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.Text;

namespace Tenka1_2018_D___Crossing
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine(solve());
        }
        static string solve()
        {
            var N = int.Parse(Console.ReadLine());
            var len = 1;
            while (true)
            {
                if (2 * N == len * (len + 1)) break;
                if (2 * N < len * (len + 1)) return "No";
                len++;
            }

            var sets = new List<int>[len + 1];
            for (int i = 0; i < len + 1; i++)
            {
                sets[i] = new List<int>();
                sets[i].Add(len);
            }
            var n = 1;
            for (int i = 0; i < len + 1; i++)
            {
                for (int j = i + 1; j < len + 1; j++)
                {
                    sets[i].Add(n);
                    sets[j].Add(n);
                    n++;
                }
            }

            var result = new StringBuilder();
            result.AppendLine("Yes");
            result.AppendLine((len + 1).ToString());
            foreach (List<int> s in sets)
            {
                result.AppendLine(string.Join(" ", s));
            }
            return result.ToString();
        }
    }
}