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()))

mx = max(a)
mn = min(a)
if (mx-mn) >= 2 :
    print('No')
elif mx == mn == N-1 :
    print('Yes')
elif mx == mn :
    if N >= mx*2 :
        print('Yes')
    else :
        print('No')
elif (mx-mn) == 1 :
    mx_cnt = 0
    mn_cnt = 0
    for i in range(N) :
        if a[i] == mx :
            mx_cnt += 1
        else :
            mn_cnt += 1

    if mn < mn_cnt :
        print('No')
    elif mx_cnt >= (mx-mn_cnt)*2:
        print('Yes')
    else :
        print('No')