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: Runtime Error)

n = int(input())

yn=1
a=2
while True:
    if n==yn:
        print('Yes')
        break
    elif yn>n:
        print('No')
        exit()
    else:
        yn+=a
        a+=1

a-=1
k=n*2//a
print(k)
print(a)
s=[[a] for i in range(k)]

l = [0]*n

for i in range(a):
    s[0].append(i+1)
    l[i]+=1

for i in range(1,k):
    for k in range(i):
        for j in range(a):
            if l[s[i-k-1][j+1]-1]==1:
                s[i].append(s[i-k-1][j+1])
                l[s[i-k-1][j+1]-1]+=1
                break
    if len(s[i]) - 1 != s[i][0]:
        if i==k-1:
            s[i].append(n)
        else:
            while len(s[i]) - 1 != s[i][0]:
                s[i].append()
    while len(s[i]) - 1 != s[i][0]:
        for m in range(s[i-1][-1]-1,n):
            if l[m] == 0:
                s[i].append(m + 1)
                l[m] += 1
                if len(s[i]) - 1 == s[i][0]:
                        break
        if len(s[i]) - 1 != s[i][0]:
            for m in range(s[i-1][-1]-1,n):
                if l[m] == 1:
                    s[i].append(m + 1)
                    l[m] += 1
                    if len(s[i]) - 1 == s[i][0]:
                        break
        break

print(k)

for i in range(len(s)):
    for j in range(len(s[i])):
        if j==len(s[i])-1:
            print(s[i][j])
        else:
            print(s[i][j], end=' ')