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()))
dic = {}
amin = n - 1
amax = 1
for ai in a:
    if ai in dic:
        dic[ai] += 1
    else:
        dic[ai] = 1
    amin = min(amin, ai)
    amax = max(amax, ai)

if 1 < amax - amin:
    print('No')
elif amin == amax:
    if a[0] == n - 1 or 2 * a[0] <= n:
        print('Yes')
    else:
        print('No')
else:
    if dic[amax] == 1:
        print('No')
    elif dic[amin] + 1 <= amax <= dic[amin] + dic[amax] // 2:
        print('Yes')
    else:
        print('No')