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
import sys
input = sys.stdin.readline
N = int(input())
a = list(map(int, input().split()))
a.sort()
mx = max(a)
mn = min(a)
c = mx + 0
b = 0
s = 0
if mx == mn and (mx != N - 1):
  mn -= 1
if mx >= N:
  print("No")
  exit(0)
for i in range(N):
  if abs(a[i] - mx) > 1:
    print("No")
    exit(0)
  if a[i] == mn:
    c = a[i] + 1
    s += 1
  else:
    b += 1
if s >= c and (b != 0 and s != 0):
  print("No")
  exit(0)
elif s > c:
  print("No")
  exit(0)
if b == 1:
  print("No")
  exit(0)
if b // 2 < c - s:
  print("No")
else: print("Yes")