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
# 解説AC
N = int(input())
A = [int(i) for i in input().split()]

MAXA = max(A)
MINA = min(A)

if MAXA - MINA >= 2:
    flag = False
elif MAXA - MINA == 0:
    # 全てalone -> 種類数はN
    flag = True if (A[0] == N - 1) else False
    # 全てaloneではない -> 種類数はN/2以下
    flag |= True if (2 * A[0] <= N) else False
else:
    x = A.count(MINA) # alonaな猫の匹数
    y = A.count(MAXA) # aloneではない猫の匹数
    # MAXA - x: aloneではない猫の種類数
    flag = True if (x < MAXA and 2 * (MAXA - x) <= y) else False

if flag:
    print('Yes')
else:
    print('No')