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 = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


n = int(input())
a = list(map(int, input().split()))
s = set(a)
if len(s)>2:
    ans = "No"
elif len(s)==2:
    if max(s)-min(s)!=1:
        ans = "No"
    else:
        x = max(s)
        n2 = sum(num==x-1 for num in a)
        if x-n2>0 and n2 + 2*(x-n2) <= n:
            ans = "Yes"
        else:
            ans = "No"
else:
    x = max(s)
    if x==n-1 or 2*x<=n:
        ans = "Yes"
    else:
        ans = "No"
print(ans)