Problem: 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.

Examples

Input

6


Output

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


Input

2


Output

-1

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
	
	public static void main(String[] args) throws IOException {
		MyScanner sc = new MyScanner();
		PrintWriter out = new PrintWriter(System.out);
		int N = sc.nextInt();
		if (N == 2) {
			out.println(-1);
		} else {
			char[][] ret = new char[N][N];
			
			for (int i = 0; i < N; i++) {
				Arrays.fill(ret[i], '.');
			}
			
			if (N % 3 == 0) {
				for (int i = 0; i < N; i+=3) {
					fill3(ret, i, i, 1, 'a');
				}
			} else if (N == 7) {
				fill7(ret, 0, 0, 'a');
			} else if (N == 11) {
				fill11(ret, 0, 0, 'a');
			} else {
				for (int four = 0; 4 * four <= N; four++) {
					if ((N - 4 * four) % 5 == 0) {
						int five = (N - 4 * four) / 5;
						int idx = 0;
						for (int i = 0; i < four; i++) {
							fill4(ret, idx, idx, 'a');
							idx += 4;
						}
						for (int i = 0; i < five; i++) {
							fill5(ret, idx, idx, 'a');
							idx += 5;
						}
						break;
					}
				}
			}
			
			for (int i = 0; i < N; i++) {
				out.println(new String(ret[i]));
			}
		}
		
		out.flush();
	}
	
	static void fill3(char[][] mat, int i, int j, int req, char from) {
		if (req == 1) {
			mat[i][j+1] = mat[i][j+2] = from;
			mat[i+1][j] = mat[i+2][j] = from;
		} else if (req == 2) {
			mat[i][j] = mat[i+1][j] = mat[i+1][j+2] = mat[i+2][j+2] = from;
			mat[i][j+1] = mat[i][j+2] = mat[i+2][j] = mat[i+2][j+1] = (char)(from + 1);
		}
	}
	
	static void fill4(char[][] mat, int i, int j, char from) {
		fillV(mat, i, j, from++);
		fillV(mat, i, j+1, from++);
		fillV(mat, i+2, j+2, from++);
		fillV(mat, i+2, j+3, from++);
		fillH(mat, i, j+2, from++);
		fillH(mat, i+1, j+2, from++);
		fillH(mat, i+2, j, from++);
		fillH(mat, i+3, j, from++);
	}
	
	static void fill5(char[][] mat, int i, int j, char from) {
		fill3(mat, i, j, 2, from);
		from+=2;
		for (int jj = j; jj < j + 3; jj++) {
			fillV(mat, i+3, jj, from++);
		}
		for (int ii = i; ii < i + 3; ii++) {
			fillH(mat, ii, j+3, from++);
		}
	}
	
	static void fill7(char[][] mat, int i, int j, char from) {
		fill3(mat, i, j, 1, from++);
		for (int jj = j; jj < j + 3; jj++) {
			fillV(mat, i+3, jj, from++);
			fillV(mat, i+5, jj, from++);
		}
		for (int ii = i; ii < i + 3; ii++) {
			fillH(mat, ii, j+3, from++);
			fillH(mat, ii, j+5, from++);
		}
	}
	
	static void fill11(char[][] mat, int i, int j, char from) {
		fill4(mat, i + 7, j + 7, from);
		fill3(mat, i, j, 2, from);
		from+=2;
		for (int jj = j; jj < j + 3; jj++) {
			fillV(mat, i+3, jj, from++);
			fillV(mat, i+5, jj, from--);
			fillV(mat, i+7, jj, from++);
			fillV(mat, i+9, jj, from);
		}
		for (int ii = i; ii < i + 3; ii++) {
			fillH(mat, ii, j+3, from++);
			fillH(mat, ii, j+5, from--);
			fillH(mat, ii, j+7, from++);
			fillH(mat, ii, j+9, from);
		}
		fill4(mat, i + 3, j + 3, from);
	}
	
	static void fillV(char[][] mat, int i, int j, char c) {
		mat[i][j] = mat[i+1][j] = c;
	}
	
	static void fillH(char[][] mat, int i, int j, char c) {
		mat[i][j] = mat[i][j+1] = c;
	}
	
	static class MyScanner {
		private BufferedReader br;
		private StringTokenizer tokenizer;
		
		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		
		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
	}
}