using System;

using System.Collections.Generic;

using System.Text;

public class Program

{

    public static void Main()

    {

        BLa();

    }

    public static void BLa()

        {

            int n = 15;

​

            var result = new List<HashSet<int>>();

​

            var graph = new Dictionary<int, HashSet<int>>();

​

            var squares = new HashSet<int> { };

​

            // calculate squares

            int counter = 1;

            while (counter * counter <= 2 * n)

            {

                squares.Add(counter * counter);

                ++counter;

            }

​

            // build graph

            for (int i = 1; i <= n; ++i)

            {

                for (int j = i + 1; j <= n; ++j)

                {

                    if (squares.Contains(i + j))

                    {

                        if(!graph.ContainsKey(i))

                        {

                            graph.Add(i, new HashSet<int>());

                        }

                        graph[i].Add(j);

​

                        if(!graph.ContainsKey(j))

                        {

                            graph.Add(j, new HashSet<int>());

                        }

                        graph[j].Add(i);

                    }

                }

            }

​

            // do the search

            foreach (var start in graph.Keys)

            {

                var candidates = new List<(HashSet<int>, int)> { (new HashSet<int> { start }, start) };

​

                while (candidates.Count > 0)

                {

                    var newCandidates = new List<(HashSet<int>, int)> { };

​

                    foreach (var (path, vertex) in candidates)

                    {

                        foreach (var candidate in graph[vertex])

                        {

                            if (!path.Contains(candidate))

                            {

                                var newPath = new HashSet<int>(path);

                                newPath.Add(candidate);

​

                                newCandidates.Add((newPath, candidate));

​

                                if (newPath.Count == n)

                                {

                                    result.Add(newPath);

                                }

​

                            }

                        }

                    }

​

                    candidates = newCandidates;

                }

            }

​

​

            // Printing the values

            foreach (var path in result)

            {

                var sb = new StringBuilder();

                foreach (var x in path)

                {

                    sb.Append(x + ", ");

                }

                Console.WriteLine(sb.ToString());

            }

        }

}