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())
a=list(map(int,input().split()))
b=sorted(a)
c=0
if(b[n-1]-b[0]>1):
    print('No')
elif(b[n-1]-b[0]==0):
    if(1<=b[0]<=n//2 or b[0]==n-1):
        print('Yes')
    else:
        print('No')
else:
    for i in range(n-1):
        if(b[i]<b[i+1]):
            c=i
            break
    if(c==n-2):
        print('No')
    elif(c+1<=b[0]<=+1+(n-c-1)//2):
        print('Yes')        
    else:
        print('No')