This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
//#pragma GCC optomize ("Ofast")
//#pragma GCC optomize ("unroll-loops")
//#pragma GCC target ("avx,avx2,fma")
#include <bits/stdc++.h>
#define F first
#define S second
#define pb push_back
#define sz size
#define cl clear
#define ins insert
#define ers erase
#define pii pair < int , int >
#define pll pair< long long , long long >
#define all(x) x.begin() , x.end()
#define ios ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define file(s) if (fopen(s".in", "r")) freopen(s".in", "r", stdin), freopen(s".out", "w", stdout)
#define tostr(x) to_string(x)
#define tonum(s) atoi(s.c_str())
#define seon(x) setprecision(x)
#define bpop(x) __builtin_popcount(x)
#define deb(x) cerr << #x << " = " << x << endl;
#define int ll
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
typedef long double ldb;
const double PI = 3.14159265;
const ll N = 1e6+5 , M = 2e3+5;
const ll mod = 1e9+7;
const ll inf = 1e9;
const ll INF = 1e18;
using namespace std;
int n;
bool u[N];
vector<int> v;
int cnt1[100005] , cnt11[100005];
void solve(){
ll k;
cin >> n >> k;
if(u[n] == 0){
ll cnt = 0 , cnt1 = 0;
for(int i = 1; i <= k; i++){
ll x , y , x1 , y1;
cin >> x >> y >> x1 >> y1;
if(x % 2 == y % 2) cnt++;
else cnt1++;
}
cout << min((n*n+1)/2-cnt+cnt1 , n*n/2-cnt1+cnt) <<"\n";
return;
} else {
ll mn = INF;
for(int i = 1; i <= sqrtl(n); i++) {
v.pb(i);
if(i > 1) v.pb(n/i);
}
for(int i = 1; i <= k; i++){
int x , y , x1 , y1;
cin >> x >> y >> x1 >> y1;
x--;
y--;
for(int i = 0; i < v.sz(); i++){
if((x/v[i])%2 == (y/v[i])%2) cnt1[i]++;
else cnt11[i]++;
}
}
for(int i = 0; i < v.sz(); i++){
ll ob = (n*n)/(v[i]*v[i]);
mn = min(mn , (ob+1)/2*v[i]*v[i] - cnt1[i] + cnt11[i]);
mn = min(mn , ob/2*v[i]*v[i] - cnt11[i] + cnt1[i]);
}
cout << mn <<"\n";
}
}
signed main(){
ios;
u[1] = 1;
for(int i = 2; i <= N-5; i++){
if(u[i] == 1) continue;
for(ll j = i*i; j <= N-5; j+=i) u[j] = 1;
}
solve();
return 0;
}
/*
6 8
3 3 3 3
1 2 1 2
3 4 3 4
5 5 5 5
4 3 4 3
4 4 4 4
2 1 2 1
3 6 3 6
*/
Compilation message (stderr)
chessboard.cpp: In function 'void solve()':
chessboard.cpp:66:21: warning: comparison of integer expressions of different signedness: 'll' {aka 'long long int'} and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
66 | for(int i = 0; i < v.sz(); i++){
| ~~^~~~~~~~
chessboard.cpp:71:20: warning: comparison of integer expressions of different signedness: 'll' {aka 'long long int'} and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
71 | for(int i = 0; i < v.sz(); i++){
| ~~^~~~~~~~
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