Grid

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define fbo find_by_order
#define ook order_of_key

typedef long long ll;
typedef pair<ll,ll> ii;
typedef vector<int> vi;
typedef long double ld; 
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pbds;
typedef set<int>::iterator sit;
typedef map<int,int>::iterator mit;
typedef vector<int>::iterator vit;

int a[1001][1001];
int n; 
int cnt[1001];
int b[1001][1001];
bool check()
{
	memset(cnt,0,sizeof(cnt));
	set<int> s;
	for(int i = 0; i < n; i++)
	{
		int sum = 0;
		for(int j = 0; j < n; j++)
		{
			if(!(a[i][j]>=1&&a[i][j]<=n)) return 0;
			cnt[a[i][j]]++;
			sum+=a[i][j];
		}
		s.insert(sum);
		//cerr<<sum<<' ';
	}
	//cerr<<'\n';
	for(int j = 0; j < n; j++)
	{
		int sum = 0;
		for(int i = 0; i < n; i++)
		{
			sum+=a[i][j];
		}
		s.insert(sum);
		//cerr<<sum<<' ';
	}
	//cerr<<'\n';
	//cerr<<s.size()<<endl;
	if(!(int(s.size()) == 2*n)) return 0;
	for(int i = 1; i <= n; i++) if(!(cnt[i]==n)){return 0;}
	return 1;
}

void out()
{
	for(int i = 0; i < n; i++)
	{
		for(int j = 0; j < n; j++)
		{
			cout<<a[i][j]<<' ';
		}
		cout<<'\n';
	}
}

void x2(int n)
{
	for(int i = 0; i < n; i++)
	{
		for(int j = 0; j < n; j++)
		{
			b[i][j] = a[i][j];
			b[i][j+n] = a[i][j];
			b[i+n][j] = a[i][j]+n;
			b[i+n][j+n] = a[n-1-i][n-1-j]+n;
		}
	}
	for(int i = 0; i < n*2; i++)
	{
		for(int j = 0; j < n*2; j++)
		{
			a[i][j]=b[i][j];
		}
	}
}

int main()
{
	ios_base::sync_with_stdio(0); cin.tie(0);
	srand(57);
	cin>>n;
	if(n<=3)
	{
		cout<<"QAQ"; return 0;
	}
	vi vec(n*n);
	for(int i = 0; i < n; i++)
	{
		for(int j = 0; j < n; j++)
		{
			vec[i*n+j] = j+1;
		}
	}
	/*
	while(1)
	{
		random_shuffle(vec.begin(),vec.end());
		for(int i = 0; i < n; i++)
		{
			for(int j = 0; j < n; j++)
			{
				a[i][j] = vec[i*n+j];
			}
		}
		if(check())
		{
			//out();
			break;
		}
	}
	while(cnt--)
	{
		x2(n);
		n<<=1;
		out();
		assert(check());
	}
	*/
	if(n==4)
	{
		cout<<"1 1 1 2\n1 2 3 4\n2 3 3 4\n2 3 4 4\n"; return 0;
	}
	int ptr = 0;
	for(int i = 0; i < n; i++)
	{
		a[0][i] = 1;
	}
	int cur = 2;
	for(int j = 0; j < n; j++)
	{
		for(int i = 1; i < n; i++)
		{
			ptr++;
			a[i][j] = cur;
			if(ptr>=n)
			{
				ptr=0;
				cur++;
			}
		}
	}
	vector<int> s1;
	for(int i = 0; i < n; i++)
	{
		int sum = 0;
		for(int j = 0; j < n; j++)
		{
			sum+=a[i][j];
		}
		s1.pb(sum);
	}
	vi s2;
	for(int j = 0; j < n; j++)
	{
		int sum = 0;
		for(int i = 0; i < n; i++)
		{
			sum+=a[i][j];
		}
		s2.pb(sum);
	}
	int r, c;
	for(int i = 0; i < n; i++)
	{
		for(int j = 0; j < n; j++)
		{
			if(s1[i]==s2[j])
			{
				r=i; c=j;
				break;
			}
		}
	}
	while(1)
	{
		int i = rand()%n;
		int j = rand()%n;
		if(rand()&1)
		{
			i = 0;
		}
		swap(a[r][i],a[j][c]);
		if(check())
		{
			out(); return 0;
		}
		swap(a[r][i],a[j][c]);
	}
	//swap(a[1][n-2],a[0][n-2]);
	//swap(a[n-1][0],a[n-1][n-2]);
	assert(0);
	out();
}

Test 1

Group: 1

Verdict: ACCEPTED

Test 2

Group: 1

Verdict: ACCEPTED

Test 3

Group: 1

Verdict: ACCEPTED

Test 4

Group: 1

Verdict: ACCEPTED

Test 5

Group: 1

Verdict: ACCEPTED

Test 6

Group: 1

Verdict: ACCEPTED

Test 7

Group: 1

Verdict: ACCEPTED

Test 8

Group: 1

Verdict: ACCEPTED

Test 9

Group: 1

Verdict: ACCEPTED

Test 10

Group: 2

Verdict: ACCEPTED

Test 11

Group: 2

Verdict: ACCEPTED

Test 12

Group: 2

Verdict: ACCEPTED

Test 13

Group: 2

Verdict: ACCEPTED

Test 14

Group: 2

Verdict: ACCEPTED

Test 15

Group: 2

Verdict: ACCEPTED

Test 16

Group: 3

Verdict: ACCEPTED

Test 17

Group: 3

Verdict: ACCEPTED

Test 18

Group: 3

Verdict: ACCEPTED

Test 19

Group: 3

Verdict: ACCEPTED

Test 20

Group: 3

Verdict: ACCEPTED

Test 21

Group: 3

Verdict: TIME LIMIT EXCEEDED