Problem Statement

Consider an amidakuji (ladder lottery) consisting of $N$ vertical lines and horizontal lines that horizontally connect adjacent vertical lines.
We call a figure obtained by connecting $2$ amidakuji of exactly the same shape one above the other a "series amidakuji".
The figure below is an example of a series amidakuji.

Given the correspondence between the starting points and ending points of an amidakuji, determine whether there exists a "series amidakuji" that satisfies this correspondence.

Input

$N$
$a_1$ $\ldots$ $a_N$

Line $1$ contains $N(2\leq N\leq50)$, the number of vertical lines.
Line $2$ contains $a_i(1\leq a_i\leq N)$, separated by spaces, which represent the correspondence between the starting points and ending points.
This means that starting from the $i$-th vertical line from the left, you arrive at the $a_i$-th vertical line from the left.
$a_1,\ldots,a_n$ are all distinct.

Output

Print Yes if there exists a "series amidakuji" that satisfies the correspondence between the starting points and ending points, and No otherwise.
Print a newline at the end.

Sample

2
1 2

Yes

3
2 3 1

Yes

2
2 1

No