Problem:
Score : 900 points

Problem Statement

Let us consider a grid of squares with N rows and N columns. You want to put some domino pieces on this grid.
Each domino piece covers two squares that have a common side. Each square can be covered by at most one piece.

For each row of the grid, let's define its quality as the number of domino pieces that cover at least one square in this row.
We define the quality of each column similarly.

Find a way to put at least one domino piece on the grid so that the quality of every row is equal to the quality of every column,
or determine that such a placement doesn't exist.

Constraints

2 \le N \le 1000

Input

Input is given from Standard Input in the following format:

N

Output

If the required domino placement doesn't exist, print a single integer -1.

Otherwise, output your placement as N strings of N characters each.
If a square is not covered, the corresponding character must be . (a dot).
Otherwise, it must contain a lowercase English letter.
Squares covered by the same domino piece must contain the same letter.
If two squares have a common side but belong to different pieces, they must contain different letters.

Sample Input 1

6

Sample Output 1

aabb..
b..zz.
ba....
.a..aa
..a..b
..a..b

The quality of every row and every column is 2.

Sample Input 2

2

Sample Output 2

-1

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#if 0
cat <<EOF >mistaken-paste
#endif
// thx Ebi-chan!

// #pragma GCC optimize("unroll-loops")
// #pragma GCC optimize("O3")

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"
#define _USE_MATH_DEFINES

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <time.h>

#define BIG 2000000007LL
#define VERYBIG 20000000000000007LL
#define ULTRABIG 3000000000000000000LL

#define MOD 1000000007LL
#define FOD  998244353LL
#define HOD 1000000009LL
#define IOD  100000007LL
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 1048576

#ifdef __cplusplus
#include <queue>
#include <stack>
// #include <tuple>
#include <set>
#include <map>
#include <string>
#include <algorithm>
// #include <functional>
// #include <array>

using std::queue;
using std::priority_queue;
using std::stack;
// using std::tuple;
using std::set;
using std::map;
using std::vector;
using std::greater;
using std::pair;
using std::string;
// using std::get;
// using std::function;
// using std::array;

template <typename T, typename U>
pair<T, U> operator+(pair<T, U> l, pair<T, U> r) {
	return pair<T, U>(l.first + r.first, l.second + r.second);
}

#endif

#ifndef M_PI
#define M_PI 3.14159265358979323846264338327950
#endif

typedef struct {
	sll a;
	sll b;
} hwll;

typedef struct {
	sll a;
	sll b;
	sll c;
} hwllc;

typedef struct {
	hwll a;
	hwll b;
} linell;

typedef struct {
	double a;
	double b;
} hwreal;

sll n, m;
sll h, w;
sll k;
sll q;
sll va, vb, vc, vd, ve, vf;
ull ua, ub, uc, ud, ue, uf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
char ch, dh;

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

double dmin (double x, double y) {
	return (x < y) ? x : y;
}

double dmax (double x, double y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

ull divide (ull a, ull b, ull modulo) {
	return (a * bitpow(b, modulo - 2, modulo)) % modulo;
}

ull udiff (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sdiff (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

#define BEGCMP(NAME) int32_t NAME (const void *left, const void *right)
#define DEFLR(TYPE) TYPE l=*(TYPE*)left,r=*(TYPE*)right
#define CMPRET(L, R) if((L)<(R))return-1;if((L)>(R))return+1

// int32_t pullcomp (const void *left, const void *right) {
// 	ull l = *(ull*)left;
// 	ull r = *(ull*)right;
// 	if (l < r) {
// 		return -1;
// 	}
// 	if (l > r) {
// 		return +1;
// 	}
// 	return 0;
// }
BEGCMP(pullcomp){
	DEFLR(ull);
	CMPRET(l, r);
	return 0;
}
BEGCMP(prevcomp){
	DEFLR(sll);
	CMPRET(r, l);
	return 0;
}
BEGCMP(psllcomp){
	DEFLR(sll);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pcharcomp){
	DEFLR(char);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pdoublecomp){
	DEFLR(double);
	CMPRET(l, r);
	return 0;
}

int32_t pstrcomp (const void *left, const void *right) {
	char* l = *(char**)left;
	char* r = *(char**)right;

	return strcmp(l, r);
}

BEGCMP(phwllABcomp){
	DEFLR(hwll);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}
BEGCMP(phwllREVcomp){
	DEFLR(hwll);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	return 0;
}
BEGCMP(ptriplecomp){
	DEFLR(hwllc);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	CMPRET(l.c, r.c);
	return 0;
}
BEGCMP(ptripleREVcomp){
	DEFLR(hwllc);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	CMPRET(l.c, r.c);
	return 0;
}
BEGCMP(ptripleCABcomp){
	DEFLR(hwllc);
	CMPRET(l.c, r.c);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}
BEGCMP(phwrealcomp){
	DEFLR(hwreal);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}

