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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;
import java.math.*;
// import java.awt.Point;
 
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
 
    static int mod = 1_000_000_007;
    // int mod = 998244353;
    // long inf = Long.MAX_VALUE/2;
    int inf = Integer.MAX_VALUE/2;

    int n,v,p;
    long m;
    long[] a;
    void solve(){
        int n = ni();
        
        char[][] board = new char[n][n];
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                board[i][j] = '.';
            }
        }

        if(n%3==0){
            for(int i = 0; i < n; i++){
                for(int j = 0; j < n; j++){
                    if(i%3==0 && j==i) board[i][j] = 'a';
                    if(i%3==0 && j==i+1) board[i][j] = 'a';
                    if(i%3==1 && j==i+1) board[i][j] = 'a';
                    if(i%3==2 && j==i) board[i][j] = 'a';
                }
            }
        }
        else if(n>5 && (n-2)%6==0){
            int val = 0;
            for(int j = 1; j < n-1; j+=2){
                board[0][j] = (char)('b'+val);
                board[0][j+1] = (char)('b'+val);
                val++;
                val %= 5;
            }
            for(int j = 1; j < n-1; j+=2){
                board[n-1][j] = (char)('b'+val);
                board[n-1][j+1] = (char)('b'+val);
                val++;
                val %= 5;
            }
            for(int i = 1; i < n-1; i+=2){
                board[i][0] = (char)('b'+val);
                board[i+1][0] = (char)('b'+val);
                val++;
                val %= 5;
            }
            for(int i = 1; i < n-1; i+=2){
                board[i][n-1] = (char)('b'+val);
                board[i+1][n-1] = (char)('b'+val);
                val++;
                val %= 5;
            }
            
            for(int i = 0; i < n-2; i++){
                for(int j = 0; j < n-2; j++){
                    if(i%3==0 && j==i) board[i+1][j+1] = 'a';
                    if(i%3==0 && j==i+1) board[i+1][j+1] = 'a';
                    if(i%3==1 && j==i+1) board[i+1][j+1] = 'a';
                    if(i%3==2 && j==i) board[i+1][j+1] = 'a';
                }
            }
        }
        else{
            out.println(-1);
            return;
        }

        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                out.print(board[i][j]);
            }
            out.println();
        }
    }



    void run() throws Exception
    {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b) && b != ' ')){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
 
}