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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main {
	int[] data = {1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,190,210,231,253,276,300,325,351,378,406,435,465,496,528,561,595,630,666,703,741,780,820,861,903,946,990,1035,1081,1128,1176,1225,1275,1326,1378,1431,1485,1540,1596,1653,1711,1770,1830,1891,1953,2016,2080,2145,2211,2278,2346,2415,2485,2556,2628,2701,2775,2850,2926,3003,3081,3160,3240,3321,3403,3486,3570,3655,3741,3828,3916,4005,4095,4186,4278,4371,4465,4560,4656,4753,4851,4950,5050,5151,5253,5356,5460,5565,5671,5778,5886,5995,6105,6216,6328,6441,6555,6670,6786,6903,7021,7140,7260,7381,7503,7626,7750,7875,8001,8128,8256,8385,8515,8646,8778,8911,9045,9180,9316,9453,9591,9730,9870,10011,10153,10296,10440,10585,10731,10878,11026,11175,11325,11476,11628,11781,11935,12090,12246,12403,12561,12720,12880,13041,13203,13366,13530,13695,13861,14028,14196,14365,14535,14706,14878,15051,15225,15400,15576,15753,15931,16110,16290,16471,16653,16836,17020,17205,17391,17578,17766,17955,18145,18336,18528,18721,18915,19110,19306,19503,19701,19900,20100,20301,20503,20706,20910,21115,21321,21528,21736,21945,22155,22366,22578,22791,23005,23220,23436,23653,23871,24090,24310,24531,24753,24976,25200,25425,25651,25878,26106,26335,26565,26796,27028,27261,27495,27730,27966,28203,28441,28680,28920,29161,29403,29646,29890,30135,30381,30628,30876,31125,31375,31626,31878,32131,32385,32640,32896,33153,33411,33670,33930,34191,34453,34716,34980,35245,35511,35778,36046,36315,36585,36856,37128,37401,37675,37950,38226,38503,38781,39060,39340,39621,39903,40186,40470,40755,41041,41328,41616,41905,42195,42486,42778,43071,43365,43660,43956,44253,44551,44850,45150,45451,45753,46056,46360,46665,46971,47278,47586,47895,48205,48516,48828,49141,49455,49770,50086,50403,50721,51040,51360,51681,52003,52326,52650,52975,53301,53628,53956,54285,54615,54946,55278,55611,55945,56280,56616,56953,57291,57630,57970,58311,58653,58996,59340,59685,60031,60378,60726,61075,61425,61776,62128,62481,62835,63190,63546,63903,64261,64620,64980,65341,65703,66066,66430,66795,67161,67528,67896,68265,68635,69006,69378,69751,70125,70500,70876,71253,71631,72010,72390,72771,73153,73536,73920,74305,74691,75078,75466,75855,76245,76636,77028,77421,77815,78210,78606,79003,79401,79800,80200,80601,81003,81406,81810,82215,82621,83028,83436,83845,84255,84666,85078,85491,85905,86320,86736,87153,87571,87990,88410,88831,89253,89676,90100,90525,90951,91378,91806,92235,92665,93096,93528,93961,94395,94830,95266,95703,96141,96580,97020,97461,97903,98346,98790,99235,99681,100128,};

	private void compute(){

		Scanner scanner = new Scanner (System.in);
		int n = scanner.nextInt();
		int num = 0;
		for (int i=0;i<data.length;i++) {
			if (data[i] == n) {
				System.out.println("Yes");
				num = i+2;
				break;
			} else if (data[i] > n) {
				System.out.print("No");
				return;
			}
		}
		
		ArrayList<ArrayList<Integer>> list = new ArrayList<>();
		for (int i=0;i<num;i++)
			list.add(new ArrayList<>());
		int next = 1;
		for (int i=0;i<num;i++) {
			for (int j=i+1;j<num;j++) {
				list.get(i).add(next);
				list.get(j).add(next);
				next++;
			}
		}
		for (ArrayList<Integer> sub : list) {
			System.out.print(sub.size());
			for (int i : sub) {
				System.out.print(" ");
				System.out.print(i);
			}
			System.out.println();
		}
	}

	public static void main(String[] args) {
//		System.out.print("{");
//		int i = 1, b = 0;
//		while (b <= 100000) {
//			b += i;
//			System.out.print(b + ",");
//			i++;
//		}
//		System.out.println("};");
		new Main().compute();
	}

}