// author lox:(
#pragma GCC optimize("O3")
#pragma GCC target("popcnt")
#include <bits/stdc++.h>
using namespace std;
#define IZhO_SILVER ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define popcnt __builtin_popcount
#define all(a) a.begin(),a.end()
#define low_b lower_bound
#define up_b upper_bound
#define vii vector<pair<ll,ll>>
#define vll vector<pair<ll,ll>>
#define pii pair<ll,ll>
#define mii map<ll,ll>
#define pll pair<ll,ll>
#define mll map<ll,ll>
#define vi vector<ll>
#define vl vector<ll>
#define pb push_back
#define endl '\n'
#define Y second
#define X first
typedef long double ld;
typedef long long ll;
const long long dx[4]={1,-1,0,0},dy[4]={0,0,1,-1},col=107,N=1e6+777;
const ll mod=1e9+7,inf=1e18;
void fre_open(){freopen("file.in","r",stdin);freopen("file.out","w",stdout);}
ll binpow(ll n,ll k){if(k<0)return 0ll;if(k==0)return 1ll;if(k%2)return (binpow(n,k-1)*n)%mod;ll kk=binpow(n,k/2)%mod;return (kk*kk)%mod;}
int a[2001][2001];
int n,k;
bool isprime(long long x)
{
if(x < 2) return 0;
if(x == 2 || x == 3) return 1;
if(x % 2 == 0 || x % 3 == 0) return 0;
for(int i = 5; i * i <= n; i += 6)
if(x % i == 0 || x % (i+2) == 0)
return 0;
return 1;
}
void f2()
{
x = n*n/2;
x2 = x + 1;
for(int c = 0, i1, i2, j1, j2; c < k; ++c)
{
cin >> i1 >> j1 >> i2 >> j2;
for(int i = i1; i <= i2; ++i)
for(int j = j1; j <= j2; ++j)
{
if(i % 2 == j % 2) x++, x2--;
if(i % 2 != j % 2) x2++, x--;
}
}
cout << min(x, x2);
}
void solve(){
cin>>n>>k;
if(k==0){
int x=n*n/2;
for(int i=n/2; i>=1; --i)if(n%i==0)x=min(x,i*i*((n/i)*(n/i)/2));
cout<<x;
return;
}
else if(isprime(n)) {f2();return;}
for(int i=1; i<=k; ++i){
ll x,y,tox,toy;
cin>>x>>y>>tox>>toy;
a[x][y]=1;
}
int ans=mod-10;
for(int d=1; d*d<=n; ++d){
if(n%d!=0) continue;
int res=0,res2=0;
for(int i=1; i<=n; ++i){
for(int j=1; j<=n; ++j){
int x=(i+(d-1))/d;
int y=(j+(d-1))/d;
if((x+y)%2 && a[i][j]) ++res2;
if((x+y)%2 && !a[i][j]) ++res;
if(!((x+y)%2) && a[i][j]) ++res;
if(!((x+y)%2) && !a[i][j]) ++res2;
}
}
ans=min({ans,res,res2});
//cout<<d<<' '<<res<<' '<<res2<<endl;
int f=n/d;
res=0,res2=0;
for(int i=1; i<=n; ++i){
for(int j=1; j<=n; ++j){
int x=(i+(f-1))/f;
int y=(j+(f-1))/f;
if((x+y)%2 && a[i][j]) ++res2;
if((x+y)%2 && !a[i][j]) ++res;
if(!((x+y)%2) && a[i][j]) ++res;
if(!((x+y)%2) && !a[i][j]) ++res2;
}
}
if(d==1){
ans=min(ans,max(res,res2));
continue;
}
ans=min({ans,res,res2});
//cout<<d<<' '<<res<<' '<<res2<<endl;
}
cout<<ans<<endl;
}
/*
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*/
int main() {
//fre_open();
IZhO_SILVER;
ll tt=1;
//cin>>tt;
while(tt--) solve();
}
Compilation message
chessboard.cpp: In function 'void f2()':
chessboard.cpp:43:2: error: 'x' was not declared in this scope
43 | x = n*n/2;
| ^
chessboard.cpp:44:2: error: 'x2' was not declared in this scope; did you mean 'f2'?
44 | x2 = x + 1;
| ^~
| f2
chessboard.cpp: In function 'void fre_open()':
chessboard.cpp:27:24: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
27 | void fre_open(){freopen("file.in","r",stdin);freopen("file.out","w",stdout);}
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
chessboard.cpp:27:53: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
27 | void fre_open(){freopen("file.in","r",stdin);freopen("file.out","w",stdout);}
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~
