#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int M=2010,E=20005;
const ll inf=-1000000000000000000ll;
int n,m,et,s,z0,z1,z2,z3,t,x,y,z;
ll ans;
int fi[M],pv[M],pe[M],mw[M],in[M],qu[M],qh,qt;
ll d[M];
struct edge{int v,w1,w2,n;}e[E];
void add(int v,int u,int w1,int w2){
//	printf("%d %d %d %d\n",v,u,w1,w2);
	e[et]=(edge){u,w1,w2,fi[v]};fi[v]=et++;
	e[et]=(edge){v,0,-w2,fi[u]};fi[u]=et++;
}
void pau(){
	int tim=time(0)+2;
	while(time(0)<tim);
}
bool bfs(){
//	printf("\n\n\n");
	for(int i=1;i<=m;i++)d[i]=inf;
	d[s]=0;mw[s]=E;
	qu[1]=s;qh=1;qt=1;
	while(qh<=qt){
		int v=qu[(qh++)%M];
		in[v]=0;//printf("v=%d\n",v);
		for(int i=fi[v];i!=-1;i=e[i].n){
			int u=e[i].v;ll w=d[v]+e[i].w2;
//			printf("u=%d w=%lld i=%d\n",u,w,i);
//			pau();
			if(e[i].w1!=0&&w>d[u]){
				d [u]=w;
				pv[u]=v;
				pe[u]=i;
				mw[u]=min(mw[v],e[i].w1);
				if(in[u]==0){in[u]=1;qu[(++qt)%M]=u;}
			}
		}
	}
//	printf("m=%d\n",m);
//	for(int i=1;i<=m;i++)printf("%lld ",d[i]);printf("\n");
	return d[t]!=inf;
}
void upd(){
//	printf("\n\n\nFindPath\n\n");
	ll tw=0ll;int tm=mw[t];
	for(int i=t;i!=s;i=pv[i]){
//		printf("i=%d\n",i);
		tw+=e[pe[i]].w2;
		e[pe[i]  ].w1-=tm;
		e[pe[i]^1].w1+=tm;
	}
//	printf("tw=%lld tm=%d\n",tw,tm);
	ans+=tw*tm;
}
int main(){
//	freopen("3.in","r",stdin);
	memset(fi,-1,sizeof(fi));
	scanf("%d",&n);m=n<<1;
	s =++m;
	t =++m;
	z0=++m;
	z1=++m;
	z2=++m;
	z3=++m;
	for(int i=1;i<=n;i++){
		scanf("%d%d%d",&x,&y,&z);
		add(s,i ,z,   0);
		add(i,z0,E, x+y);
		add(i,z1,E, x-y);
		add(i,z2,E,-x+y);
		add(i,z3,E,-x-y);
	}
	for(int i=n+1;i<=n<<1;i++){
		scanf("%d%d%d",&x,&y,&z);
		add(i ,t,z,   0);
		add(z3,i,E, x+y);
		add(z2,i,E, x-y);
		add(z1,i,E,-x+y);
		add(z0,i,E,-x-y);
	}
	while(bfs())upd();
	printf("%lld",ans);
	return 0;
}
### Prompt

Please create a solution in cpp 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<bits/stdc++.h>
using namespace std;
#define ll long long
const int M=2010,E=20005;
const ll inf=-1000000000000000000ll;
int n,m,et,s,z0,z1,z2,z3,t,x,y,z;
ll ans;
int fi[M],pv[M],pe[M],mw[M],in[M],qu[M],qh,qt;
ll d[M];
struct edge{int v,w1,w2,n;}e[E];
void add(int v,int u,int w1,int w2){
//	printf("%d %d %d %d\n",v,u,w1,w2);
	e[et]=(edge){u,w1,w2,fi[v]};fi[v]=et++;
	e[et]=(edge){v,0,-w2,fi[u]};fi[u]=et++;
}
void pau(){
	int tim=time(0)+2;
	while(time(0)<tim);
}
bool bfs(){
//	printf("\n\n\n");
	for(int i=1;i<=m;i++)d[i]=inf;
	d[s]=0;mw[s]=E;
	qu[1]=s;qh=1;qt=1;
	while(qh<=qt){
		int v=qu[(qh++)%M];
		in[v]=0;//printf("v=%d\n",v);
		for(int i=fi[v];i!=-1;i=e[i].n){
			int u=e[i].v;ll w=d[v]+e[i].w2;
//			printf("u=%d w=%lld i=%d\n",u,w,i);
//			pau();
			if(e[i].w1!=0&&w>d[u]){
				d [u]=w;
				pv[u]=v;
				pe[u]=i;
				mw[u]=min(mw[v],e[i].w1);
				if(in[u]==0){in[u]=1;qu[(++qt)%M]=u;}
			}
		}
	}
//	printf("m=%d\n",m);
//	for(int i=1;i<=m;i++)printf("%lld ",d[i]);printf("\n");
	return d[t]!=inf;
}
void upd(){
//	printf("\n\n\nFindPath\n\n");
	ll tw=0ll;int tm=mw[t];
	for(int i=t;i!=s;i=pv[i]){
//		printf("i=%d\n",i);
		tw+=e[pe[i]].w2;
		e[pe[i]  ].w1-=tm;
		e[pe[i]^1].w1+=tm;
	}
//	printf("tw=%lld tm=%d\n",tw,tm);
	ans+=tw*tm;
}
int main(){
//	freopen("3.in","r",stdin);
	memset(fi,-1,sizeof(fi));
	scanf("%d",&n);m=n<<1;
	s =++m;
	t =++m;
	z0=++m;
	z1=++m;
	z2=++m;
	z3=++m;
	for(int i=1;i<=n;i++){
		scanf("%d%d%d",&x,&y,&z);
		add(s,i ,z,   0);
		add(i,z0,E, x+y);
		add(i,z1,E, x-y);
		add(i,z2,E,-x+y);
		add(i,z3,E,-x-y);
	}
	for(int i=n+1;i<=n<<1;i++){
		scanf("%d%d%d",&x,&y,&z);
		add(i ,t,z,   0);
		add(z3,i,E, x+y);
		add(z2,i,E, x-y);
		add(z1,i,E,-x+y);
		add(z0,i,E,-x-y);
	}
	while(bfs())upd();
	printf("%lld",ans);
	return 0;
}
```