p03688 AtCoder Grand Contest 016 - Colorful Hats
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
```python
N = int(input())
hat = list(map(int, input().split()))
hat.sort()
min, max = hat[0], hat[N - 1]
count_min = 0
count_max = N
if max - min > 1:
    print("No")
elif max == min:
    if max <= N // 2 or max == N-1:
        print("Yes")
    else:
        print("No")
else:
    for i in range(N):
        if hat[i] < max:
            count_min += 1
            count_max -= 1
        else:
            break
    # 種類はcount_min+1 <= max <= count_min + count_max // 2
    if count_min < max <= count_min + count_max // 2:
        print("Yes")
    else:
        print("No")

```