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 Kotlin (1.0.0) (judge verdict: Wrong Answer)


import java.util.*

fun main(args:Array<String>): Unit {
    val n = readLine()!!.toInt()
    val k = (1 .. n).find{it * (it - 1) / 2 == n}
    when(k){
        null -> println("No")
        else -> {
            println("Yes")
            val array = Array(k){LinkedList<Int>() as Queue<Int>}
            var count = 1
            for (a in 0 until k){
                for (b in (a + 1) until k){
                    array[a].add(count)
                    array[b].add(count)
                    ++count
                }
            }
            for (queue in array){
                println(
                        queue.joinToString(" ", "${queue.size} "){it.toString()}
                )
            }
        }
    }
}