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 Python (3.4.3) (judge verdict: Wrong Answer)

# -*- coding: utf-8 -*-
# 
import math
import sys
import itertools
import numpy as np


# いっこ入力
n =int(input())

k=0
for i in range(3,500):
    a = i *(i-1) // 2
    if n == a:
        k = i
        break

if k >= 1:
    print("Yes")
else:
    print("No")
    exit()

print(k)
m = [[0]*(k-1) for i in range(k)]

# print(m)
t = 1
for i in range(0,k):
    print(k-1, end=" ")
    for j in range(0,i):
        m[i][j]=m[j][i-1]
        print(m[i][j], end=" ")
    for j in range(i,k-1):
        m[i][j]=t
        t = t + 1
        print(m[i][j], end=" ")
    print("")

#print(m)