Problem:
Score : 500 points

Problem Statement

You are given an integer N. Determine if there exists a tuple of subsets of \{1,2,...N\}, (S_1,S_2,...,S_k), that satisfies the following conditions:

Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.

Any two of the sets S_1,S_2,...,S_k have exactly one element in common.

If such a tuple exists, construct one such tuple.

Constraints

1 \leq N \leq 10^5

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If a tuple of subsets of \{1,2,...N\} that satisfies the conditions does not exist, print No.
If such a tuple exists, print Yes first, then print such subsets in the following format:

k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}

where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.

If there are multiple such tuples, any of them will be accepted.

Sample Input 1

3

Sample Output 1

Yes
3
2 1 2
2 3 1
2 2 3

It can be seen that (S_1,S_2,S_3)=(\{1,2\},\{3,1\},\{2,3\}) satisfies the conditions.

Sample Input 2

4

Sample Output 2

No

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

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

namespace Tenak1PBC
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());

            double root = Math.Sqrt(1 + 8 * N);

            if ((int)root != root)
            {
                Console.WriteLine("No");
                return;
            }
            else Console.WriteLine("Yes");

            int k = ((int)root - 1) / 2;

            int[,] S = new int[k + 1, k];

            Queue<int>[] ques = new Queue<int>[k + 1];
            int count = 1;
            for (int i = 0; i < k + 1; i++)
            {
                ques[i] = new Queue<int>();
                for (int j = 0; j < k - i; j++)
                {
                    ques[i].Enqueue(count);
                    count++;
                }
            }

            for (int i = 0; i < k + 1; i++)
            {
                int[] que = new int[ques[i].Count];
                ques[i].CopyTo(que, 0);

                for (int j = 0; j < que.Length; j++)
                {
                    S[i, j] = que[j];
                }

                for (int j = que.Length; j < k; j++)
                {
                    S[i, j] = ques[j - que.Length].Dequeue();
                }
            }

            Console.WriteLine(k + 1);
            for (int i = 0; i < k + 1; i++)
            {
                Console.Write(k);
                for (int j = 0; j < k; j++)
                {
                    Console.Write(" " + S[i, j]);
                }
                Console.WriteLine();
            }

            Console.ReadKey();
        }

        static int[] ReadInt()
        {
            int[] ret = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return ret;
        }
        static long[] ReadLong()
        {
            long[] ret = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return ret;
        }
    }
}