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 (3.8.2) (judge verdict: Accepted)

def main():
    n = int(input())
    col = list(map(int, input().split()))
    col_min, col_max = min(col), max(col)
    if col_min == col_max:
        if col_min == 1 or col_min == n-1:
            print("Yes")
        elif 2*col_min <= n:
            print("Yes")
        else:
            print("No")
    elif col_min + 1 == col_max:
        cnt_min, cnt_max = 0, 0
        for v in col:
            if v == col_min:
                cnt_min += 1
            else:
                cnt_max += 1
        if cnt_max == 1:
            print("No")
        else:
            m = cnt_max//2
            if col_min < cnt_min-1 + 1 or cnt_min-1 + m < col_min:
                print("No")
            else:
                p = col_min - (cnt_min-1)
                if p + cnt_min == col_max:
                    print("Yes")
                else:
                    print("No")
    else:
        print("No")

if __name__ == "__main__":
    main()