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
sys.setrecursionlimit(10**9)
input = sys.stdin.readline

N = int(input())
L = list(map(int, input().split()))
ans = "Yes"

L_max = max(L)
L_min = min(L)

if L_max - L_min >= 2:
    ans = "No"
elif L_max == L_min:
    if not(N >= L[0]*2 or L[0] == N-1):
        ans = "No"
else:
    num_alone = L.count(L_min)
    not_alone_L = [v-num_alone for v in L if v == L_max]
    if not_alone_L[0] <= 0 or len(not_alone_L) < not_alone_L[0]*2:
        ans = "No"
print(ans)
