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.util.Scanner;

public class Main {

    public static void main(String[] args) throws Exception {
        try (Scanner sc = new Scanner(System.in)) {
            int N = sc.nextInt();

            if (N % 3 == 0) {
                StringBuilder sb1 = new StringBuilder();
                StringBuilder sb2 = new StringBuilder();

                for (int i = 0; i < N / 3; i++) {
                    sb1.append("aa.");
                    sb2.append("..b");
                }

                StringBuilder ans = new StringBuilder();
                for (int i = 0; i < N / 3; i++) {
                    ans.append(sb1.toString()).append("\n");
                    ans.append(sb2.toString()).append("\n");
                    ans.append(sb2.toString()).append("\n");
                }

                System.out.print(ans.toString());
                return;
            }

            String a40 = "....";
            String a41 = "aabc";
            String a42 = "ddbc";
            String a43 = "efgg";
            String a44 = "efhh";

            String a50 = ".....";
            String a51 = "aaehh";
            String a52 = "b.eii";
            String a53 = "bcff.";
            String a54 = ".cg.j";
            String a55 = "ddg.j";

            String a70 = ".......";
            String a71 = "aabbcc.";
            String a72 = "deeh...";
            String a73 = "d..h..i";
            String a74 = "f.jj..i";
            String a75 = "f...okk";
            String a76 = ".g..o.m";
            String a77 = ".g..nnm";

            for (int K = 0; K <= N / 7; K++) {
                for (int M = 0; M <= (N - K * 7) / 5; M++) {
                    if ((N - K * 7 - M * 5) % 4 != 0) {
                        continue;
                    }

                    int L = (N - K * 7 - M * 5) / 4;

                    StringBuilder[] sb = new StringBuilder[N];
                    for (int i = 0; i < N; i++) {
                        sb[i] = new StringBuilder();
                    }

                    for (int i = 0; i < L; i++) {
                        for (int j = 0; j < i; j++) {
                            sb[i * 4].append(a40);
                            sb[i * 4 + 1].append(a40);
                            sb[i * 4 + 2].append(a40);
                            sb[i * 4 + 3].append(a40);
                        }

                        sb[i * 4].append(a41);
                        sb[i * 4 + 1].append(a42);
                        sb[i * 4 + 2].append(a43);
                        sb[i * 4 + 3].append(a44);

                        for (int j = i + 1; j < L; j++) {
                            sb[i * 4].append(a40);
                            sb[i * 4 + 1].append(a40);
                            sb[i * 4 + 2].append(a40);
                            sb[i * 4 + 3].append(a40);
                        }

                        for (int j = 0; j < M; j++) {
                            sb[i * 4].append(a50);
                            sb[i * 4 + 1].append(a50);
                            sb[i * 4 + 2].append(a50);
                            sb[i * 4 + 3].append(a50);
                        }

                        for (int j = 0; j < K; j++) {
                            sb[i * 4].append(a70);
                            sb[i * 4 + 1].append(a70);
                            sb[i * 4 + 2].append(a70);
                            sb[i * 4 + 3].append(a70);
                        }
                    }

                    for (int i = 0; i < M; i++) {
                        for (int j = 0; j < L; j++) {
                            sb[L * 4 + i * 5].append(a40);
                            sb[L * 4 + i * 5 + 1].append(a40);
                            sb[L * 4 + i * 5 + 2].append(a40);
                            sb[L * 4 + i * 5 + 3].append(a40);
                            sb[L * 4 + i * 5 + 4].append(a40);
                        }

                        for (int j = 0; j < i; j++) {
                            sb[L * 4 + i * 5].append(a50);
                            sb[L * 4 + i * 5 + 1].append(a50);
                            sb[L * 4 + i * 5 + 2].append(a50);
                            sb[L * 4 + i * 5 + 3].append(a50);
                            sb[L * 4 + i * 5 + 4].append(a50);
                        }

                        sb[L * 4 + i * 5].append(a51);
                        sb[L * 4 + i * 5 + 1].append(a52);
                        sb[L * 4 + i * 5 + 2].append(a53);
                        sb[L * 4 + i * 5 + 3].append(a54);
                        sb[L * 4 + i * 5 + 4].append(a55);

                        for (int j = i + 1; j < M; j++) {
                            sb[L * 4 + i * 5].append(a50);
                            sb[L * 4 + i * 5 + 1].append(a50);
                            sb[L * 4 + i * 5 + 2].append(a50);
                            sb[L * 4 + i * 5 + 3].append(a50);
                            sb[L * 4 + i * 5 + 4].append(a50);
                        }

                        for (int j = 0; j < K; j++) {
                            sb[L * 4 + i * 5].append(a70);
                            sb[L * 4 + i * 5 + 1].append(a70);
                            sb[L * 4 + i * 5 + 2].append(a70);
                            sb[L * 4 + i * 5 + 3].append(a70);
                            sb[L * 4 + i * 5 + 4].append(a70);
                        }
                    }

                    for (int i = 0; i < K; i++) {
                        for (int j = 0; j < L; j++) {
                            sb[L * 4 + M * 5 + i * 7].append(a40);
                            sb[L * 4 + M * 5 + i * 7 + 1].append(a40);
                            sb[L * 4 + M * 5 + i * 7 + 2].append(a40);
                            sb[L * 4 + M * 5 + i * 7 + 3].append(a40);
                            sb[L * 4 + M * 5 + i * 7 + 4].append(a40);
                            sb[L * 4 + M * 5 + i * 7 + 5].append(a40);
                            sb[L * 4 + M * 5 + i * 7 + 6].append(a40);
                        }

                        for (int j = 0; j < M; j++) {
                            sb[L * 4 + M * 5 + i * 7].append(a50);
                            sb[L * 4 + M * 5 + i * 7 + 1].append(a50);
                            sb[L * 4 + M * 5 + i * 7 + 2].append(a50);
                            sb[L * 4 + M * 5 + i * 7 + 3].append(a50);
                            sb[L * 4 + M * 5 + i * 7 + 4].append(a50);
                            sb[L * 4 + M * 5 + i * 7 + 5].append(a50);
                            sb[L * 4 + M * 5 + i * 7 + 6].append(a50);
                        }

                        for (int j = 0; j < i; j++) {
                            sb[L * 4 + M * 5 + i * 7].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 1].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 2].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 3].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 4].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 5].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 6].append(a70);
                        }

                        sb[L * 4 + M * 5 + i * 7].append(a71);
                        sb[L * 4 + M * 5 + i * 7 + 1].append(a72);
                        sb[L * 4 + M * 5 + i * 7 + 2].append(a73);
                        sb[L * 4 + M * 5 + i * 7 + 3].append(a74);
                        sb[L * 4 + M * 5 + i * 7 + 4].append(a75);
                        sb[L * 4 + M * 5 + i * 7 + 5].append(a76);
                        sb[L * 4 + M * 5 + i * 7 + 6].append(a77);

                        for (int j = i + 1; j < M; j++) {
                            sb[L * 4 + M * 5 + i * 7].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 1].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 2].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 3].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 4].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 5].append(a70);
                            sb[L * 4 + M * 5 + i * 7 + 6].append(a70);
                        }
                    }

                    StringBuilder ans = new StringBuilder();
                    for (int i = 0; i < N; i++) {
                        ans.append(sb[i]).append("\n");
                    }

                    System.out.print(ans.toString());
                    return;
                }
            }

            System.out.println(-1);
        }
    }

}