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

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