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
n = int(input())
a = list(map(int, input().split()))
cnt = [[a[0], 0]]
for i in a:
    if cnt[0][0] == i:
        cnt[0][1] += 1
    else:
        if len(cnt) == 1:
            cnt.append([i, 1])
            if not abs(cnt[0][0] - cnt[1][0]) == 1:
                print("No")
                exit()
        else:
            if cnt[1][0] == i:
                cnt[1][1] += 1
            else:
                print("No")
                exit()
cnt.sort()
if len(cnt) == 1:
    print("Yes" if cnt[0][0] <= cnt[0][1] // 2 or cnt[0][0] + 1 == n else "No")
else:
    print("Yes" if 1 <= cnt[1][0] - cnt[0][1] <= cnt[1][1] // 2 else "No")