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
sys.setrecursionlimit(10**6)
ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
nn = lambda: list(stdin.readline().split())
ns = lambda: stdin.readline().rstrip()

n = ni()
a = na()

mx,mxc = 0,0
mn,mnc = 1000000,0
for i in a:
    if mx == i:
        mxc += 1
    if mn == i:
        mnc += 1
    if mx < i:
        mx = i
        mxc = 1
    if mn > i:
        mn = i
        mnc = 1

d = mx-mn


if d > 1:
    print('No')
elif d == 1:
    if mx > mnc and 2*(mx-mnc) <= mxc:
        print('Yes')
    else:
        print('No')
elif d == 0:
    if a[0] == n-1 or 2*a[0] <= n:
        print('Yes')
    else:
        print('No')