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 OCaml (4.02.3) (judge verdict: Wrong Answer)

print_endline @@
  Scanf.scanf "%d" @@ fun n ->
  let a = Array.init n (fun _ -> Scanf.scanf " %d" ((+) 0)) in
  Array.sort (-) a;
  let l, r = a.(0), a.(n-1) in
  if r-l >= 2 then "No" else
  if l = r then
    if n = l + 1 || n >= 2 * l then "Yes" else "No"
  else
  (* l+1 = r *)
  let lc = Array.fold_left (fun s x -> s + a.(n-1) - x) 0 a in
  let rc = n - lc in
  if lc < l && rc >= 2 * (r-lc) then "Yes" else "No"