#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

ll sum[2][101010];
int dx[3]={0,-1,0},dy[3]={0,0,-1};

int main(){
  int N; cin>>N;
  vector<int> L(N),R(N);
  rep(i,N) cin>>L[i]>>R[i];
  sort(L.rbegin(),L.rend());
  sort(R.begin(),R.end());
  rep(i,N){
    sum[0][i+1]=sum[0][i]+L[i];
    sum[1][i+1]=sum[1][i]+R[i];
  }
  ll ans=0;
  for(int k=1;k<=N;k++){
    rep(i,3) ans=max(ans,2*(sum[0][k+dx[i]]-sum[1][k+dy[i]]));
  }
  cout<<ans<<endl;
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

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 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 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.

Examples

Input

3
-5 1
3 7
-4 -2


Output

10


Input

3
1 2
3 4
5 6


Output

12


Input

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


Output

34

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

ll sum[2][101010];
int dx[3]={0,-1,0},dy[3]={0,0,-1};

int main(){
  int N; cin>>N;
  vector<int> L(N),R(N);
  rep(i,N) cin>>L[i]>>R[i];
  sort(L.rbegin(),L.rend());
  sort(R.begin(),R.end());
  rep(i,N){
    sum[0][i+1]=sum[0][i]+L[i];
    sum[1][i+1]=sum[1][i]+R[i];
  }
  ll ans=0;
  for(int k=1;k<=N;k++){
    rep(i,3) ans=max(ans,2*(sum[0][k+dx[i]]-sum[1][k+dy[i]]));
  }
  cout<<ans<<endl;
  return 0;
}

```