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()))

minColor = min(A)
maxColor = max(A)

if minColor == maxColor:
    if minColor == N - 1:  # 各色の猫が1匹ずつ
        print('Yes')
    elif minColor * 2 <= N:  # 各色の猫が2匹以上
        print('Yes')
    else:
        print('No')
    exit()

if minColor + 1 != maxColor:
    print('No')
    exit()

minCnt = 0
maxCnt = 0

for a in A:
    if a == minColor:
        minCnt += 1
    elif a == maxColor:
        maxCnt += 1
    else:
        print('No')
        exit()

# minCnt : 1匹だけの色
# maxCnt : 2匹以上の色
# 全体でmaxColor個の色

if (maxColor - minCnt) * 2 <= maxCnt and maxColor >= minCnt + 1:
    print('Yes')
else:
    print('No')
