#include<set>
#include<map>
#include<cmath>
#include<stack>
#include<queue>
#include<vector>
#include<cstdio>
#include<cstring>
#include<climits>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#define LL long long
using namespace std;
int read(){
	int f=0,x=0;char c=getchar();
	while(c<'0'||'9'<c){if(c=='-')f=1;c=getchar();}
	while('0'<=c&&c<='9') x=(x<<3)+(x<<1)+(c^48),c=getchar();
	return f?-x:x;
}
#define MAXN 5000
#define MAXM 100000
#define INF 0x3f3f3f3f
struct Edge{
	int nxt,v,cap,w;
}edge[MAXM+5];
int ncnt=-1,head[MAXN+5];
void Addedge(int u,int v,int cap,int w){
	edge[++ncnt]=(Edge){head[u],v,cap,w},head[u]=ncnt;
	edge[++ncnt]=(Edge){head[v],u,0,-w},head[v]=ncnt;
	return ;
}
int N,S,T;
bool vis[MAXN+5];
int cur[MAXN+5];
LL dep[MAXN+5];
bool BFS(){
	queue<int> Q;
	for(int i=0;i<=N;i++)
		vis[i]=0,dep[i]=1ll*10000*INF;
	dep[S]=0,vis[S]=1,Q.push(S);
	while(!Q.empty()){
		int u=Q.front();Q.pop();
		vis[u]=0;
		for(int i=head[u];~i;i=edge[i].nxt){
			int v=edge[i].v,cap=edge[i].cap,w=edge[i].w;
			if(cap&&dep[v]>dep[u]+w){
				dep[v]=dep[u]+w;
				if(!vis[v])
					vis[v]=1,Q.push(v);
			}
		}
	}
	return dep[T]<1ll*10000*INF;
}
LL cost;
int DFS(int u,int aug){
	if(u==T) return aug;
	vis[u]=1;
	int flow=0,f;
	for(int i=cur[u];i!=-1;i=edge[i].nxt){
		cur[u]=i;
		int v=edge[i].v,cap=edge[i].cap,w=edge[i].w;
		if(!vis[v]&&dep[v]==dep[u]+w&&cap&&(f=DFS(v,min(cap,aug)))){
			aug-=f,flow+=f,cost+=1ll*f*w;
			edge[i].cap-=f,edge[i^1].cap+=f;
			if(!aug) break;
		}
	}
	vis[u]=0;
	return flow;
}
#define Flow 0x3f3f3f3f
void Dinic(){
	//int Max_Flow=0;
	while(BFS())
		memcpy(cur,head,sizeof(head)),DFS(S,Flow);
	return ;
}
int main(){
	memset(head,-1,sizeof(head));
	int n=read();
	N=2*n+6,S=2*n+1,T=2*n+2;
	int n1=2*n+3,n2=2*n+4,n3=2*n+5,n4=2*n+6;
	for(int i=1;i<=n;i++){
		int x=read(),y=read(),c=read();
		Addedge(S,i,c,0);
		Addedge(i,n1,INF,-x-y);
		Addedge(i,n2,INF,-x+y);
		Addedge(i,n3,INF,x-y);
		Addedge(i,n4,INF,x+y);
	}
	for(int i=1;i<=n;i++){
		int x=read(),y=read(),c=read();
		Addedge(n+i,T,c,0);
		Addedge(n1,n+i,INF,x+y);
		Addedge(n2,n+i,INF,x-y);
		Addedge(n3,n+i,INF,-x+y);
		Addedge(n4,n+i,INF,-x-y);
	}
	Dinic();
	printf("%lld\n",-cost);
    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<set>
#include<map>
#include<cmath>
#include<stack>
#include<queue>
#include<vector>
#include<cstdio>
#include<cstring>
#include<climits>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#define LL long long
using namespace std;
int read(){
	int f=0,x=0;char c=getchar();
	while(c<'0'||'9'<c){if(c=='-')f=1;c=getchar();}
	while('0'<=c&&c<='9') x=(x<<3)+(x<<1)+(c^48),c=getchar();
	return f?-x:x;
}
#define MAXN 5000
#define MAXM 100000
#define INF 0x3f3f3f3f
struct Edge{
	int nxt,v,cap,w;
}edge[MAXM+5];
int ncnt=-1,head[MAXN+5];
void Addedge(int u,int v,int cap,int w){
	edge[++ncnt]=(Edge){head[u],v,cap,w},head[u]=ncnt;
	edge[++ncnt]=(Edge){head[v],u,0,-w},head[v]=ncnt;
	return ;
}
int N,S,T;
bool vis[MAXN+5];
int cur[MAXN+5];
LL dep[MAXN+5];
bool BFS(){
	queue<int> Q;
	for(int i=0;i<=N;i++)
		vis[i]=0,dep[i]=1ll*10000*INF;
	dep[S]=0,vis[S]=1,Q.push(S);
	while(!Q.empty()){
		int u=Q.front();Q.pop();
		vis[u]=0;
		for(int i=head[u];~i;i=edge[i].nxt){
			int v=edge[i].v,cap=edge[i].cap,w=edge[i].w;
			if(cap&&dep[v]>dep[u]+w){
				dep[v]=dep[u]+w;
				if(!vis[v])
					vis[v]=1,Q.push(v);
			}
		}
	}
	return dep[T]<1ll*10000*INF;
}
LL cost;
int DFS(int u,int aug){
	if(u==T) return aug;
	vis[u]=1;
	int flow=0,f;
	for(int i=cur[u];i!=-1;i=edge[i].nxt){
		cur[u]=i;
		int v=edge[i].v,cap=edge[i].cap,w=edge[i].w;
		if(!vis[v]&&dep[v]==dep[u]+w&&cap&&(f=DFS(v,min(cap,aug)))){
			aug-=f,flow+=f,cost+=1ll*f*w;
			edge[i].cap-=f,edge[i^1].cap+=f;
			if(!aug) break;
		}
	}
	vis[u]=0;
	return flow;
}
#define Flow 0x3f3f3f3f
void Dinic(){
	//int Max_Flow=0;
	while(BFS())
		memcpy(cur,head,sizeof(head)),DFS(S,Flow);
	return ;
}
int main(){
	memset(head,-1,sizeof(head));
	int n=read();
	N=2*n+6,S=2*n+1,T=2*n+2;
	int n1=2*n+3,n2=2*n+4,n3=2*n+5,n4=2*n+6;
	for(int i=1;i<=n;i++){
		int x=read(),y=read(),c=read();
		Addedge(S,i,c,0);
		Addedge(i,n1,INF,-x-y);
		Addedge(i,n2,INF,-x+y);
		Addedge(i,n3,INF,x-y);
		Addedge(i,n4,INF,x+y);
	}
	for(int i=1;i<=n;i++){
		int x=read(),y=read(),c=read();
		Addedge(n+i,T,c,0);
		Addedge(n1,n+i,INF,x+y);
		Addedge(n2,n+i,INF,x-y);
		Addedge(n3,n+i,INF,-x+y);
		Addedge(n4,n+i,INF,-x-y);
	}
	Dinic();
	printf("%lld\n",-cost);
    return 0;
}
```