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 = list(map(int, raw_input().split()))

def no():
	print "No"
	exit(0)

def yes():
	print 'Yes'
	exit(0)

a = list(sorted(a))
if a[0] == a[-1] and a[0] == n - 1:
	yes()

X = max(a)
alone = 0
many = 0

for e in a:
	if e != X and e != X - 1:
		no()
	if e == X - 1:
		alone += 1
	else:
		many += 1

rest = X - alone

if rest < 0:
	no()

if rest == 0 and many > 0:
	no()

if rest * 2 > many:
	no()

yes()