int32_t pquadcomp (const void *left, const void *right) {
	linell l = *(linell*)left;
	linell r = *(linell*)right;

	sll ac = phwllABcomp(&(l.a), &(r.a));
	if (ac) return ac;
	sll bc = phwllABcomp(&(l.b), &(r.b));
	if (bc) return bc;

	return 0;
}
int32_t pfracomp (const void *left, const void *right) {
	hwllc l = *(hwllc*)left;
	hwllc r = *(hwllc*)right;

	CMPRET(l.a * r.b, l.b * r.a);
	return 0;
}
bool isinrange (sll left, sll x, sll right) {
	return (left <= x && x <= right);
}

bool isinrange_soft (sll left, sll x, sll right) {
	return (left <= x && x <= right) || (left >= x && x >= right);
}

void sw (sll *l, sll *r) {
	if (*l == *r) return;
	sll t = *l;
	*l = *r;
	*r = t;
}

void uw (ull *l, ull *r) {
	if (*l == *r) return;
	ull t = *l;
	*l = *r;
	*r = t;
}

ull frac[N_MAX * 3], invf[N_MAX * 3];
void f_init (ull n, ull m) {
	frac[0] = 1;
	for (sll i = 1; i <= n; i++) {
		frac[i] = frac[i - 1] * i % m;
	}

	invf[n] = divide(1, frac[n], m);
	for (sll i = n - 1; i >= 0; i--) {
		invf[i] = invf[i + 1] * (i + 1) % m;
	}
}
ull ncr (sll n, sll r, ull m) {
	if (n < 0 || r < 0 || n < r) return 0;
	return frac[n] * (invf[r] * invf[n - r] % m) % m;
}

sll a[N_MAX * 5];
// ull a[N_MAX + 5];
// sll a[3001][3001];
sll b[N_MAX * 5];
// ull b[N_MAX + 5];
// sll b[3001][3001];
sll c[N_MAX * 5];
sll d[N_MAX * 5];
sll e[N_MAX * 4];
// char s[N_MAX + 1];
char s[3010][3010];
// char t[N_MAX + 1];
char t[3010][3010];
char u[N_MAX + 1];
hwll xy[N_MAX + 5];
hwllc tup[N_MAX + 5];
// sll table[3005][3005];
sll table[2005][2005];
ull gin[N_MAX];
// here we go

ull dp[4019][4019];

bool func (sll index) {
	if (k <= q + index) {
		sll bound = a[n - q];
		if (a[index] + m >= bound) return true;
		return false;
	}

	sll v = a[index] + m;
	if (v < a[n - q]) return false;

	sll x = k - q - index;
	sll len = 0;
	sll sum = 0;
	for (sll i = index + 1; i <= n - q; i++) {
		// printf("%lld,\n", v - a[i]);
		sum += b[len++] = v - a[i];
	}
	sll sum2 = 0;
	for (sll i = x - 1; i < len; i++) {
		sum2 += b[i];
	}
	sll maxv = smin(sum / x, sum2);
	// printf("%lld >= %lld\n", maxv, m);
	if (maxv >= m) return true;
	return false;
}

ull solve () {
	sll i, j, ki, li;
	// ull result = 0;
	sll result = 0;
	double dresult = 0;
	// ull maybe = 0;
	sll maybe = 0;
	// ull sum = 0;
	sll sum = 0;
	sll item;
	sll *dpcell;

	if (n == 2) {
		puts("-1");
	} else if (n % 3 == 0) {
		for (i = 0; i < n; i++) {
			for (j = 0; j < n; j++) {
				char s[3][4] = {
					"aab",
					"c.b",
					"cdd"
				};

				putchar(s[i % 3][j % 3]);
			}
			putchar('\n');
		}
	} else if (n % 4 == 0) {
		for (i = 0; i < n; i++) {
			for (j = 0; j < n; j++) {
				char s[4][5] = {
					"aaby",
					"zzby",
					"cdee",
					"cdff"
				};

				putchar(s[i % 4][j % 4]);
			}
			putchar('\n');
		}
	} else {
		m = n;
		while (m % 2 == 0) m /= 2;

		for (i = 0; i < m; i++) {
			for (j = 0; j < m; j++) {
				s[i][j] = '.';
			}
		}

		for (i = 0; i < m / 2; i++) {
			sll hi = smax(i - 1, 0), wi = i * 2;
			s[hi][wi] = s[hi][wi + 1] = (i ? 'a' : 'b');
			s[m - 1 - hi][m - 1 - wi] = s[m - 1 - hi][m - 1 - (wi + 1)] = (i ? 'c' : 'd');

			s[wi][m - 1 - hi] = s[wi + 1][m - 1 - hi] = (i ? 'e' : 'f');
			s[m - 1 - wi][hi] = s[m - 1 - (wi + 1)][hi] = (i ? 'g' : 'h');

