#include<bits/stdc++.h>
using namespace std;
const int N=1e5+7,inf=1e9+7; bool fl[N];
int n,s,t,cnt,tot,ch[4],f[N],pre[N],que[N<<2];
long long sum,dis[N];
struct edge{int u,v,t,q,s;}ed[N<<1];
inline int read(){
	int num=0; char g=getchar(); while(g<48||57<g) g=getchar();
	while(47<g&&g<58) num=(num<<1)+(num<<3)+g-48,g=getchar(); return num;
}
inline void add(int a,int b,int c,int d){
	tot++,ed[tot].u=a,ed[tot].v=b,ed[tot].t=c,ed[tot].q=d,ed[tot].s=f[a],f[a]=tot;
}
inline void addedge(int a,int b,int c,int d){
	add(a,b,c,d),add(b,a,0,-d);
}
inline void flows(){
	for(int i=1;i<=cnt;i++) dis[i]=0;
	int head=1,tail=1; que[head]=s; dis[s]=1e18;
	while(head<=tail){
		int x=que[head++]; fl[x]=0;
		for(int i=f[x];i>0;i=ed[i].s){
			if(!ed[i].t) continue;
			int u=ed[i].v;
			if(dis[u]<dis[x]+ed[i].q){
				dis[u]=dis[x]+ed[i].q,pre[u]=i;
				if(!fl[u]) fl[u]=1,que[++tail]=u;
			}
		}
	}
	
	int z=inf,u=t; if(!dis[u]) return; long long xs=0;
	while(u!=s) z=min(z,ed[pre[u]].t),xs=xs+ed[pre[u]].q,u=ed[pre[u]].u; sum=sum+xs*z,u=t;
	while(u!=s) ed[pre[u]].t-=z,ed[pre[u]^1].t+=z,u=ed[pre[u]].u;
}
int main(){
	n=read(),s=++cnt,t=++cnt,ch[0]=++cnt,ch[1]=++cnt,ch[2]=++cnt,ch[3]=++cnt,tot=1;
	for(int i=1;i<=n;i++){
		int x=read(),y=read(),c=read(),q=++cnt;
		addedge(s,q,c,0);
		for(int z=0;z<4;z++){
			int h=0; if(z&1) h=h+x; else h=h-x; if(z&2) h=h+y; else h=h-y; 
			addedge(q,ch[z],inf,h);
		}
	}
	for(int i=1;i<=n;i++){
		int x=read(),y=read(),c=read(),q=++cnt;
		addedge(q,t,c,0);
		for(int z=0;z<4;z++){
			int h=0; if(z&1) h=h-x; else h=h+x; if(z&2) h=h-y; else h=h+y; 
			addedge(ch[z],q,inf,h);
		}
	}
	dis[t]=1; while(dis[t]) flows(); cout<<sum<<endl;
    return 0;
}
### Prompt

In Cpp, your task is to solve 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;
const int N=1e5+7,inf=1e9+7; bool fl[N];
int n,s,t,cnt,tot,ch[4],f[N],pre[N],que[N<<2];
long long sum,dis[N];
struct edge{int u,v,t,q,s;}ed[N<<1];
inline int read(){
	int num=0; char g=getchar(); while(g<48||57<g) g=getchar();
	while(47<g&&g<58) num=(num<<1)+(num<<3)+g-48,g=getchar(); return num;
}
inline void add(int a,int b,int c,int d){
	tot++,ed[tot].u=a,ed[tot].v=b,ed[tot].t=c,ed[tot].q=d,ed[tot].s=f[a],f[a]=tot;
}
inline void addedge(int a,int b,int c,int d){
	add(a,b,c,d),add(b,a,0,-d);
}
inline void flows(){
	for(int i=1;i<=cnt;i++) dis[i]=0;
	int head=1,tail=1; que[head]=s; dis[s]=1e18;
	while(head<=tail){
		int x=que[head++]; fl[x]=0;
		for(int i=f[x];i>0;i=ed[i].s){
			if(!ed[i].t) continue;
			int u=ed[i].v;
			if(dis[u]<dis[x]+ed[i].q){
				dis[u]=dis[x]+ed[i].q,pre[u]=i;
				if(!fl[u]) fl[u]=1,que[++tail]=u;
			}
		}
	}
	
	int z=inf,u=t; if(!dis[u]) return; long long xs=0;
	while(u!=s) z=min(z,ed[pre[u]].t),xs=xs+ed[pre[u]].q,u=ed[pre[u]].u; sum=sum+xs*z,u=t;
	while(u!=s) ed[pre[u]].t-=z,ed[pre[u]^1].t+=z,u=ed[pre[u]].u;
}
int main(){
	n=read(),s=++cnt,t=++cnt,ch[0]=++cnt,ch[1]=++cnt,ch[2]=++cnt,ch[3]=++cnt,tot=1;
	for(int i=1;i<=n;i++){
		int x=read(),y=read(),c=read(),q=++cnt;
		addedge(s,q,c,0);
		for(int z=0;z<4;z++){
			int h=0; if(z&1) h=h+x; else h=h-x; if(z&2) h=h+y; else h=h-y; 
			addedge(q,ch[z],inf,h);
		}
	}
	for(int i=1;i<=n;i++){
		int x=read(),y=read(),c=read(),q=++cnt;
		addedge(q,t,c,0);
		for(int z=0;z<4;z++){
			int h=0; if(z&1) h=h-x; else h=h+x; if(z&2) h=h-y; else h=h+y; 
			addedge(ch[z],q,inf,h);
		}
	}
	dis[t]=1; while(dis[t]) flows(); cout<<sum<<endl;
    return 0;
}
```