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: Runtime Error)

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

class Dmondai
{
    static void Main()
    {
        var N = Int32.Parse(Console.ReadLine());
        var k = 0;
        for(int i = 0; i <= N; ++i) if (i * (i - 1) == 2 * N) k = i;
        if (k == 0)
        {
            Console.WriteLine("No");
            return;
        }
        Console.WriteLine("YES");
        var array = new int[k,k-1];
        for (int i = 0; i < k; ++i) for (int j = 0; j < k - 1; ++j) array[i, j] = -1;
        for (int i = 0; i < k; ++i)
        {
            Console.Write(k - 1);
            var num = 0;
            var index = 1;
            for (int j = 0; j < k - 1; ++j)
            {
                Console.Write(" ");
                if (i == 0) num = j + 1;
                else if (i == 1)
                {
                    if (j == 0) num = j + 1;
                    else num = array[i - 1, k - 2] + j;
                }
                else
                {
                    if (array[j, i] == -1) {
                        num = array[i - 1, k - 2] + index;
                        index++;
                    }
                    else num = array[j, i];
                }
                array[i, j] = num;
                Console.Write(num);
            }
            Console.WriteLine();
        }
    }
}