Problem:
Score : 700 points

Problem Statement

There are N cats.
We number them from 1 through N.

Each of the cats wears a hat.
Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints

2 ≤ N ≤ 10^5

1 ≤ a_i ≤ N-1

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print Yes if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print No otherwise.

Sample Input 1

3
1 2 2

Sample Output 1

Yes

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Sample Input 2

3
1 1 2

Sample Output 2

No

From the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.
Also, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.
Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.

Sample Input 3

5
4 3 4 3 4

Sample Output 3

No

Sample Input 4

3
2 2 2

Sample Output 4

Yes

Sample Input 5

4
2 2 2 2

Sample Output 5

Yes

Sample Input 6

5
3 3 3 3 3

Sample Output 6

No

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

n=int(input())
arr=list(map(int,input().split()))
amax=max(arr)
amin=min(arr)
if amax-amin>=2:
  print('No')
elif amax-amin==0:
  flag=False
  for i in range(n):
    if arr[i]!=n-1:
      break
  else:
    flag=True
  for i in range(n):
    if 2*arr[i]>n:
      break
  else:
    flag=True
  if flag==True:
    print('Yes')
  else:
    print('No')
elif amax-amin==1:
  cnt1=0
  cnt2=0
  for i in range(n):
    if arr[i]==amax:
      cnt1+=1
    else:
      cnt2+=1
  if cnt1<amax and 2*(amax-cnt1)<=cnt2:
    print('Yes')
  else:
    print('No')