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 Lua (5.3.2) (judge verdict: Accepted)

n = io.read("*n")
local t = {}
for i = 1, n do
  t[i] = io.read("*n")
end
table.sort(t)
local function solve()
  if t[1] + 1 < t[n] then
    return false
  end
  if t[1] == t[n] then
    if t[n] == n - 1 then return true end
  end
  local major = 0
  for i = 1, n do
    if t[i] == t[n] then
      major = n + 1 - i
      break
    end
  end
  local minor = n - major
  local minhats = minor + 1
  local maxhats = minor + major // 2
  return minhats <= t[n] and t[n] <= maxhats
end

print(solve() and "Yes" or "No")