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;
class P
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        int k = 0;
        bool f = Judge(ref k, n);
        Console.WriteLine(f ? "Yes" : "No");
        if (!f)
            return;
        Console.WriteLine(k);
        List<List<int>> ans = new List<List<int>>();
        for (int i = 0; i < k; i++)
            ans.Add(new List<int>());
        int c = 1;
        for (int i = 0; i < k; i++)
        {
            for (int j = i + 1; j < k; j++)
            {
                ans[i].Add(c);
                ans[j].Add(c);
                c++;
            }
        }
        foreach (var l in ans)
        {
            Console.Write(k - 1);
            foreach (var i in l)
                Console.Write(" {0}", i);
            Console.WriteLine();
        }
    }
    static bool Judge(ref int k, int n)
    {
        int m = (int)Math.Pow(1 + 8 * n, 0.5);
        if (m * m != 1 + 8 * n)
            return false;
        else if (m % 2 == 0)
            return false;
        k = (1 + m) / 2;
        return true;
    }
}