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
import sys
from collections import Counter

# sys.stdin = open('b1.in')


def read_int_list():
    return list(map(int, input().split()))


def read_int():
    return int(input())


def read_str_list():
    return input().split()


def read_str():
    return input()


yes, no = 'Yes', 'No'


def solve(n, a):
    s = set(a)
    c = Counter(a)
    if len(s) == 1:
        a = list(s)[0]
        n_colors = a + 1
        if n_colors == n:
            return yes
        n_colors = a
        if 2 * n_colors <= n:
            return yes
    if len(s) == 2:
        a, b = sorted(s)
        if a + 1 == b:
            n_colors = b
            appear_once = c[a]
            appear_twice_or_more = n_colors - appear_once
            if appear_once < n_colors:
                if c[b] >= 2 * appear_twice_or_more:
                    return yes
    return no

n = read_int()
a = read_int_list()
res = solve(n, a)
print(res)

