Score : $700$ points

Problem Statement

Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate $0$. Aoki has $N$ segments. The $i$-th segment is $[L_i,R_i]$, that is, a segment consisting of points with coordinates between $L_i$ and $R_i$ (inclusive).

The game has $N$ steps. The $i$-th step proceeds as follows:

• First, Aoki chooses a segment that is still not chosen yet from the $N$ segments and tells it to Takahashi.
• Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.

After $N$ steps are performed, Takahashi will return to coordinate $0$ and the game ends.

Let $K$ be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that $K$ will be as large as possible, and Takahashi walks along the line so that $K$ will be as small as possible. What will be the value of $K$ in the end?

Constraints

• $1 \leq N \leq 10^5$
• $-10^5 \leq L_i < R_i \leq 10^5$
• $L_i$ and $R_i$ are integers.

Input

Input is given from Standard Input in the following format:

$N$

$L_1$ $R_1$

:

$L_N$ $R_N$

Output

Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that $K$ is always an integer when $L_i,R_i$ are integers.

3
-5 1
3 7
-4 -2

10

One possible sequence of actions of Takahashi and Aoki is as follows:

• Aoki chooses the first segment. Takahashi moves from coordinate $0$ to $-4$, covering a distance of $4$.
• Aoki chooses the third segment. Takahashi stays at coordinate $-4$.
• Aoki chooses the second segment. Takahashi moves from coordinate $-4$ to $3$, covering a distance of $7$.
• Takahashi moves from coordinate $3$ to $0$, covering a distance of $3$.

The distance covered by Takahashi here is $14$ (because Takahashi didn't move optimally). It turns out that if both players move optimally, the distance covered by Takahashi will be $10$.

3
1 2
3 4
5 6

12

5
-2 0
-2 0
7 8
9 10
-2 -1

34