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()))

a = max(A)
b = min(A)

# import sys
# if a - b > 1:
#     print("No")
#     sys.exit()

ok = 0

if a - b == 1:
    C = [0, 0]
    for i in range(n):
        C[A[i] - b] += 1
    if a - C[0] > 0 and C[1] // 2 >= a - C[0]:
        ok = 1
elif a == b:
    if n == a + 1:
        ok = 1   
    if n // 2 >= a:
        ok = 1

if ok == 1:
    print("Yes")
else:
    print("No")