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()))
B = []
C = []
for num in A:
    if len(B) >= 3:
        print("No")
        break
    elif num in B: 
        C[B.index(num)] += 1
    else:
        B.append(num)
        C.append(1)


if len(B) >= 3:
    pass
elif len(B) == 1:
    if n == B[0] +1:
        print('Yes')
    elif n//B[0] >= 2:
        print('Yes')
    else:
        print('No')
elif B[0]  == (B[1]+1):
    k = C[1]
    m = B[1]
    if m-k+1 <= 0:
        print('No')
    elif (n-k) % (m-k+1) == 0:
        print('Yes')
    else:
        print('No')
elif B[1] == (B[0]+1):
    k = C[0]
    m = B[0]
    if m-k+1 <= 0:
        print('No')
    elif (n-k) % (m-k+1) == 0:
        print('Yes')
    else:
        print('No')
else:
    print('No')
    