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()))

ma = max(a)
for ai in a:
    if ai < ma - 1:
        print("No")
        exit()

flag = 0
for ai in a:
    if ai == ma - 1:
        flag = 1

# 数字が異なるものが存在
if flag:
    count = 0
    for ai in a:
        if ai == ma - 1:
            count += 1
    if (n - count) == 1:
        print("No")
        exit()
    count_min = count + 1
    count_max = count + (n - count) // 2
    if (count_min <= ma) and (ma <= count_max):
        print("Yes")
        exit()
    else:
        print("No")
        exit()

# 数字が全て同じ
if ma == n-1:
    print("Yes")
    exit()
if (1 <= ma) and (ma <= n // 2):
    print("Yes")
    exit()
print("No")