#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i <= n; i++)
#define rep3(i, x, n) for(int i = x; i >= n; i--)
#define elif else if
typedef long long ll;
typedef pair<ll, ll> P;
const ll MOD = 1e9+7;
const ll MOD2 = 998244353;
const ll INF = 1e18;
const string alpha = "abcdefghijklmnopqrstuvwxyz";

int main(){
    int N;
    cin >> N;
    ll L[N], R[N];
    rep(i, N) cin >> L[i] >> R[i];
    sort(L, L+N, greater<ll>());
    sort(R, R+N);
    int i = 0;
    ll sum = 0;
    while(L[i] > R[i]){sum += L[i]-R[i]; i++;}
    ll ans = sum;
    if(i >= 1){
        ans = max(ans, sum-L[i-1]);
        ans = max(ans, sum+R[i-1]);
    }
    if(i*2 != N){
        ans = max(ans, sum+L[i]);
        ans = max(ans, sum-R[i]);
    }
    cout << ans*2 << endl;
}
### Prompt

Create a solution in cpp for 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;
#define rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i <= n; i++)
#define rep3(i, x, n) for(int i = x; i >= n; i--)
#define elif else if
typedef long long ll;
typedef pair<ll, ll> P;
const ll MOD = 1e9+7;
const ll MOD2 = 998244353;
const ll INF = 1e18;
const string alpha = "abcdefghijklmnopqrstuvwxyz";

int main(){
    int N;
    cin >> N;
    ll L[N], R[N];
    rep(i, N) cin >> L[i] >> R[i];
    sort(L, L+N, greater<ll>());
    sort(R, R+N);
    int i = 0;
    ll sum = 0;
    while(L[i] > R[i]){sum += L[i]-R[i]; i++;}
    ll ans = sum;
    if(i >= 1){
        ans = max(ans, sum-L[i-1]);
        ans = max(ans, sum+R[i-1]);
    }
    if(i*2 != N){
        ans = max(ans, sum+L[i]);
        ans = max(ans, sum-R[i]);
    }
    cout << ans*2 << endl;
}
```