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

N=int(raw_input())
a=map(int,raw_input().split())

T=0
for i in a:
    if i != a[0]:
        if i - a[0] >= 2 or a[0] - i >= 2:
            print "No"
            sys.exit()
        T=max(i,a[0])
        break

if T == 0:
    if a[0] <= N/2 or a[0] == N-1:
        print "Yes"
    else:
        print "No"
    sys.exit()

uni=0
nu=0
for i in a:
    if i==T:
        nu+=1
    else:
        uni+=1

if T>=uni+1 and T<=uni+nu/2:
    print "Yes"
else:
    print "No"