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: Accepted)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int m = (int) Math.sqrt(1 + 8 * N);

        if (m * m != 1 + 8 * N) {
            System.out.println("No");
            return;
        }

        if (1 + m % 2 == 1) {
            System.out.println("No");
            return;
        }

        System.out.println("Yes");

        int k = (1 + m) / 2;
        System.out.println(k);

        int[][] mattix = new int[k][k];

        int cnt = 1;
        for (int i = 0; i < k; i++) {
            for (int j = 0; j < k; j++) {
                if (i >= j) continue;
                mattix[i][j] = cnt;
                mattix[j][i] = cnt;
                cnt++;
            }
        }

        for (int i = 0; i < k; i++) {
            System.out.print(k-1);
            System.out.print(" ");
            int printedCnt = 0;

            for (int j = 0; j < k; j++) {
                if (i == j) continue;
                System.out.print(mattix[i][j]);
                printedCnt++;

                if (printedCnt != k - 1) {
                    System.out.print(" ");
                }

            }

            System.out.print("\n");
        }
    }
}