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
stdin = sys.stdin

def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x)-1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())

n = ni()
a = list(li())

exist = True

if max(a) - min(a) > 1:
    exist = False
    
elif max(a) >= n:
    exist = False
    
elif max(a) - min(a) == 1:
    if a.count(min(a)) < max(a) and 2*(max(a)-a.count(min(a))) <= a.count(max(a)):
        exist = True
    else:
        exist = False
        
elif max(a) == min(a):
    if 2*a[0] <= n or a[0]+1 == n:
        exist = True
    else:
        exist = False
        
print("Yes") if exist else print("No")