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

res = True
maxvar = max(A)

x = 0
y = 0

for i in range(N):
    if A[i] == maxvar:
        x += 1
    elif A[i] == maxvar - 1:
        y += 1
    else:
        res = False
        break
else:
    if (maxvar - y) * 2 + y > N or y >= maxvar:
        res = False

    if maxvar == N - 1 and y == 0:
        res = True

print('Yes' if res else 'No')