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.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
from collections import Counter
N = int(input())

a= list(map(int,input().split()))


X = Counter(a)

min_val = min(a)
max_val = max(a)
if not min_val == max_val-1 and not min_val==max_val:
    print("No")
    exit()
if max_val==min_val and max_val == N-1:
    #all unique
    print("Yes")
    exit()

#only 1 color cat
unique_cat = X[min_val] if min_val!=max_val else 0

# 2 or more cat color  : max_val - unique_cat
last_cat =  N- unique_cat
last_colors = max_val - unique_cat


#print(last_cat,last_colors,unique_cat)
if last_cat>0 and last_colors <=0:
    print("No")
elif  0< 2*last_colors <= last_cat:
    print("Yes")

else:
    print("No")
