#include<bits/stdc++.h>
using namespace std;

const int MAXN=2100+5,MAXM=50000+10;
const long long int INF = 1e18;
bool visit[MAXN],inqueue[MAXN];
long long int head[MAXN],dist[MAXN],parent[MAXN],stamp;
long long int maxflow,mincost;
//parent indicates the index of the in-edge
queue<long long int> q;
struct EDGE{
   long long int to,r,cost,next;
}edge[MAXM*2];
long long int SPFA(int s,int t){
   for(int i=0;i<MAXN;i++)
      dist[i]=INF;
   memset(inqueue,0,sizeof inqueue);
   while(!q.empty()) q.pop();
   dist[s]=0;inqueue[s]=true;q.push(s);
   while(!q.empty()){
      long long int now=q.front();q.pop();inqueue[now]=false;
      for(long long int i=head[now];i!=-1;i=edge[i].next){
         if(edge[i].r>0){
            long long int next=edge[i].to;
            long long int cost=edge[i].cost;
            if(dist[next]>dist[now]+cost){
               parent[next]=i;
               dist[next]=dist[now]+cost;
               if(!inqueue[next]){
                  inqueue[next]=true;
                  q.push(next);
               }
            }
         }
      }
   }
   return dist[t];
}
void addedge(int a,int b,long long int r,long long int cost){
   edge[stamp]={b,r,cost,head[a]};
   head[a]=stamp++;
   edge[stamp]={a,0,-cost,head[b]};
   head[b]=stamp++;
}
void init(){
   stamp=maxflow=mincost=0;
   memset(head,-1,sizeof head);
}
void Minimum_Cost_Flow(int s,int t){
   while(SPFA(s,t)!=INF){
      long long int flow=INF,cost=0;
      long long int tmpnode=t;
      while(tmpnode!=s){
         flow=min(flow,edge[parent[tmpnode]].r);
         cost+=edge[parent[tmpnode]].cost;
         tmpnode=edge[parent[tmpnode]^1].to;
      }
      maxflow+=flow;
      mincost+=flow*cost;
      tmpnode=t;
      while(tmpnode!=s){
         edge[parent[tmpnode]].r-=flow;
         edge[parent[tmpnode]^1].r+=flow;
         tmpnode=edge[parent[tmpnode]^1].to;
      }
   }
}



int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	init();
	int n;
	cin>>n;
	long long int x,y,c;
	for(int i=1;i<=n;i++){
		cin>>x>>y>>c;
		addedge(2005,i,c,0);
		addedge(i,2001,INF,-(x+y));
		addedge(i,2002,INF,x-y);
		addedge(i,2003,INF,y-x);
		addedge(i,2004,INF,x+y);
	}
	for(int i=1;i<=n;i++){
		cin>>x>>y>>c;
		addedge(i+1000,2006,c,0);
		addedge(2001,i+1000,INF,(x+y));
		addedge(2002,i+1000,INF,y-x);
		addedge(2003,i+1000,INF,x-y);
		addedge(2004,i+1000,INF,-(x+y));
	}
	Minimum_Cost_Flow(2005,2006);
	cout<<-mincost<<endl;
}

### Prompt

Generate 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<bits/stdc++.h>
using namespace std;

const int MAXN=2100+5,MAXM=50000+10;
const long long int INF = 1e18;
bool visit[MAXN],inqueue[MAXN];
long long int head[MAXN],dist[MAXN],parent[MAXN],stamp;
long long int maxflow,mincost;
//parent indicates the index of the in-edge
queue<long long int> q;
struct EDGE{
   long long int to,r,cost,next;
}edge[MAXM*2];
long long int SPFA(int s,int t){
   for(int i=0;i<MAXN;i++)
      dist[i]=INF;
   memset(inqueue,0,sizeof inqueue);
   while(!q.empty()) q.pop();
   dist[s]=0;inqueue[s]=true;q.push(s);
   while(!q.empty()){
      long long int now=q.front();q.pop();inqueue[now]=false;
      for(long long int i=head[now];i!=-1;i=edge[i].next){
         if(edge[i].r>0){
            long long int next=edge[i].to;
            long long int cost=edge[i].cost;
            if(dist[next]>dist[now]+cost){
               parent[next]=i;
               dist[next]=dist[now]+cost;
               if(!inqueue[next]){
                  inqueue[next]=true;
                  q.push(next);
               }
            }
         }
      }
   }
   return dist[t];
}
void addedge(int a,int b,long long int r,long long int cost){
   edge[stamp]={b,r,cost,head[a]};
   head[a]=stamp++;
   edge[stamp]={a,0,-cost,head[b]};
   head[b]=stamp++;
}
void init(){
   stamp=maxflow=mincost=0;
   memset(head,-1,sizeof head);
}
void Minimum_Cost_Flow(int s,int t){
   while(SPFA(s,t)!=INF){
      long long int flow=INF,cost=0;
      long long int tmpnode=t;
      while(tmpnode!=s){
         flow=min(flow,edge[parent[tmpnode]].r);
         cost+=edge[parent[tmpnode]].cost;
         tmpnode=edge[parent[tmpnode]^1].to;
      }
      maxflow+=flow;
      mincost+=flow*cost;
      tmpnode=t;
      while(tmpnode!=s){
         edge[parent[tmpnode]].r-=flow;
         edge[parent[tmpnode]^1].r+=flow;
         tmpnode=edge[parent[tmpnode]^1].to;
      }
   }
}



int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	init();
	int n;
	cin>>n;
	long long int x,y,c;
	for(int i=1;i<=n;i++){
		cin>>x>>y>>c;
		addedge(2005,i,c,0);
		addedge(i,2001,INF,-(x+y));
		addedge(i,2002,INF,x-y);
		addedge(i,2003,INF,y-x);
		addedge(i,2004,INF,x+y);
	}
	for(int i=1;i<=n;i++){
		cin>>x>>y>>c;
		addedge(i+1000,2006,c,0);
		addedge(2001,i+1000,INF,(x+y));
		addedge(2002,i+1000,INF,y-x);
		addedge(2003,i+1000,INF,x-y);
		addedge(2004,i+1000,INF,-(x+y));
	}
	Minimum_Cost_Flow(2005,2006);
	cout<<-mincost<<endl;
}

```