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 pb push_back
#define LL long long
#define Kultivator ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define int LL
using namespace std;
const LL Mxn = 1e6 + 7;
const LL Mod = 1e9 + 7;
const LL Inf = 1e14 + 7;
bool Prime(int N){
    bool Used = false;
    for(int i = 2; i <= sqrt(N); i++){
        if(N % i == 0){
            Used = true;
            break;
        }
    }
    return Used;
}
bool Get(int x, int y, int d){
    return (x / d + y / d) % 2;
}
void Ans1(int N){
    int Ans = Mxn;
    for(int i = 1; i < N; i++){
        if(N % i == 0){
            Ans = min(Ans, (N * N) / (2 * i * i) * (i * i));
        }
    }
    cout << Ans;
}
void Ans2(int N, int K){
    LL Cnt1 = 0, Cnt2 = 0;
    for(int i = 1, x1, y1, x2, y2; i <= K; i++){
        cin >> x1 >> y1 >> x2 >> y2;
        bool Num = Get(x2, y2, 1);
        if(!Num){
            Cnt1++;
        } else {
            Cnt2++;
        }
    }
    cout << min(N * N / 2 - Cnt2 + Cnt1, N * N / 2 + 1 - Cnt1 + Cnt2);
}
void Ans3(int N, int K){
    int Ans = LONG_MAX;
    vector <int> F;
    vector <pair <int, int>> P(N, {0, 0});
    for(int i = 1; i <= sqrt(N); i++){
        if(N % i == 0){
            F.pb(i);
            if(N / i != i && i > 1){
                F.pb(N / i);
            }
        }
    }
    for(int i = 1, x1, y1, x2, y2; i <= K; i++){
        cin >> x1 >> y1 >> x2 >> y2;
        for(auto i : F){
            if(Get(x1, y1, i)){
                P[i].first++;
            } else {
                P[i].second++;
            }
        }
    }
    for(auto i : F){
        Ans = min(Ans, ((N * N) / (2 * i * i)) * (i * i) + (i * i) - P[i].first + P[i].second);
        Ans = min(Ans, ((N * N) / (2 * i * i)) * (i * i) + P[i].first - P[i].second);
    }
    cout << Ans;
}
signed main(){
    Kultivator;
    LL N, K;
    cin >> N >> K;
    if(!K){
        Ans1(N);
    } else if(!Prime(N)){
        Ans2(N, K);
    } else {
        Ans3(N, K);
    }
}
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