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"
#define F first
#define S second
#define ALL(a) a.begin() , a.end()
#ifndef ONLINE_JUDGE
#define OK cout << __LINE__ << "| "<< "---------------------------OK-----------------------" << endl;
#define deb(x) cout << __LINE__ << "| "<< #x << " = " << x << endl;
#else
#define OK
#define deb(x)
#endif
typedef long double ld;
typedef long long ll;
using namespace std ;
const ll N = 1e3 + 7 ;
const ll INF = 1e9;
const ll mod = 1e9 + 7 ;
const double eps = 1e-9 ;
const int dx[] = { 0 , 0 , 1 , -1, 1 , -1 , 1 , -1} , dy[] = {1 , -1 , 0 , 0 , 1 , 1, -1 , -1} ;
int n, k;
struct query{
int x1, x2 ,y1 ,y2;
query(int _x1, int _x2 ,int _y1, int _y2){
x1 = _x2, x2 = _x2, y1 = _y1, y2 = _y2;
}
};
vector<query> vec;
void test_solve(int test_index){
cin >> n >> k;
for(int i = 1; i <= k; i++){
int x1, x2, y1, y2;
cin >> x1 >> y1 >> x2 >> y2;
vec.push_back(query(x1 , x2 ,y1 ,y2));
}
int ans = INF;
for(int i = 1; i < n; i++){
if(n % i)
continue;
int cnt[2] = {0 , 0};
for(auto [x1 ,x2 ,y1, y2] : vec){
int dnt[2] = {0 , 0};
for(int j = x1; j <= x2; j++){
if((j - 1) / i % 2){
dnt[1]++;
}
else{
dnt[0]++;
}
}
for(int j = y1; j <= y2; j++){
if((j - 1) / i % 2){
cnt[1] += dnt[0];
cnt[0] += dnt[1];
}
else{
cnt[0] += dnt[0];
cnt[1] += dnt[1];
}
}
}
int d = n / i , less , big;
if(d % 2){
less = (d * d - 1) / 2 * (i * i);
big = less + i * i;
}
else{
less = (d * d) / 2 * (i * i);
big = less;
}
// deb(big);
// deb(less);
// deb(cnt[0]);
// deb(cnt[1]);
// deb(i);
ans = min({ans, (big - cnt[0]) + cnt[1] , cnt[0] + (less- cnt[1])});
}
cout << ans << endl;
}
signed main(){
ios_base::sync_with_stdio(false) ;
cin.tie(0) ;
cout.tie(0);
int test = 1;
//cin >> test ;
for(int i = 1 ; i <= test ; i++){
// cout << "Case " << i << ": " ;
test_solve(i) ;
}
return 0;
}
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