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>
using namespace std;
struct Data
{
int x1, y1, x2, y2;
Data() = default;
Data(int _x1, int _y1, int _x2, int _y2) : x1(_x1), y1(_y1), x2(_x2), y2(_y2) {}
};
const long long INF = 1e18;
int main()
{
cin.tie(0)->sync_with_stdio(0);
int M, n; cin >> M >> n;
vector<Data> a(n);
for (int i = 0; i < n; i++)
{
int x1, y1, x2, y2;
cin >> x1 >> y1 >> x2 >> y2;
x1--, y1--;
a[i] = Data(x1, y1, x2, y2);
}
auto solve = [&](int K) -> long long
{
long long ret1 = 1ll * (M / K) * (M / K) / 2 + M / K % 2;
for (int i = 0; i < n; i++)
{
int xx = a[i].x1 / K, yy = a[i].y1 / K;
if ((xx + yy) % 2 == 0)
ret1--;
else
ret1++;
}
long long ret2 = 1ll * (M / K) * (M / K) / 2;
for (int i = 0; i < n; i++)
{
int xx = a[i].x1 / K, yy = a[i].y1 / K;
if ((xx + yy) % 2 == 1)
ret2--;
else
ret2++;
}
return min(ret1, ret2);
};
long long ans = INF;
for (int t = 1; t < M; t++)
if (M % t == 0)
ans = min(ans, solve(t));
cout << ans << '\n';
return 0;
}
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