#include<set>
#include<map>
#include<queue>
#include<cmath>
#include<string>
#include<cstdio>
#include<vector>
#include<cstring>
#include<iomanip>
#include<iostream>
#include<algorithm>
#define rep(i,a,b) for (int i=a; i<=b; i++)
#define per(i,a,b) for (int i=a; i>=b; i--)
using namespace std;

const int maxn=3010, maxm=2022000;
const long long inf=9999999999;
typedef long long LL;

struct Edge{
	Edge(){};
	Edge(int a,int b,LL c,int d){v=a;f=b;w=c;nxt=d;};
	int v,f,nxt;
	LL w;
};

int n,lmt;
int g[maxn+10];
Edge e[maxm+10];
int nume;
int src,sink;

void addedge(int u,int v,int c,LL w){
	e[++nume]=Edge(v,c,w,g[u]);
	g[u]=nume;
	e[++nume]=Edge(u,0,-w,g[v]);
	g[v]=nume;
}

queue<int> que;
bool inQue[maxn+10];
LL dist[maxn+10];
int pren[maxn+10];
int pree[maxn+10];

bool findPath(){
	while(!que.empty())que.pop();
	que.push(src);
	memset(dist,0x3f,sizeof(dist));
	dist[src]=0;inQue[src]=true;
	while(!que.empty()){
		int u=que.front();
		//cout<<u<<endl;
		que.pop();
		for(int i=g[u];i;i=e[i].nxt){
			if((e[i].f>0) && (dist[u]+e[i].w<dist[e[i].v])){
				dist[e[i].v]=dist[u]+e[i].w;
				pren[e[i].v]=u;pree[e[i].v]=i;
				if(!inQue[e[i].v]){
					inQue[e[i].v]=true;
					que.push(e[i].v);
				}
			}
		}
		inQue[u]=false;
	}
	if(dist[sink]<dist[3001])return true;
	return false;
}

LL augment(){
	int u=sink;
	LL delta=inf;
	while(u!=src){
		if(e[pree[u]].f<delta)delta=e[pree[u]].f;
		u=pren[u];
	}
	u=sink;
	while(u!=src){
		e[pree[u]].f-=delta;
		e[pree[u]^1].f+=delta;
		u=pren[u];
	}
	return dist[sink]*delta;
}

LL mincostflow(){
	LL cur=0;
	while(findPath()){
		cur+=augment();
		//rep(i,1,2*n+1)cout<<i<<" "<<dist[i]<<endl;
	}
	return cur;
}

LL RX[1010],RY[1010],BX[1010],BY[1010];
int RC[1010],BC[1010];
int A,B,C,D;
int main() {
	std::ios::sync_with_stdio(false);
	//freopen("ttt.txt","r",stdin);
	cin>>n;
	rep(i,1,n)cin>>RX[i]>>RY[i]>>RC[i];
	rep(i,1,n)cin>>BX[i]>>BY[i]>>BC[i];
	sink=1;src=0;nume=1;

	memset(g,0,sizeof(g));
	rep(i,1,n)addedge(0,i+1,RC[i],0);
	rep(i,1,n)addedge(i+n+1,1,BC[i],0);
	A=2*n+2;B=A+1;C=B+1;D=C+1;
	rep(i,1,n){
		addedge(i+1,A,10,RX[i]+RY[i]);
		addedge(i+1,B,10,RX[i]-RY[i]);
		addedge(i+1,C,10,-RX[i]+RY[i]);
		addedge(i+1,D,10,-RX[i]-RY[i]);
	}
	rep(i,1,n){
		addedge(A,i+n+1,10,-BX[i]-BY[i]);
		addedge(B,i+n+1,10,-BX[i]+BY[i]);
		addedge(C,i+n+1,10,BX[i]-BY[i]);
		addedge(D,i+n+1,10,BX[i]+BY[i]);
	}
	
	//cout<<"prep"<<endl;
	cout<<-mincostflow()<<endl;
	return 0;
}
### Prompt

Create a solution in Cpp for the following problem:

