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

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			int n = int.Parse(Console.ReadLine());
			if (n % 3 != 0) {
				Console.WriteLine("No");
				return;
			}

			var sb = new StringBuilder();
			sb.AppendLine("Yes");
			sb.AppendLine("3");

			int m = n / 3 + 1;
			for (int i = 0; i < 3; i++) {
				var nums = new List<int>(m + 1);
				nums.Add(m);
				for (int j = 0; j < m; j++) {
					nums.Add(j + ((m - 1) * i) + 1);
				}

				if (i == 2) {
					nums[m] = 1;
				}

				sb.AppendLine(
					string.Join(" ", nums.Select(x => x.ToString())));
			}

			Console.WriteLine(sb.ToString());
		}
	}
}