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: Wrong Answer)

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

class Program
{

    static void Main(string[] args)
    {
        var N = int.Parse(Console.ReadLine());
        if (N % 2 == 0)
        {
            Console.WriteLine("No");
            return;
        }

        var SList = new List<S>();
        for (int i = 1; i <= N; i++)
        {
            var start = i;
            int end;
            if (i + 1 <= N)
            {
                end = i + 1;
            }
            else
            {
                end = 1;
            }
            var s = new S(start, end);
            SList.Add(s);
        }

        Console.WriteLine("Yes");
        Console.WriteLine(SList.Count);
        for (int i = 0; i < SList.Count; i++)
        {
            var s = SList[i];
            Console.WriteLine(2 + " " + s.start + " " + s.end);
        }

    }

    struct S
    {
        internal int start;
        internal int end;
        internal S(int start, int end)
        {
            this.start = start;
            this.end = end;
        }
    }
}