#include <iostream>
#include <complex>
#include <vector>
#include <string>
#include <algorithm>
#include <cstdio>
#include <numeric>
#include <cstring>
#include <ctime>
#include <cstdlib>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <cmath>
#include <bitset>
#include <cassert>
#include <queue>
#include <stack>
#include <deque>
#include <random>
 
using namespace std;
template<class T1, class T2> inline void chkmin(T1 &x, const T2 &y) {if (x > y) x = y;}
template<class T1, class T2> inline void chkmax(T1 &x, const T2 &y) {if (x < y) x = y;}
#define all(c) (c).begin(), (c).end()
#define sz(c) (int)(c).size()
#define mp make_pair
#define pb push_back
#define read(FILENAME) freopen((string(FILENAME) + ".in").c_str(), "r", stdin)
#define write(FILENAME) freopen((string(FILENAME) + ".out").c_str(), "w", stdout);
const int S=0,T=2001,inf=0x3f3f3f3f;
const long long finf=0xc0c0c0c0c0c0c0c0ll;
struct bian
{
	int to,nxt,f,va;
}bi[3000030];
int n,head[2020],num=1,rx[1010],ry[1010],rc[1010],bx[1010],by[1010],bc[1010],from[2020];
long long dis[2020],ans;
bool bj[2020];
queue<int>q;
void add(int from,int to,int f,int va)
{
	bi[++num].nxt=head[from];
	head[from]=num;
	bi[num].to=to;
	bi[num].f=f;
	bi[num].va=va;
}
void ADD(int from,int to,int f,int va)
{
	add(from,to,f,va);
	add(to,from,0,-va);
}
bool spfa()
{
	bj[S]=1;
	q.push(S);
	memset(dis,0xc0,sizeof(dis));
	dis[S]=0;
	int x,y;
	while(!q.empty())
	{
		x=q.front();q.pop();
		bj[x]=0;
		for(int i=head[x];i;i=bi[i].nxt)
			if(bi[i].f)
			{
				y=bi[i].to;
				if(dis[x]+bi[i].va>dis[y])
				{
					dis[y]=dis[x]+bi[i].va;
					from[y]=i;
					if(!bj[y])bj[y]=1,q.push(y);
				}
			}
	}
	return dis[T]>finf;
}
 
 
int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	//read("input");
	cin >> n;
	for (int i = 1; i <= n; i++) {
		cin >> rx[i] >> ry[i] >> rc[i]; 
		ADD(S,i,rc[i],0);
	} 
	for (int i = 1; i <= n; i++) {
		cin >> bx[i] >> by[i] >> bc[i]; 
		ADD(i+n,T,bc[i],0);
	}
	for (int i = 1; i <= n; i++) {
		ADD(i,2002,inf,rx[i]+ry[i]);
		ADD(i,2003,inf,rx[i]-ry[i]);
		ADD(i,2004,inf,-rx[i]+ry[i]);
		ADD(i,2005,inf,-rx[i]-ry[i]);
	}
	for (int i = 1; i <= n; i++) {
		ADD(2002,i+n,inf,-bx[i]-by[i]);
		ADD(2003,i+n,inf,-bx[i]+by[i]);
		ADD(2004,i+n,inf,bx[i]-by[i]);
		ADD(2005,i+n,inf,bx[i]+by[i]);
	}
	while(spfa()) {
		int x=T,flow=inf;
		while(x)flow=min(flow,bi[from[x]].f),x=bi[from[x]^1].to;
		ans+=1ll*flow*dis[T];
		x=T;
		while(x)bi[from[x]].f-=flow,bi[from[x]^1].f+=flow,x=bi[from[x]^1].to;
	}
	cout << ans << endl;
	return 0;
}
### Prompt

Please provide a CPP coded solution to the problem described below:

Snuke is playing with red and blue balls, placing them on a two-dimensional plane.

First, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i). Then, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i). The total number of red balls placed and the total number of blue balls placed are equal, that is, \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i. Let this value be S.

Snuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair. Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.

Snuke wants to maximize the sum of the scores of the pairs. Help him by finding the maximum possible sum of the scores of the pairs.

Constraints

* 1 \leq N \leq 1000
* 0 \leq RX_i,RY_i,BX_i,BY_i \leq 10^9
* 1 \leq RC_i,BC_i \leq 10
* \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
RX_1 RY_1 RC_1
RX_2 RY_2 RC_2
\vdots
RX_N RY_N RC_N
BX_1 BY_1 BC_1
BX_2 BY_2 BC_2
\vdots
BX_N BY_N BC_N


Output

Print the maximum possible sum of the scores of the pairs.

