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 Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

func main() {
	var n int
	fmt.Scan(&n)

	k := 0
	for i := 0; i <= n; i++ {
		j := i * (i - 1) / 2
		if j == n {
			k = i
			break
		}
	}
	if k <= 2 {
		fmt.Println("No")
		return
	}

	c := 1
	ss := make([][]int, k)
	for i := 0; i < k-1; i++ {
		for j := i + 1; j < k; j++ {
			ss[i] = append(ss[i], c)
			ss[j] = append(ss[j], c)
			c++
		}
	}

	fmt.Println("Yes")
	fmt.Println(k)
	for i := 0; i < len(ss); i++ {
		l := len(ss[i])
		fmt.Printf("%d ", l)
		for j := 0; j < l; j++ {
			if j < l-1 {
				fmt.Printf("%d ", ss[i][j])
			} else {
				fmt.Println(ss[i][j])
			}
		}
	}
}