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
N = int(input())
a = list(map(int, input().split()))

cat = {}
for c in a:
  if c in cat:
    cat[c] += 1
  else:
    cat[c] = 1

min_cat = N
min_cat_cnt = 0
max_cat = 0
max_cat_cnt = 0
for c in cat:
  if c < min_cat:
    min_cat = c
    min_cat_cnt = cat[c]
  if c > max_cat:
    max_cat = c
    max_cat_cnt = cat[c]
    
if max_cat - min_cat == 1 and min_cat_cnt <= min_cat and 2 * min_cat - min_cat_cnt + 2 <= N:
  print("Yes")
elif max_cat == min_cat and 2 * (max_cat) <= N:
  print("Yes")
elif max_cat == min_cat and min_cat_cnt - 1 == min_cat:
  print("Yes")
else:
  print("No")