Examples

Input

2
0 0 1
3 2 1
2 2 1
5 0 1


Output

8


Input

3
0 0 1
2 2 1
0 0 2
1 1 1
1 1 1
3 3 2


Output

16


Input

10
582463373 690528069 8
621230322 318051944 4
356524296 974059503 6
372751381 111542460 9
392867214 581476334 6
606955458 513028121 5
882201596 791660614 9
250465517 91918758 3
618624774 406956634 6
426294747 736401096 5
974896051 888765942 5
726682138 336960821 3
715144179 82444709 6
599055841 501257806 6
390484433 962747856 4
912334580 219343832 8
570458984 648862300 6
638017635 572157978 10
435958984 585073520 7
445612658 234265014 6


Output

45152033546

### Response

```cpp
#include <iostream>
#include <complex>
#include <vector>
#include <string>
#include <algorithm>
#include <cstdio>
#include <numeric>
#include <cstring>
#include <ctime>
#include <cstdlib>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <cmath>
#include <bitset>
#include <cassert>
#include <queue>
#include <stack>
#include <deque>
#include <random>
 
using namespace std;
template<class T1, class T2> inline void chkmin(T1 &x, const T2 &y) {if (x > y) x = y;}
template<class T1, class T2> inline void chkmax(T1 &x, const T2 &y) {if (x < y) x = y;}
#define all(c) (c).begin(), (c).end()
#define sz(c) (int)(c).size()
#define mp make_pair
#define pb push_back
#define read(FILENAME) freopen((string(FILENAME) + ".in").c_str(), "r", stdin)
#define write(FILENAME) freopen((string(FILENAME) + ".out").c_str(), "w", stdout);
const int S=0,T=2001,inf=0x3f3f3f3f;
const long long finf=0xc0c0c0c0c0c0c0c0ll;
struct bian
{
	int to,nxt,f,va;
}bi[3000030];
int n,head[2020],num=1,rx[1010],ry[1010],rc[1010],bx[1010],by[1010],bc[1010],from[2020];
long long dis[2020],ans;
bool bj[2020];
queue<int>q;
void add(int from,int to,int f,int va)
{
	bi[++num].nxt=head[from];
	head[from]=num;
	bi[num].to=to;
	bi[num].f=f;
	bi[num].va=va;
}
void ADD(int from,int to,int f,int va)
{
	add(from,to,f,va);
	add(to,from,0,-va);
}
bool spfa()
{
	bj[S]=1;
	q.push(S);
	memset(dis,0xc0,sizeof(dis));
	dis[S]=0;
	int x,y;
	while(!q.empty())
	{
		x=q.front();q.pop();
		bj[x]=0;
		for(int i=head[x];i;i=bi[i].nxt)
			if(bi[i].f)
			{
				y=bi[i].to;
				if(dis[x]+bi[i].va>dis[y])
				{
					dis[y]=dis[x]+bi[i].va;
					from[y]=i;
					if(!bj[y])bj[y]=1,q.push(y);
				}
			}
	}
	return dis[T]>finf;
}
 
 
int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	//read("input");
	cin >> n;
	for (int i = 1; i <= n; i++) {
		cin >> rx[i] >> ry[i] >> rc[i]; 
		ADD(S,i,rc[i],0);
	} 
	for (int i = 1; i <= n; i++) {
		cin >> bx[i] >> by[i] >> bc[i]; 
		ADD(i+n,T,bc[i],0);
	}
	for (int i = 1; i <= n; i++) {
		ADD(i,2002,inf,rx[i]+ry[i]);
		ADD(i,2003,inf,rx[i]-ry[i]);
		ADD(i,2004,inf,-rx[i]+ry[i]);
		ADD(i,2005,inf,-rx[i]-ry[i]);
	}
	for (int i = 1; i <= n; i++) {
		ADD(2002,i+n,inf,-bx[i]-by[i]);
		ADD(2003,i+n,inf,-bx[i]+by[i]);
		ADD(2004,i+n,inf,bx[i]-by[i]);
		ADD(2005,i+n,inf,bx[i]+by[i]);
	}
	while(spfa()) {
		int x=T,flow=inf;
		while(x)flow=min(flow,bi[from[x]].f),x=bi[from[x]^1].to;
		ans+=1ll*flow*dis[T];
		x=T;
		while(x)bi[from[x]].f-=flow,bi[from[x]^1].f+=flow,x=bi[from[x]^1].to;
	}
	cout << ans << endl;
	return 0;
}
```