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 Ruby (2.7.1) (judge verdict: Accepted)

# a[i] + 1 < a[i+1] -> not exist
# a[i] + 1 == a[i+1] -> x[i] (only), x[i+1] (nonly) or reverse
# a[i] (nonly) == a[i+1] -> x[i+1] (nonly)
# a[i] (only) == a[i+1] -> x[i+1] (only)

n = gets.to_i
a = gets.split.map(&:to_i).sort
Y = "Yes"
N = "No"

if a[0] + 1 < a[-1]
    puts N
elsif a[0] + 1 == a[-1]
    x = a.index(a[-1])
    y = n - x

    s = a[0] - x + 1
    t = a[-1] - y + 1
    puts (s > 0 && s <= y / 2) || (t > 0 && t <= x / 2) ? Y : N
else
    puts a[0] == n - 1 || a[0] <= n / 2 ? Y : N
end