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
#!/usr/bin/python
# -*- coding: utf-8 -*-
import sys
import math

N, = map(int, sys.stdin.readline().rstrip().split())
a_s = list(map(int, sys.stdin.readline().rstrip().split()))

mina = min(a_s)
maxa = max(a_s)
if (maxa - mina > 1):
    print("No")
    exit(0)
if(maxa == mina):
    if(maxa <= N//2 or N == (maxa+1)):
        print("Yes")
    else:
        print("No")
    exit(0)
if maxa - mina == 1:
    alones = sum(a == mina for a in a_s)
    #print(alones)
    #print(N-alones)
    #print(maxa-alones)
    if  (N-alones) >= (maxa - alones) * 2 and alones < maxa:
        print("Yes")
    else:
        print("No")
    exit(0)

raise Exception()
exit(0)
