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 optimize("O3")
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
#define precision(n) fixed << setprecision(n)
#define pb push_back
#define ub upper_bound
#define lb lower_bound
#define mp make_pair
#define eps (double)1e-9
#define PI 2*acos(0.0)
#define endl "\n"
#define sz(v) int((v).size())
#define all(v) v.begin(),v.end()
#define rall(v) v.rbegin(),v.rend()
#define do_not_disturb ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define OK cout << "OK" << endl;
inline bool isvowel(char ch){
ch = tolower(ch);
return (ch == 'a' || ch == 'e' || ch == 'i' || ch == 'o' || ch == 'u');
}
inline bool isprime(int n){
if(n < 2 || (n%2 == 0 && n != 2)) return false;
for(int i = 3; i*i <= n; i++)
if(n%i == 0) return false;
return true;
}
class Union{
private:
vector <int> saizu, link;
public:
Union(int n){
saizu.assign(n, 1); link.resize(n);
iota(all(link), 0);
}
int find(int n){
if(link[n] == n) return n;
return link[n] = find(link[n]);
}
int same(int a, int b){
return find(a) == find(b);
}
void unite(int a, int b){
if(same(a, b)) return;
a = find(a); b = find(b);
if(saizu[a] < saizu[b]) swap(a, b);
saizu[a] += saizu[b];
link[b] = a;
}
int getsize(int a){
return saizu[find(a)];
}
};
const int mod = 1e9+7;
ll mode(ll a){
a %= mod;
if(a < 0) a += mod;
return a;
}
ll subt(ll a, ll b){
return mode(mode(a)-mode(b));
}
ll add(ll a, ll b){
return mode(mode(a)+mode(b));
}
ll mult(ll a, ll b){
return mode(mode(a)*mode(b));
}
ll binpow(ll a, ll b){
ll res = 1;
while(b){
if(b&1) res = mult(res, a);
a = mult(a, a);
b >>= 1;
}
return res;
}
#define vl vector <ll>
const int N = 1e5+7;
ll n, k;
inline ll rect_size(ll x1, ll y1, ll x2, ll y2){
return (x2-x1+1)*(y2-y1+1);
}
inline ll pref(ll x, ll y, ll div){
ll res = 0;
ll x_1_mod_div = (x+1)%div, y_1_mod_div = (y+1)%div;
ll x_full = x-x_1_mod_div, y_full = y-y_1_mod_div;
ll full_s1 = (x_full+1)/div, full_s2 = (y_full+1)/div;
ll x_full_div = (x_full+1)/div, y_full_div = (y_full+1)/div;
res += ((full_s1*full_s2)&1 ? full_s1*full_s2/2+1 : full_s1*full_s2/2)*div*div;
ll tmp;
if((y_full_div)&1){
int flag = x/div+y_full/div;
if(flag&1){
res += (x_1_mod_div)*(y_full_div/2)*div;
}
else{
res += (x_1_mod_div)*(y_full_div/2+1)*div;
}
}
else{
tmp = (y_full+1)/2*(x_1_mod_div);
res += tmp;
}
if((x_full_div)&1){
int flag = y/div+x_full/div;
if(flag&1){
res += (y_1_mod_div)*(x_full_div/2)*div;
}
else{
res += (y_1_mod_div)*(x_full_div/2+1)*div;
}
}
else{
tmp = (x_full+1)/2*(y_1_mod_div);
res += tmp;
}
int flag = x/div+y/div;
if(!(flag&1)){
res += rect_size(x_full+1, y_full+1, x, y);
}
return res;
}
inline ll calc1(ll div, vl x1, vl y1, vl x2, vl y2){
ll to_white = 0, to_black = ((n*n/div/div)&1 ? (n*n/div/div/2+1)*div*div : (n*n/2));
for(ll i = 0; i < k; i++){
ll blacks_in = pref(x2[i], y2[i], div)-(x1[i]-1 > -1 ? pref(x1[i]-1, y2[i], div) : 0)-(y1[i]-1 > -1 ? pref(x2[i], y1[i]-1, div) : 0)+
((x1[i]-1 > -1) && (y1[i]-1 > -1) ? pref(x1[i]-1, y1[i]-1, div) : 0);
to_black -= blacks_in;
to_white += rect_size(x1[i], y1[i], x2[i], y2[i])-blacks_in;
}
return to_white+to_black;
}
int main(){
do_not_disturb
ll ans = 2e18, i;
cin >> n >> k;
vector <ll> x1(k), y1(k), x2(k), y2(k);
for(i = 0; i < k; i++){
cin >> x1[i] >> y1[i] >> x2[i] >> y2[i];
x1[i]--; y1[i]--; x2[i]--; y2[i]--;
}
for(i = 1; i*i <= n; i++){
if(n%i == 0){
auto tmp = calc1(i, x1, y1, x2, y2);
ans = min(ans, min(tmp, n*n-tmp));
if(i > 1){
tmp = calc1(n/i, x1, y1, x2, y2);
ans = min(ans, min(tmp, n*n-tmp));
}
}
}
cout << ans;
return 0;
}
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