Score : $300$ points

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.

Constraints

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

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.

5
1 2 3 4 5

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.

5
1 6 1 6 1

Yes

The given sequence $A$ itself is M-type.

5
1 6 6 6 1

No

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