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<set>
#include<map>
#include<queue>
#include<cmath>
#include<string>
#include<cstdio>
#include<vector>
#include<cstring>
#include<iomanip>
#include<iostream>
#include<algorithm>
#define rep(i,a,b) for (int i=a; i<=b; i++)
#define per(i,a,b) for (int i=a; i>=b; i--)
using namespace std;

const int maxn=3010, maxm=2022000;
const long long inf=9999999999;
typedef long long LL;

struct Edge{
	Edge(){};
	Edge(int a,int b,LL c,int d){v=a;f=b;w=c;nxt=d;};
	int v,f,nxt;
	LL w;
};

int n,lmt;
int g[maxn+10];
Edge e[maxm+10];
int nume;
int src,sink;

void addedge(int u,int v,int c,LL w){
	e[++nume]=Edge(v,c,w,g[u]);
	g[u]=nume;
	e[++nume]=Edge(u,0,-w,g[v]);
	g[v]=nume;
}

queue<int> que;
bool inQue[maxn+10];
LL dist[maxn+10];
int pren[maxn+10];
int pree[maxn+10];

bool findPath(){
	while(!que.empty())que.pop();
	que.push(src);
	memset(dist,0x3f,sizeof(dist));
	dist[src]=0;inQue[src]=true;
	while(!que.empty()){
		int u=que.front();
		//cout<<u<<endl;
		que.pop();
		for(int i=g[u];i;i=e[i].nxt){
			if((e[i].f>0) && (dist[u]+e[i].w<dist[e[i].v])){
				dist[e[i].v]=dist[u]+e[i].w;
				pren[e[i].v]=u;pree[e[i].v]=i;
				if(!inQue[e[i].v]){
					inQue[e[i].v]=true;
					que.push(e[i].v);
				}
			}
		}
		inQue[u]=false;
	}
	if(dist[sink]<dist[3001])return true;
	return false;
}

LL augment(){
	int u=sink;
	LL delta=inf;
	while(u!=src){
		if(e[pree[u]].f<delta)delta=e[pree[u]].f;
		u=pren[u];
	}
	u=sink;
	while(u!=src){
		e[pree[u]].f-=delta;
		e[pree[u]^1].f+=delta;
		u=pren[u];
	}
	return dist[sink]*delta;
}

LL mincostflow(){
	LL cur=0;
	while(findPath()){
		cur+=augment();
		//rep(i,1,2*n+1)cout<<i<<" "<<dist[i]<<endl;
	}
	return cur;
}

LL RX[1010],RY[1010],BX[1010],BY[1010];
int RC[1010],BC[1010];
int A,B,C,D;
int main() {
	std::ios::sync_with_stdio(false);
	//freopen("ttt.txt","r",stdin);
	cin>>n;
	rep(i,1,n)cin>>RX[i]>>RY[i]>>RC[i];
	rep(i,1,n)cin>>BX[i]>>BY[i]>>BC[i];
	sink=1;src=0;nume=1;

	memset(g,0,sizeof(g));
	rep(i,1,n)addedge(0,i+1,RC[i],0);
	rep(i,1,n)addedge(i+n+1,1,BC[i],0);
	A=2*n+2;B=A+1;C=B+1;D=C+1;
	rep(i,1,n){
		addedge(i+1,A,10,RX[i]+RY[i]);
		addedge(i+1,B,10,RX[i]-RY[i]);
		addedge(i+1,C,10,-RX[i]+RY[i]);
		addedge(i+1,D,10,-RX[i]-RY[i]);
	}
	rep(i,1,n){
		addedge(A,i+n+1,10,-BX[i]-BY[i]);
		addedge(B,i+n+1,10,-BX[i]+BY[i]);
		addedge(C,i+n+1,10,BX[i]-BY[i]);
		addedge(D,i+n+1,10,BX[i]+BY[i]);
	}
	
	//cout<<"prep"<<endl;
	cout<<-mincostflow()<<endl;
	return 0;
}
```