Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 2 2

Sample Output 1

Yes

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Sample Input 2

3
1 1 2

Sample Output 2

No

From the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.
Also, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.
Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.

Sample Input 3

5
4 3 4 3 4

Sample Output 3

No

Sample Input 4

3
2 2 2

Sample Output 4

Yes

Sample Input 5

4
2 2 2 2

Sample Output 5

Yes

Sample Input 6

5
3 3 3 3 3

Sample Output 6

No

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

n = int(input())
a = list(map(int, input().split()))

d = {}

for ai in a:
    if ai not in d:
        d[ai] = 0
    d[ai] += 1

f = 1

k = list(d.keys())
k.sort()

# ボッチ猫の数
b = 0

if len(k) > 2:
    f = 0
elif len(k) == 2:
    if k[1] - k[0] != 1:
        f = 0
    b = d[k[0]]

# グループ数
g = k[-1] - b

if g <= 0 or g > d[k[-1]] // 2:
    f = 0

if b == 0 and k[-1] == n - 1:
    f = 1

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