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()))

d = {}

for ai in a:
    if ai not in d:
        d[ai] = 0
    d[ai] += 1

f = 1

k = list(d.keys())
k.sort()

# ボッチ猫の数
b = 0

if len(k) > 2:
    f = 0
elif len(k) == 2:
    if k[1] - k[0] != 1:
        f = 0
    b = d[k[0]]

# グループ数
g = k[-1] - b

if g <= 0 or g > d[k[-1]] // 2:
    f = 0

if len(k) == 1 and k[-1] == n - 1:
    f = 1

if f:
    print('Yes')
else:
    print('No')
