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.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
#https://img.atcoder.jp/agc016/editorial.pdf
def solve():
  n = int(input())
  a = list(int(i) for i in input().split())
  ans = 'Yes'
  alone = 0
  group = 0
  ha = max(a)
  la = min(a)
  if ha - la >= 2: ans = 'No'
  
  elif ha - la == 1:
   for i in a:
     if i == ha-1 : alone += 1
     else: group += 1
   if alone < ha and 2*(ha-alone)<= group: pass
   else: ans = 'No'
  
  
  elif ha - la == 0:
    if a[0] == n-1 or 2*a[0] <= n:
      pass
    else: ans = 'No'
  return ans

if __name__ == '__main__':
  print(solve())