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>
#include<fstream>
using namespace std;
#define sz(a) (int)a.size()
#define ALL(v) v.begin(), v.end()
#define ALLR(v) v.rbegin(), v.rend()
#define ll long long
#define pb push_back
#define forr(i, a, b) for(int i = a; i < b; i++)
#define dorr(i, a, b) for(int i = a; i >= b; i--)
#define ld long double
#define vt vector
#include<fstream>
#define fi first
#define se second
#define pll pair<ll, ll>
#define pii pair<int, int>
#define mpp make_pair
const ld PI = 3.14159265359, prec = 1e-9;;
//using u128 = __uint128_t;
//const int x[4] = {1, 0, -1, 0};
//const int y[4] = {0, -1, 0, 1};
const ll mod = 1e9 + 7, pr = 31;
const int mxn = 5e5 + 5, mxq = 1e5 + 5, sq = 450, mxv = 5e4 + 1;
//const int base = (1 <<18);
const ll inf = 1e10 + 5, neg = -69420, inf2 = 1e14;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
// have fun!
ll n, k;
ll ans = inf;
ll x[mxn + 1], y[mxn + 1], x2[mxn + 1], y2[mxn + 1];
void solve(int cand){
ll odd = 0, even = 0;
for(int i = 1; i <= k; i++){
ll sm = x[i] / cand + y[i] / cand;
if(sm & 1)odd++;
else even++;
}
ll totodd = 0, toteven = 0;
if((n / cand) & 1){
toteven = (n * n / (cand * cand) + 1) / 2 * cand * cand;
totodd = (n * n / (cand * cand)) / 2 * cand * cand;
}else{
toteven = (n * n / (cand * cand)) / 2 * cand * cand;
totodd = (n * n / (cand * cand)) / 2 * cand * cand;
}
//cout << cand << " " << abs(toteven - even) + k - even << " " << abs(totodd - odd) + k - odd << "\n";
ans = min(ans, min(abs(toteven - even) + k - even, abs(totodd - odd) + k - odd));
}
void solve(){
cin >> n >> k;
for(int i = 1; i <= k; i++){
cin >> x[i] >> y[i] >> x2[i] >> y2[i]; --x[i]; --y[i]; --x2[i]; --y2[i];
}
for(int i = 1; i < n; i++){
if(n % i == 0){
solve(i);
}
}
cout << ans;
}
signed main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
//freopen("netw.inp", "r", stdin);
//freopen("netw.out", "w", stdout)
int tt; tt = 1;
while(tt--){
solve();
}
return(0);
}
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