There are $n$ fishers numbered $1,2,\dots,n$ scattered around a round lake. Each of the fishers has picked a fixed point on the shoreline and is casting their line to that exact direction. Check if there is a risk of the lines getting tangled up. Tangling may only happen when two lines cross each other.

The fishers and their line casting directions are represented in the array $f$ of $2n$ integers. If the $i$-th integer of $f$ is $X$ then it means that position $i$ is occupied by fisher $X$ and if it is $-X$ then this is the point to which the fisher is casting their line. Positions $i$ and $i+1$ are next to each other and as the lake is round, consider positions $2n$ and $1$ to be next to each other also.

Input

The first line contains a single integer $n$. The second line contains $2n$ integers $f_1,\,f_2,\dots,\,f_{2n}$.

Output

Print "Yes" if the lines might get tangled up and "No" otherwise.

Constraints

• $1 \leq n \leq 10^5$
• $-n \leq f_i \leq n$
• $f_i \neq 0$
• $f_i \neq f_j$ if $i \neq j$

Example 1

Input:

5
-1 -4 5 3 2 -5 1 4 -3 -2

Output:

Yes

Example 2

Input:

5
-2 4 -4 2 3 1 5 -5 -1 -3

Output:

No