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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            input_iter = LazyLoadAllLines();
            //------------------------------------------------//
            var n = Read<long>();
            //var m = Read<long>();
            //var v = Read<long>();
            //var s = Read();
            /*List<string> sls = new List<string>();
            for(int i = 0; i < h; ++i)
            {
                sls.Add(Read());
            }*/
            //var als = Read<long>(n);
            //var bls = Read<long>(n);
            /*List<List<long>> abls = new List<List<long>>();
            for (int i = 0; i < n - 1; ++i)
            {
                var x = Read<long>(2);
                if (x[0] > x[1]) x.Reverse();
                abls.Add(x);
            }*/
            //List<List<long>> abls = new List<List<long>>();
            //List<long> cls = new List<long>();
            /*List<long> edgeNum = Enumerable.Repeat(0L, (int)n).ToList();
            for (int i = 0; i < n - 1; ++i)
            {
                abls.Add(Read<long>(2));
                abls[i].Add(i);
                abls[i].Add(-1);
                --abls[i][0];
                --abls[i][1];
                //cls.Add(Read<long>());
                ++edgeNum[(int)abls[i][0]];
                ++edgeNum[(int)abls[i][1]];
            }*/

            //als.Sort((l, r) => (int)(r - l));

            var pat3 = new List<string>();
            pat3.Add("aab");
            pat3.Add("b.b");
            pat3.Add("baa");

            var pat4 = new List<string>();
            pat4.Add("aabc");
            pat4.Add("ccbc");
            pat4.Add("abaa");
            pat4.Add("abcc");


            if (n == 2 || n == 5)
            {
                Console.WriteLine(-1);
            }
            else
            {
                for(int i = 0; i < (int)n % 3; ++i)
                {
                    printPat(pat4, (int)n, i * 4);
                }

                var pad = (n % 3) * 4;

                for (int i = (int)pad; i < n; i += 3)
                {
                    printPat(pat3, (int)n, i);
                }
            }

            //Console.WriteLine(cnt);
        }

        public static void printPat(List<string> pat, int length, int padding)
        {
            var patLen = pat[0].Length;
            var padStr = new string('.', padding);
            var rightStr = new string('.', length - patLen - padding);

            foreach(var patElem in pat)
            {
                Console.WriteLine(padStr + patElem + rightStr);
            }
        }

        static IEnumerator<string> input_iter;

        static IEnumerator<string> LazyLoadAllLines()
        {
            string line;
            do
            {
                line = Console.ReadLine();
                foreach (var s in line.Split(' '))
                    yield return s;
            } while (line != null);
        }
        static _T Read<_T>() where _T : struct
        {
            input_iter.MoveNext();
            return (_T)Convert.ChangeType(input_iter.Current, typeof(_T));
        }
        static string Read()
        {
            input_iter.MoveNext();
            return input_iter.Current;
        }
        static List<_T> Read<_T>(long num) where _T : struct {
            List<_T> res = new List<_T>();
            for (long i = 0; i < num; ++i)
            {
                input_iter.MoveNext();
                res.Add((_T)Convert.ChangeType(input_iter.Current, typeof(_T)));
            }
            return res;
        }
        

        public class PriorityQueue<T> where T : IComparable
        {
            private IComparer<T> comparer = null;
            private bool isAccendingOrder;

            private List<T> heap;
            private int heapCurrentSize = 0;

            public PriorityQueue(IComparer<T> comparer, int initialHeapSize = 256)
            {
                heap = new List<T>(initialHeapSize);
                this.comparer = comparer;
            }

            public PriorityQueue(bool isAccending = true, int initialHeapSize = 256)
            {
                heap = new List<T>(initialHeapSize);
                isAccendingOrder = isAccending;
            }

            private int Compare(T x, T y)
            {
                if (comparer != null) return comparer.Compare(x, y);
                return isAccendingOrder ? x.CompareTo(y) : y.CompareTo(x);
            }

            public bool Empty()
            {
                return Count() == 0;
            }

            public int Count()
            {
                return heapCurrentSize;
            }

            public void Push(T x)
            {
                //node number
                var idx = heapCurrentSize++;
                if (heapCurrentSize > heap.Count) heap.Capacity *= 2;

                while (idx > 0)
                {
                    //parent node number
                    var parentIdx = (idx - 1) / 2;

                    if (Compare(heap[parentIdx], x) <= 0) break;

                    heap[idx] = heap[parentIdx];
                    idx = parentIdx;
                }

                heap[idx] = x;
            }

            public T Pop()
            {
                T ret = heap[0];
                T x = heap[--heapCurrentSize];

                int idx = 0;
                while (idx * 2 + 1 < heapCurrentSize)
                {
                    //children
                    int a = idx * 2 + 1;
                    int b = idx * 2 + 2;

                    if (b < heapCurrentSize && Compare(heap[b], heap[a]) < 0) a = b;

                    if (Compare(heap[a], x) >= 0) break;

                    heap[idx] = heap[a];
                    idx = a;
                }

                heap[idx] = x;

                return ret;
            }

            public T Peek()
            {
                return heap[0];
            }

            public bool Contains(T x)
            {
                for (int i = 0; i < heapCurrentSize; i++) if (x.Equals(heap[i])) return true;
                return false;
            }

            public void Clear()
            {
                while (heapCurrentSize > 0) Pop();
            }

            public IEnumerator<T> GetEnumerator()
            {
                var temp = new List<T>();

                while (heapCurrentSize > 0)
                {
                    temp.Add(Pop());
                }

                foreach (var value in temp)
                {
                    Push(value);
                    yield return value;
                }
            }

            public T[] ToArray()
            {
                T[] array = new T[heapCurrentSize];
                int i = 0;

                foreach (var r in this)
                {
                    array[i] = r;
                    ++i;
                }

                return array;
            }
        }
    }
}