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 <iostream>
#include <fstream>
#include <algorithm>
#include <cstring>
#include <string>
#include <vector>
#include <cstdio>
#include <queue>
#include <deque>
#include <stack>
#include <cmath>
#include <list>
#include <set>
#include <map>
using namespace std;
typedef long long ll;
#define MP make_pair
#define PB push_back
ll n,k,p,u,ans,color[100005],i,j,v,x[100005],y[100005],p1,p2,q1,q2,ans1,ans2,t,q;
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
for(i=2;i<=100000;i++)
{
if(!color[i])
{
for(j=2*i;j<=100000;j+=i)
color[j]=1;
}
}
cin>>n>>k;
for(i=1;i<=k;i++)
{
cin>>x[i]>>y[i]>>x[i]>>y[i];
if(x[i]%2==y[i]%2)
u++;
else
v++;
}
if(n%2==0)
p=n*n/2;
else
p=n*n/2+1;
q=n*n/2;
ans=min(p-u+v,q-v+u);
for(j=2;j<=n;j++)
{
if(color[j]==0 && n%j==0)
{
u=0;
v=0;
t=n/j;
for(i=1;i<=k;i++)
{
ll g,h;
if(x[i]%t==0)
g=x[i]/t;
else
g=x[i]/t+1;
if(y[i]%t==0)
h=y[i]/t;
else
h=y[i]/t+1;
if(h%2==g%2)
u++;
else
v++;
}
q=n/j;
ans1=j*j/2+1;
ans1=ans1*q*q;
ans1=ans1-u+v;
ans2=j*j/2;
ans2=ans2*q*q;
ans2=ans2-v+u;
ans=min(ans,ans2);
ans=min(ans,ans1);
}
}
cout<<ans<<endl;
return 0;
}
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