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;
using System.Text;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			int n = int.Parse(Console.ReadLine());
			if (n == 1) {
				Console.WriteLine("Yes");
				Console.WriteLine("2");
				Console.WriteLine("1 1");
				Console.WriteLine("1 1");
				return;
			}

			int m = 2 * n;
			int k = 0;
			for (int i = 2; i < m; i++) {
				if (m % i == 0 && i * (i + 1) == m) {
					k = i;
					break;
				}
			}

			if (k == 0) {
				Console.WriteLine("No");
				return;
			}

			var values = new List<int>[k + 1];
			int[] counts = new int[n];
			int current = 0;
			for (int i = 0; i < k + 1; i++) {
				values[i] = new List<int>();

				for (int j = 0; j < i; j++) {
					foreach (int t in values[j]) {
						if (counts[t] == 1) {
							values[i].Add(t);
							counts[t]++;
							break;
						}
					}
				}

				for (int j = i; j < k; j++) {
					values[i].Add(current);
					counts[current]++;
					++current;
				}
			}

			var sb = new StringBuilder();
			sb.AppendLine("Yes");
			sb.AppendLine((k + 1).ToString());

			for (int i = 0; i < k + 1; i++) {
				sb.Append($"{k} ");
				sb.AppendLine(
					string.Join(" ", values[i].Select(x => (x + 1).ToString())));
			}

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