			// for (j = 0; j < m; j++) {
			// 	puts(s[j]);
			// }
			// puts("");
		}

		s[m / 2 - 1][m / 2 - 1] = s[m / 2][m / 2 - 1] = 'i';
		s[m / 2 + 1][m / 2] = s[m / 2 + 1][m / 2 + 1] = 'j';

		for (i = 0; i < n; i++) {
			for (j = 0; j < n; j++) {
				s[i][j] = s[i % m][j % m];
			}
		}

		for (i = 0; i < n; i++) {
			puts(s[i]);
		}
	}

	// printf("%lld\n", result);
	// printf("%.15f\n", dresult);
	// puts(s);

	return 0;

	success:
	// puts("YES");
	puts("Yes");
	// printf("%llu\n", result);
	// puts("0");
	// puts("First");
	return 0;

	fail:
	// puts("NO");
	puts("No");
	// puts("0");
	// puts("-1");
	// puts("-1 -1 -1");
	// puts("Second");
	return 1;
}

int32_t main (int argc, char *argv[]) {
	int32_t i, j;

	n = 3;
	m = 0;
	h = 5;

	// scanf("%llu", &m);
	// scanf("%llu%llu", &h, &w);
	scanf("%lld", &n, &m);
	// scanf("%lld", &k, &n, &m);
	// scanf("%llu%llu", &h, &w);
	// scanf("%llu", &q);
	// scanf("%lld%lld", &va, &vb, &vc, &vd);
	// va--;
	// vb--;
	// scanf("%llu%llu%llu%llu", &ua, &ub, &uc, &ud, &ue);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%s", u);
	// scanf("%lld", &k);
	// scanf("%lld", &m);
	// for (i = 0; i < n; i++) {
	// 	// scanf("%lld", &a[i]);
	// 	scanf("%lld", &d[i]);
	// }
	// scanf(" %c", &ch);
	// scanf("%llu", &q);
	for (i = 0; i < 0; i++) {
		// scanf("%lld%lld", &xy[i].a, &xy[i].b);
		// scanf("%lld%lld%lld", &tup[i].a, &tup[i].b, &tup[i].c);
		// scanf("%lld", &c[i]);

		scanf("%lld", &a[i]);
		// scanf("%lld", &b[i]);
		// scanf("%lld", &c[i]);
		// scanf("%lld", &d[i]);
		// a[i]--;
		// b[i]--;
		// c[i]--;
		// d[i]--;
		// xy[i].a--;
		// xy[i].b--;
		// tup[i].a--;
		// tup[i].b--;
	}
	// scanf("%lld%lld", &va, &vb);
	// scanf("%llu", &m);
	// scanf("%llu", &q);
	// scanf("%s", s);
	// for (i = 0; i < m; i++) {
	// 	// scanf("%lld%lld", &xy[i].a, &xy[i].b);
	// 	// xy[i].a--;
	// 	// xy[i].b--;
	// 	// scanf("%lld", &a[i], &b[i]);
	// 	scanf("%lld", &b[i]);
	// 	// a[i]--;
	// 	// b[i]--;
	// 	// scanf("%lld", &c[i]);
	// 	// scanf("%lld", &d[i]);
	// 	// scanf("%lld", &e[i]);
	// 	// c[i]--;
	// 	// d[i]--;
	// }

	// for (i = 0; i < q; i++) {
	// 	// scanf("%lld%lld", &xy[i].a, &xy[i].b);
	// 	scanf("%lld", &c[i]);
	// 	// xy[i].a--;
	// 	// xy[i].b--;
	// }

	// for (i = 0; i < n; i++) {
	// 	for (j = 0; j < m; j++) {
	// 		scanf("%lld", &table[i][j]);
	// 		// table[i][j]--;
	// 	}
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%s", s[i]);
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%s", t[i]);
	// }
	// scanf("%llu", &q);
	// for (i = 0; i < q; i++) {
	// 	scanf("%lld%lld%lld", &e[i], &c[i], &d[i]);
	// 	c[i]--;
	// }

	solve();

	return 0;
}