Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 2 2

Sample Output 1

Yes

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Sample Input 2

3
1 1 2

Sample Output 2

No

From the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.
Also, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.
Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.

Sample Input 3

5
4 3 4 3 4

Sample Output 3

No

Sample Input 4

3
2 2 2

Sample Output 4

Yes

Sample Input 5

4
2 2 2 2

Sample Output 5

Yes

Sample Input 6

5
3 3 3 3 3

Sample Output 6

No

Solution in Python (3.4.3) (judge verdict: Accepted)

#!/usr/bin/env python3
import sys

YES = "Yes"  # type: str
NO = "No"  # type: str


def solve(N: int, a: "List[int]"):
    from collections import Counter
    ma, mi = max(a), min(a)
    if ma >= N or mi < 1:
        raise
    if ma - mi > 1:
        return False
    # 全員aloneか、全員crowd
    if ma == mi:
        return ma == N - 1 or  2 * ma <= N
    c = Counter(a)
    # pairがpairでない
    if c[ma] % 2 != 0:
        return False
    x = ma - c[ma] // 2
    # pair以外、すべてalone(crowdが0個)
    if x == c[mi]:
        return True
    # crowdを1つ以上作れるなら1以上c[mi]-2以下の好きな數を作れる
    return 1 <= x <= c[mi] - 2

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    a = [int(next(tokens)) for _ in range(N)]  # type: "List[int]"
    print(YES if solve(N, a) else NO)

if __name__ == '__main__':
    main()