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
n=input()
m=map(int,input().split())
a=[int(i) for i in m]
d=max(a)-min(a)
if d>1:
    ans=False
elif d==0:
    if (max(a)==len(a)-1 or max(a)*2<=len(a)):
        ans=True
    else:
        ans=False
else:
    max_num=a.count(max(a))
    min_num=a.count(min(a))
    dif=max(a)-min_num
    if (min_num<max(a) and dif*2<=max_num):
            ans=True
    else:
        ans=False
        
if ans:
    print("Yes")
else:
    print("No")
        