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()))
a.sort()

cnt = 0
for i in range(n):
    if a[i] == a[0]:
        cnt = i+1
    else:
        break

if a[-1] - a[0] > 1:
    print('No')
    exit()
elif a[-1] - a[0] == 1:
    actual = a[-1]
    if actual >= n:
        print('No')
    elif cnt <= actual - 1 and actual <= cnt  + (n - cnt) // 2:
        print('Yes')
    else:
        print('No')
    exit()
elif a[-1] - a[0] == 0:
    solve = False
    actual = a[0]
    if n >= actual * 2 or n-1 == actual:
        solve = True
    if solve:
        print('Yes')
    else:
        print('No')
    exit()
else:
    print('No')