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 = int(input())
A = [int(a) for a in input().split()]

A.sort()
flag = True
for a in A:
    if a > A[0]+1:
        flag = False

ans = "No"
if flag:
    cnt = A.count(A[0])
    if cnt == N and (A[0] == N-1 or A[0]*2 <= N):
        ans = "Yes"
    elif cnt == A[0] and cnt < N-1:
        ans = "Yes"
    elif cnt < A[0] and N-cnt >= 2*(A[0]-cnt+1):
        ans = "Yes"
        
print(ans)