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
#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import array
from bisect import *
from collections import *
import fractions
import heapq 
from itertools import *
import math
import re
import string

N = int(input())
As = list(map(int, input().split()))

mn = min(As)
mx = max(As)
if mx > mn + 1:
    print('No')
elif mx == mn:
    if 1 <= mx <= N // 2 or mx == N - 1:
        print('Yes')
    else:
        print('No')
else:
    mn_num = As.count(mn)
    mx_num = As.count(mx)
    k = mn + 1 - mn_num
    # print("can i make {} groups from {}?".format(k, mx_num))
    if mx_num == 0:
        if k == 0:
            print('Yes')
        else:
            print('No')
    else:
        if 1 <= k <= (mx_num // 2):
            print('Yes')
        else:
            print('No')
