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()))


dic = {}

for i in a:

    if i not in dic:
        dic[i] = 1
    else:
        dic[i] += 1

if len(dic) > 2:
    print ("No")

else:
    mi = float("inf")
    ma = -1

    for i in dic:
        mi = min(mi,i)
        ma = max(ma,i)

    if ma - mi > 1:
        print ("No")

    elif ma - mi == 1:
        

        if dic[mi] + dic[ma] // 2 == ma and dic[ma] > 1:
            print ("Yes")
        else:
            print ("No")

    else:

        if ma == N-1 or N // 2 >= ma:
            print ("Yes")
        else:
            print ("No")
