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)

N = int(input())
alist=[]
if N ==1:
    print("Yes")
    print("1")
    print("1")
    exit()
if N==2:
    print("Yes")
    print("1 2")
    print("1 2")
    exit()

for i in range(100):
    if i*(i+1)/2 > 100000:
        break
    else:
        alist.append(int(i*(i+1)/2) )

#print(alist)

if N in alist:
    print("Yes")
else:
    print("No")
    exit()

tate=alist.index(N)+1
yoko=alist.index(N)
#print(tate,yoko)
s=[]
tmp=[]
cnt=1
for j in range(tate):
    stmp=[]
    ntmp=[]
    for l in range(len(tmp)):
        #print("nowtmp:",tmp)
        stmp.append(tmp[l].pop(0))
        #print("tmp:",stmp)
    for m in range(yoko-len(stmp)):
        stmp.append(cnt)
        ntmp.append(cnt)
        #print("cnt:",stmp)
        cnt=cnt+1
    #print(stmp)
    s.append(stmp)
    #print("append ntmp:",ntmp)
    tmp.append(ntmp)
    tmp2=[x for x in tmp if x ]
    tmp=tmp2

print(len(s))

for j in range(len(s)):
    #print(" ".join( s[j] ))
    list1= [ str(s[j][i]) for i in range(len(s[j]))]
    print(" ".join(list1))