Problem Statement

Let N be a positive odd number.
A sequence of integers of length $N, S = (S_1, S_2, \dots, S_N)$, is said to be M-type if "for each even number $i = 2, 4, \dots, N - 1$, it holds that S_{i-1} < S_i and S_i > S_{i+1}".
You are given a sequence of positive integers of length $N, A = (A_1, A_2, \dots, A_N)$.
Determine if it is possible to rearrange A to be M-type.

Input

The input is given from Standard Input in the following format:
N
A_1 \ A_2 \ $\dots$ \ A_N

Output

If it is possible to rearrange the given integer sequence A to be M-type, print Yes; otherwise, print No.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• N is an odd number.
• $1 \leq A_i \leq 10^9$ \ \ $(1 \leq i \leq N)$

Sample Input 1

5
1 2 3 4 5

Sample Output 1

Yes

The given sequence is A = (1, 2, 3, 4, 5).
After rearranging it, for example, to B = (4, 5, 1, 3, 2),

• for i = 2, it holds that B_1 = 4 < 5 = B_2 and B_2 = 5 > 1 = B_3;
• for i = 4, it holds that B_3 = 1 < 3 = B_4 and B_4 = 3 > 2 = B_5.

Therefore, this sequence B is M-type, and the answer is Yes.

Sample Input 2

5
1 6 1 6 1

Sample Output 2

Yes

The given sequence A itself is M-type.

Sample Input 3

5
1 6 6 6 1

Sample Output 3

No

It is impossible to rearrange it to be M-type.

见题面 Input 部分

见题面 Output 部分