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=[int(i) for i in input().split()]
A.sort()
K=A[0]
x=0
y=0
for i in range(N):
    if A[i]!=K and A[i]!=K+1:
        print('No')
        sys.exit()
    if A[i]==K:
        x+=1
    elif A[i]==K+1:
        y+=1

if x==N and x >=2*K:
    print('Yes')
    sys.exit()
if x==N and N==K+1:
    print('Yes')
    sys.exit()
if x<=K and y>=(K-x+1)*2:
    print('Yes')
    sys.exit()
print('No')