#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>

int N;
int X[2050],Y[2050],C[2050];

struct edge{int to,nxt,flow;long long cost;}E[50050];
int H[4050],tot=1;
void add_edge(int a,int b,int f,long long c){
	E[++tot]=(edge){b,H[a],f,c},H[a]=tot;
	E[++tot]=(edge){a,H[b],0,-c},H[b]=tot;
}

int S,T,M0,M1,M2,M3;
const int inf=0x3f3f3f3f;
const long long dinf=0xcfcfcfcfcfcfcfcf;

long long dis[4050];
int lst[4050],fl[4050];
bool inQ[4050];

bool SPFA(){
	memset(dis,0xcf,sizeof(long long)*(M3+1));
	memset(inQ,0,sizeof(bool)*(M3+1));
	memset(lst,0,sizeof(int)*(M3+1));
	dis[S]=0,fl[S]=inf;
	std::queue<int> Q;
	Q.push(S);
	while (!Q.empty()){
		int now=Q.front();
		Q.pop();
		for (int i=H[now];i;i=E[i].nxt){
			if (E[i].flow&&dis[now]+E[i].cost>dis[E[i].to]){
				dis[E[i].to]=dis[now]+E[i].cost;
				if (!inQ[E[i].to]) inQ[E[i].to]=true,Q.push(E[i].to);
				lst[E[i].to]=i,fl[E[i].to]=std::min(fl[now],E[i].flow);
			}
		}
		inQ[now]=false;
	}
	return dis[T]!=dinf;
};

long long EK(){
	long long ret=0;
	while (SPFA()){
		ret+=fl[T]*dis[T];
		for (int i=lst[T];i;i=lst[E[i^1].to]) E[i].flow-=fl[T],E[i^1].flow+=fl[T];
	}
	return ret;
}

int main(){
	scanf("%d",&N);
	for (int i=1;i<=N+N;i++) scanf("%d%d%d",&X[i],&Y[i],&C[i]);
	S=N+N+1,T=S+1,M0=T+1,M1=M0+1,M2=M1+1,M3=M2+1;

	for (int i=1;i<=N;i++) add_edge(S,i,C[i],0);
	for (int i=N+1;i<=N+N;i++) add_edge(i,T,C[i],0);

	for (int i=1;i<=N;i++) add_edge(i,M0,inf,X[i]+Y[i]),add_edge(M0,i+N,inf,-X[i+N]-Y[i+N]);
	for (int i=1;i<=N;i++) add_edge(i,M1,inf,X[i]-Y[i]),add_edge(M1,i+N,inf,-X[i+N]+Y[i+N]);
	for (int i=1;i<=N;i++) add_edge(i,M2,inf,-X[i]+Y[i]),add_edge(M2,i+N,inf,X[i+N]-Y[i+N]);
	for (int i=1;i<=N;i++) add_edge(i,M3,inf,-X[i]-Y[i]),add_edge(M3,i+N,inf,X[i+N]+Y[i+N]);

	printf("%lld\n",EK());
}

### Prompt

Please formulate a cpp solution to 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<iostream>
#include<cstdio>
#include<cstring>
#include<queue>

int N;
int X[2050],Y[2050],C[2050];

struct edge{int to,nxt,flow;long long cost;}E[50050];
int H[4050],tot=1;
void add_edge(int a,int b,int f,long long c){
	E[++tot]=(edge){b,H[a],f,c},H[a]=tot;
	E[++tot]=(edge){a,H[b],0,-c},H[b]=tot;
}

int S,T,M0,M1,M2,M3;
const int inf=0x3f3f3f3f;
const long long dinf=0xcfcfcfcfcfcfcfcf;

long long dis[4050];
int lst[4050],fl[4050];
bool inQ[4050];

bool SPFA(){
	memset(dis,0xcf,sizeof(long long)*(M3+1));
	memset(inQ,0,sizeof(bool)*(M3+1));
	memset(lst,0,sizeof(int)*(M3+1));
	dis[S]=0,fl[S]=inf;
	std::queue<int> Q;
	Q.push(S);
	while (!Q.empty()){
		int now=Q.front();
		Q.pop();
		for (int i=H[now];i;i=E[i].nxt){
			if (E[i].flow&&dis[now]+E[i].cost>dis[E[i].to]){
				dis[E[i].to]=dis[now]+E[i].cost;
				if (!inQ[E[i].to]) inQ[E[i].to]=true,Q.push(E[i].to);
				lst[E[i].to]=i,fl[E[i].to]=std::min(fl[now],E[i].flow);
			}
		}
		inQ[now]=false;
	}
	return dis[T]!=dinf;
};

long long EK(){
	long long ret=0;
	while (SPFA()){
		ret+=fl[T]*dis[T];
		for (int i=lst[T];i;i=lst[E[i^1].to]) E[i].flow-=fl[T],E[i^1].flow+=fl[T];
	}
	return ret;
}

int main(){
	scanf("%d",&N);
	for (int i=1;i<=N+N;i++) scanf("%d%d%d",&X[i],&Y[i],&C[i]);
	S=N+N+1,T=S+1,M0=T+1,M1=M0+1,M2=M1+1,M3=M2+1;

	for (int i=1;i<=N;i++) add_edge(S,i,C[i],0);
	for (int i=N+1;i<=N+N;i++) add_edge(i,T,C[i],0);

	for (int i=1;i<=N;i++) add_edge(i,M0,inf,X[i]+Y[i]),add_edge(M0,i+N,inf,-X[i+N]-Y[i+N]);
	for (int i=1;i<=N;i++) add_edge(i,M1,inf,X[i]-Y[i]),add_edge(M1,i+N,inf,-X[i+N]+Y[i+N]);
	for (int i=1;i<=N;i++) add_edge(i,M2,inf,-X[i]+Y[i]),add_edge(M2,i+N,inf,X[i+N]-Y[i+N]);
	for (int i=1;i<=N;i++) add_edge(i,M3,inf,-X[i]-Y[i]),add_edge(M3,i+N,inf,X[i+N]+Y[i+N]);

	printf("%lld\n",EK());
}

```