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()))
ans=False
aa=a[0]

s1=0
s2=0
check=True
for i in range(n):
    if a[i]==aa:
        s1+=1
    elif a[i]==aa+1:
        s2+=1
    else:
        check=False
        break
if check:
    if s2==0:
        if aa==n-1:
            ans=True
    else:
        if 2<=(aa+1-s1)*2<=s2:
            ans=True
s1=0
s2=0
check=True
for i in range(n):
    if a[i]==aa-1:
        s1+=1
    elif a[i]==aa:
        s2+=1
    else:
        check=False
        break
if check:
    if s2==0:
        pass
    else:
        if 2<=(aa-s1)*2<=s2:
            ans=True

if ans:
    print('Yes')
else:
    print('No')