/*

for a potato at (x,y), only need to consider the line X+Y=x+y
determine energy when this line is hit

to work forwards, need 2 operations
1. spread i to [i,i+k]
2. insert potato at j, so increase i by |i-j|

convexity is maintained
how do i use convexity

*/


#include <bits/stdc++.h>
using namespace std;
const int DEBUG=0;

int n;

map<int,vector<int>> m;

multiset<int> lo,hi;    // maintain median
int offset;             // for hi

void op1(int k)
{
    if (DEBUG) printf("1 %d\n",k);
    offset+=k;
    if (DEBUG) {
        for (int i:lo) printf("(%d)",i);
        for (int i:hi) printf("[%d]",i+offset);
        printf("\n");
    }
}

long long ans=0;        // answer for median
void op2(int i)
{
    if (DEBUG) printf("2 %d\n",i);
    if (lo.empty() && hi.empty()) {
        lo.insert(i);
        hi.insert(i-offset);
        return;
    }
    int med=*lo.rbegin();
    if (i<med) {
        lo.insert(i);
        lo.insert(i);
        // update median
        lo.erase(lo.find(med));
        hi.insert(med-offset);
        int med2=*lo.rbegin();
        ans+=abs(med-med2);
        ans+=abs(i-med2);
    }
    else if (i>*hi.begin()+offset) {
        hi.insert(i-offset);
        hi.insert(i-offset);
        // update median
        int moved=*hi.begin()+offset;
        lo.insert(moved);
        hi.erase(hi.begin());
        int med2=*lo.rbegin();
        ans+=abs(moved-med2);
        ans+=abs(i-med2);
    }
    else {
        lo.insert(i);
        hi.insert(i-offset);
    }
    if (DEBUG) {
        for (int i:lo) printf("(%d)",i);
        for (int i:hi) printf("[%d]",i+offset);
        printf("ans now %I64d\n",ans);
    }
}

int main()
{
    #ifdef NOT_DMOJ
    freopen("data.txt","r",stdin);
    #endif // NOT_DMOJ
    scanf("%d",&n);
    for (int i=0; i<n; i++) {
        int t1,t2;
        scanf("%d%d",&t1,&t2);
        m[t1+t2].push_back(t1);
    }
    int prevf=0;
    for (auto &p:m) {
        // prevf to p.first
        op1(p.first-prevf);
        prevf=p.first;
        for (int i:p.second) op2(i);
    }
    cout << ans << endl;
}

### Prompt

Please create a solution in Cpp to the following problem:

Annie has gotten bored of winning every coding contest and farming unlimited rating. Today, she is going to farm potatoes instead.

Annie's garden is an infinite 2D plane. She has n potatoes to plant, and the i-th potato must be planted at (x_i,y_i). Starting at the point (0, 0), Annie begins walking, in one step she can travel one unit right or up (increasing her x or y coordinate by 1 respectively). At any point (X,Y) during her walk she can plant some potatoes at arbitrary points using her potato gun, consuming max(|X-x|,|Y-y|) units of energy in order to plant a potato at (x,y). Find the minimum total energy required to plant every potato.

Note that Annie may plant any number of potatoes from any point.

Input

The first line contains the integer n (1 ≤ n ≤ 800 000).

The next n lines contain two integers x_i and y_i (0 ≤ x_i,y_i ≤ 10^9), representing the location of the i-th potato. It is possible that some potatoes should be planted in the same location.

Output

Print the minimum total energy to plant all potatoes.

Examples

Input


2
1 1
2 2


Output


0


Input


2
1 1
2 0


Output


1


Input


3
5 5
7 7
4 9


Output


2


Input


10
5 1
4 0
9 6
0 2
10 1
9 10
3 10
0 10
8 9
1 5


Output


19


Input


10
1 1
2 2
2 0
4 2
4 0
2 0
0 2
4 0
4 2
5 1


Output


6

Note

In example 1, Annie can travel to each spot directly and plant a potato with no energy required.

In example 2, moving to (1,0), Annie plants the second potato using 1 energy. Next, she travels to (1,1) and plants the first potato with 0 energy.

### Response

```cpp
/*

for a potato at (x,y), only need to consider the line X+Y=x+y
determine energy when this line is hit

to work forwards, need 2 operations
1. spread i to [i,i+k]
2. insert potato at j, so increase i by |i-j|

convexity is maintained
how do i use convexity

*/


#include <bits/stdc++.h>
using namespace std;
const int DEBUG=0;

int n;

map<int,vector<int>> m;

multiset<int> lo,hi;    // maintain median
int offset;             // for hi

void op1(int k)
{
    if (DEBUG) printf("1 %d\n",k);
    offset+=k;
    if (DEBUG) {
        for (int i:lo) printf("(%d)",i);
        for (int i:hi) printf("[%d]",i+offset);
        printf("\n");
    }
}

long long ans=0;        // answer for median
void op2(int i)
{
    if (DEBUG) printf("2 %d\n",i);
    if (lo.empty() && hi.empty()) {
        lo.insert(i);
        hi.insert(i-offset);
        return;
    }
    int med=*lo.rbegin();
    if (i<med) {
        lo.insert(i);
        lo.insert(i);
        // update median
        lo.erase(lo.find(med));
        hi.insert(med-offset);
        int med2=*lo.rbegin();
        ans+=abs(med-med2);
        ans+=abs(i-med2);
    }
    else if (i>*hi.begin()+offset) {
        hi.insert(i-offset);
        hi.insert(i-offset);
        // update median
        int moved=*hi.begin()+offset;
        lo.insert(moved);
        hi.erase(hi.begin());
        int med2=*lo.rbegin();
        ans+=abs(moved-med2);
        ans+=abs(i-med2);
    }
    else {
        lo.insert(i);
        hi.insert(i-offset);
    }
    if (DEBUG) {
        for (int i:lo) printf("(%d)",i);
        for (int i:hi) printf("[%d]",i+offset);
        printf("ans now %I64d\n",ans);
    }
}

int main()
{
    #ifdef NOT_DMOJ
    freopen("data.txt","r",stdin);
    #endif // NOT_DMOJ
    scanf("%d",&n);
    for (int i=0; i<n; i++) {
        int t1,t2;
        scanf("%d%d",&t1,&t2);
        m[t1+t2].push_back(t1);
    }
    int prevf=0;
    for (auto &p:m) {
        // prevf to p.first
        op1(p.first-prevf);
        prevf=p.first;
        for (int i:p.second) op2(i);
    }
    cout << ans << endl;
}

```