#include<algorithm>
#include<cstring>
#include<cctype>
#include<cstdio>
#define rep(i,x,y) for(int i=x; i<=y; ++i)

using namespace std;
const int N=2050,INF=1000000000;
typedef long long LL;
bool vis[N];
int n,h[N],cnt,q[10000000],from[N],s,t,head,tail;
LL ans,dis[N];
struct edge{int v,f,n; LL c;} e[N*20];

int getint()
{
	char ch;
	while(!isdigit(ch=getchar()));
	int x=ch-48;
	while(isdigit(ch=getchar())) x=x*10+ch-48;
	return x;
}

void addedge(int u,int v,int f,int c)
{
	e[cnt]=(edge){v,f,h[u],c},h[u]=cnt++;
	e[cnt]=(edge){u,0,h[v],-c},h[v]=cnt++;
}

bool spfa()
{
    rep(i,1,t) dis[i]=-1000000000000000ll,from[i]=-1;
   q[dis[s]=head=tail=0]=s,vis[s]=1;
    while(head<=tail)
    {
        int u=q[head++];
        for(int i=h[u],v; i!=-1; i=e[i].n)
            if(e[i].f>0 && dis[v=e[i].v]<dis[u]+e[i].c)
                if(dis[v]=dis[u]+e[i].c,from[v]=i,!vis[v])
                    vis[q[++tail]=v]=1;
        vis[u]=0;
    }
    return dis[t]!=-1000000000000000ll;
}

void mcf()
{
    int i=from[t],x=INF;
    while(i!=-1)
    {
        x=min(x,e[i].f);
        i=from[e[i^1].v];
    }
    i=from[t];
    ans+=x*dis[t];
    while(i!=-1)
    {
        e[i].f-=x,e[i^1].f+=x;
        i=from[e[i^1].v];
    }
}
 

int main()
{
	n=getint();
	memset(h,-1,sizeof(h));
	s=n*2+8+1,t=s+1;
	rep(i,1,n)
	{
		int x=getint(),y=getint(),c=getint();
		addedge(s,i,c,0);
		addedge(i,2*n+1,INF,x+y);
		addedge(i,2*n+2,INF,x-y);
		addedge(i,2*n+3,INF,-x+y);
		addedge(i,2*n+4,INF,-x-y);
	}
	
	rep(i,1,n)
	{
		int x=getint(),y=getint(),c=getint();
		addedge(i+n,t,c,0);
		addedge(2*n+5,i+n,INF,x+y);
		addedge(2*n+6,i+n,INF,x-y);
		addedge(2*n+7,i+n,INF,-x+y);
		addedge(2*n+8,i+n,INF,-x-y);
	}

	addedge(2*n+1,2*n+8,INF,0);
	addedge(2*n+2,2*n+7,INF,0);
	addedge(2*n+3,2*n+6,INF,0);
	addedge(2*n+4,2*n+5,INF,0);
	
	while(spfa())
		mcf();
	printf("%lld\n",ans);
	return 0;
}
### Prompt

Your task is to create 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<algorithm>
#include<cstring>
#include<cctype>
#include<cstdio>
#define rep(i,x,y) for(int i=x; i<=y; ++i)

using namespace std;
const int N=2050,INF=1000000000;
typedef long long LL;
bool vis[N];
int n,h[N],cnt,q[10000000],from[N],s,t,head,tail;
LL ans,dis[N];
struct edge{int v,f,n; LL c;} e[N*20];

int getint()
{
	char ch;
	while(!isdigit(ch=getchar()));
	int x=ch-48;
	while(isdigit(ch=getchar())) x=x*10+ch-48;
	return x;
}

void addedge(int u,int v,int f,int c)
{
	e[cnt]=(edge){v,f,h[u],c},h[u]=cnt++;
	e[cnt]=(edge){u,0,h[v],-c},h[v]=cnt++;
}

bool spfa()
{
    rep(i,1,t) dis[i]=-1000000000000000ll,from[i]=-1;
   q[dis[s]=head=tail=0]=s,vis[s]=1;
    while(head<=tail)
    {
        int u=q[head++];
        for(int i=h[u],v; i!=-1; i=e[i].n)
            if(e[i].f>0 && dis[v=e[i].v]<dis[u]+e[i].c)
                if(dis[v]=dis[u]+e[i].c,from[v]=i,!vis[v])
                    vis[q[++tail]=v]=1;
        vis[u]=0;
    }
    return dis[t]!=-1000000000000000ll;
}

void mcf()
{
    int i=from[t],x=INF;
    while(i!=-1)
    {
        x=min(x,e[i].f);
        i=from[e[i^1].v];
    }
    i=from[t];
    ans+=x*dis[t];
    while(i!=-1)
    {
        e[i].f-=x,e[i^1].f+=x;
        i=from[e[i^1].v];
    }
}
 

int main()
{
	n=getint();
	memset(h,-1,sizeof(h));
	s=n*2+8+1,t=s+1;
	rep(i,1,n)
	{
		int x=getint(),y=getint(),c=getint();
		addedge(s,i,c,0);
		addedge(i,2*n+1,INF,x+y);
		addedge(i,2*n+2,INF,x-y);
		addedge(i,2*n+3,INF,-x+y);
		addedge(i,2*n+4,INF,-x-y);
	}
	
	rep(i,1,n)
	{
		int x=getint(),y=getint(),c=getint();
		addedge(i+n,t,c,0);
		addedge(2*n+5,i+n,INF,x+y);
		addedge(2*n+6,i+n,INF,x-y);
		addedge(2*n+7,i+n,INF,-x+y);
		addedge(2*n+8,i+n,INF,-x-y);
	}

	addedge(2*n+1,2*n+8,INF,0);
	addedge(2*n+2,2*n+7,INF,0);
	addedge(2*n+3,2*n+6,INF,0);
	addedge(2*n+4,2*n+5,INF,0);
	
	while(spfa())
		mcf();
	printf("%lld\n",ans);
	return 0;
}
```