
enter[l].pb(r);
}
rep1(i,n) diff[i] += diff[i-1];
vector<pll> pick;
auto go = [&](ll d){
vector<ll> close(n+5);
ll curr = 0;
priority_queue<pll> pq;
ll res = 0;
rep1(i,n){
trav(r,enter[i]){
pq.push({r,i});
}
curr -= close[i];
ll val = diff[i]-curr*2;
while(val > d){
auto [r,l] = pq.top();
pq.pop();
res++;
curr++;
val -= 2;
close[r]++;
pick.pb({l,r});
}
}
return res;
};
vector<pll> prev_pick;
for(int d = m; d >= 0; d -= 2){
pick.clear();
go(d);
multiset<pll> ms(all(pick));
for(auto [l,r] : prev_pick){
auto it = ms.find({l,r});
if(it == ms.end()){
assert(0);
}
ms.erase(it);
}
prev_pick = pick;
}
prev_pick.clear();
for(int d = m-1; d >= 0; d -= 2){
pick.clear();
go(d);
multiset<pll> ms(all(pick));
for(auto [l,r] : prev_pick){
auto it = ms.find({l,r});
if(it == ms.end()){
assert(0);
}
ms.erase(it);
}
prev_pick = pick;
}
ll ans = inf2;
rep(d,m+1){
amin(ans,go(d)+d);
}
cout << ans << endl;
}
int main()
{
fastio;
int t = 1;
// cin >> t;
rep1(i, t) {
solve(i);
}
return 0;
}
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