#include <bits/stdc++.h>
//#pragma comment(linker, "/stack:200000000")
//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define fast ios_base::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);
#define all(v) v.begin(),v.end()
#define pb push_back
#define sz size()
#define ft first
#define sd second
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef unsigned long long ull;
const int N = 1e6 + 5;
const ll M = 1e8;
const ll inf = 1e9;
const ll mod = 1e9;
const double Pi = acos(-1);
ll binpow(ll x, ll ti) { ll res = 1;while (ti){if(ti & 1)res *= x;x *= x;ti >>= 1; x %= mod; res %= mod;} return res;}
ll binmul(ll x, ll ti) { ll res = 0;while (ti){if(ti & 1)res += x;x += x;ti >>= 1; x %= mod; res %= mod;} return res;}
ll nok(ll a, ll b) { return (a*b)/__gcd(abs(a),abs(b)) * (a*b > 0 ? 1 : -1); }
bool odd(ll n) { return (n % 2 == 1); }
bool even(ll n) { return (n % 2 == 0); }
struct node {
ll x1, y1, x2, y2;
};
ll n, k, ans = inf;
bool bl[1005][1005];
node que[100005];
void check(int razmer) {
ll cnt = 0;
for (int i = 1; i <= n; ++ i) {
for (int j = 1; j <= n; ++ j) {
int num = ((i - 1) / razmer) + ((j - 1) / razmer);
if (even(num) && !bl[i][j]) ++ cnt;
if (odd(num) && bl[i][j]) ++ cnt;
}
}
//cout << razmer << " " << min(cnt, n * n - cnt) << "\n";
ans = min(ans, min(cnt, n * n - cnt));
return;
}
const void solve(/*Armashka*/) {
cin >> n >> k;
ll c1 = (n * n) / 2, c2 = (n * n) - c1, cnt1 = 0, cnt2 = 0;
bool ok = 1;
for (int i = 1; i <= k; ++ i) {
ll x1, y1, x2, y2;
cin >> x1 >> y1 >> x2 >> y2;
que[i] = {x1, y1, x2, y2};
if (x1 % 2 == y1 % 2) ++ cnt2;
else ++ cnt1;
if (x1 != x2 || y1 != y2) ok = 0;
}
if (k == 0) {
cout << n * n / 2 << "\n";
return;
}
if (ok && k > 0) {
for (int i = 1; i * i <= n; ++ i) {
if (n % i == 0) { ok = 0; break; }
}
if (ok) cout << min((c1 - cnt1) + cnt2, (c2 - cnt2) + cnt1) << "\n";
else {
vector <ll> v;
for (int i = 1; i * i <= n; ++ i) {
if (n % i == 0) {
v.pb(i);
if (n / i != i && i > 1) v.pb(n / i);
}
}
for (int j = 0; j < v.sz; ++ j) {
set <int> st;
map <int, int> cnt;
for (int i = 1; i <= k; ++ i) {
int num = (que[i].x1 - 1) / v[j] + (que[i].y1 - 1) / v[j];
st.insert(num);
++ cnt[num];
}
ll res = 0;
for (auto x : st) {
if (even(x)) res += (v[j] * v[j]) - cnt[x];
else res += cnt[x];
}
ans = min(ans, min(res, n * n - res));
}
cout << ans << "\n";
}
return;
}
for (int i = 1; i <= k; ++ i) {
for (int j = que[i].y1; j <= que[i].y2; ++ j) {
for (int h = que[i].x1; h <= que[i].x2; ++ h) bl[j][h] = 1;
}
}
for (int i = 1; i * i <= n; ++ i) {
if (n % i == 0) {
check(i);
if (n / i != i && i > 1) check(n / i);
}
}
cout << ans << "\n";
}
signed main() {
fast;
//freopen("divide.in", "r", stdin);
//freopen("divide.out", "w", stdout);
int tt = 1;
//cin >> tt;
while (tt --) {
solve();
}
}
/*
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
*/
/*
9 12
1 9 4
1 2 5
2 3 7
2 4 3
4 3 6
3 6 4
8 7 10
6 7 5
5 8 1
9 5 7
5 4 12
6 8 2
2
4 7
5
1 6
5 3
4 8
5 8
1 5
*/
Compilation message
chessboard.cpp: In function 'const void solve()':
chessboard.cpp:82:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
82 | for (int j = 0; j < v.sz; ++ j) {
| ^
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
204 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
59 ms |
6580 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
332 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
332 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
59 ms |
6580 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
204 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
