#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int Maxn=1005;
int rx[Maxn],ry[Maxn],rc[Maxn];
int bx[Maxn],by[Maxn],bc[Maxn];
int dx[]={1,1,-1,-1},dy[]={1,-1,1,-1};
namespace mcmf{
    const int MAXN=2*Maxn,MAXM=10*Maxn;
    struct node{int to,next,v,k,pair;}e[MAXM*2];
    int h[MAXN],cur[MAXN],Instack[MAXN],cnt,S,T;
    ll dis[MAXN];
    void AddEdge(int x,int y,int v,int k,int pair){
        e[cnt]=(node){y,h[x],v,k,pair};h[x]=cnt;
    }
    void AddEdge(int x,int y,int v,int k){
        AddEdge(x,y,v,+k,++cnt+1);
        AddEdge(y,x,0,-k,++cnt-1);
    }
    bool SPFA(){
        static int vis[MAXN];
        memset(vis,0,sizeof(vis));
        memset(dis,0x3f,sizeof(dis));
        queue<int>Q;Q.push(S);
        dis[S]=0;vis[S]=true;
        while(Q.size()){
            int x=Q.front();Q.pop();
            vis[x]=false;
            for(int p=h[x];p;p=e[p].next){
                int y=e[p].to;
                if(e[p].v&&dis[y]>dis[x]+e[p].k){
                    dis[y]=dis[x]+e[p].k;
                    if(!vis[y]){
                        vis[y]=true;
                        Q.push(y);
                    }
                }
            }
        }
        return dis[T]!=0x3f3f3f3f3f3f3f3f;
    }
    int dfs(int x,int Maxflow){
        int flow=0;
        if(x==T||!Maxflow)return Maxflow;
        Instack[x]=true;
        for(int&p=cur[x];p;p=e[p].next){
            int y=e[p].to,ret;
            if(dis[y]!=dis[x]+e[p].k||Instack[y])continue;
            ret=dfs(y,min(Maxflow,e[p].v));
            e[p].v-=ret;e[e[p].pair].v+=ret;
            Maxflow-=ret;flow+=ret;
            if(!Maxflow)break;
        }
        Instack[x]=false;
        return flow;
    }
    pair<int,ll>mcmf(int s,int t){
        S=s,T=t;
        pair<int,ll>ret;
        while(SPFA()){
            memcpy(cur,h,sizeof(h));
            int flow=dfs(S,INT_MAX);
            ret.first+=flow;
            ret.second+=flow*dis[T];
        }
        return ret;
    }
}
int main(){
    int n;scanf("%d",&n);
    for(int i=1;i<=n;i++)scanf("%d%d%d",&rx[i],&ry[i],&rc[i]);
    for(int i=1;i<=n;i++)scanf("%d%d%d",&bx[i],&by[i],&bc[i]);
    int S=0,T=2*n+1;
    for(int i=1;i<=n;i++){
        mcmf::AddEdge(S,i,rc[i],0);
        mcmf::AddEdge(i+n,T,bc[i],0);
        for(int d=0;d<4;d++){
            mcmf::AddEdge(i,T+d+1,INT_MAX,+dx[d]*rx[i]+dy[d]*ry[i]);
            mcmf::AddEdge(T+d+1,i+n,INT_MAX,-dx[d]*bx[i]-dy[d]*by[i]);
        }
    }
    cout<<-mcmf::mcmf(S,T).second<<"\n";
    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;
typedef long long ll;
const int Maxn=1005;
int rx[Maxn],ry[Maxn],rc[Maxn];
int bx[Maxn],by[Maxn],bc[Maxn];
int dx[]={1,1,-1,-1},dy[]={1,-1,1,-1};
namespace mcmf{
    const int MAXN=2*Maxn,MAXM=10*Maxn;
    struct node{int to,next,v,k,pair;}e[MAXM*2];
    int h[MAXN],cur[MAXN],Instack[MAXN],cnt,S,T;
    ll dis[MAXN];
    void AddEdge(int x,int y,int v,int k,int pair){
        e[cnt]=(node){y,h[x],v,k,pair};h[x]=cnt;
    }
    void AddEdge(int x,int y,int v,int k){
        AddEdge(x,y,v,+k,++cnt+1);
        AddEdge(y,x,0,-k,++cnt-1);
    }
    bool SPFA(){
        static int vis[MAXN];
        memset(vis,0,sizeof(vis));
        memset(dis,0x3f,sizeof(dis));
        queue<int>Q;Q.push(S);
        dis[S]=0;vis[S]=true;
        while(Q.size()){
            int x=Q.front();Q.pop();
            vis[x]=false;
            for(int p=h[x];p;p=e[p].next){
                int y=e[p].to;
                if(e[p].v&&dis[y]>dis[x]+e[p].k){
                    dis[y]=dis[x]+e[p].k;
                    if(!vis[y]){
                        vis[y]=true;
                        Q.push(y);
                    }
                }
            }
        }
        return dis[T]!=0x3f3f3f3f3f3f3f3f;
    }
    int dfs(int x,int Maxflow){
        int flow=0;
        if(x==T||!Maxflow)return Maxflow;
        Instack[x]=true;
        for(int&p=cur[x];p;p=e[p].next){
            int y=e[p].to,ret;
            if(dis[y]!=dis[x]+e[p].k||Instack[y])continue;
            ret=dfs(y,min(Maxflow,e[p].v));
            e[p].v-=ret;e[e[p].pair].v+=ret;
            Maxflow-=ret;flow+=ret;
            if(!Maxflow)break;
        }
        Instack[x]=false;
        return flow;
    }
    pair<int,ll>mcmf(int s,int t){
        S=s,T=t;
        pair<int,ll>ret;
        while(SPFA()){
            memcpy(cur,h,sizeof(h));
            int flow=dfs(S,INT_MAX);
            ret.first+=flow;
            ret.second+=flow*dis[T];
        }
        return ret;
    }
}
int main(){
    int n;scanf("%d",&n);
    for(int i=1;i<=n;i++)scanf("%d%d%d",&rx[i],&ry[i],&rc[i]);
    for(int i=1;i<=n;i++)scanf("%d%d%d",&bx[i],&by[i],&bc[i]);
    int S=0,T=2*n+1;
    for(int i=1;i<=n;i++){
        mcmf::AddEdge(S,i,rc[i],0);
        mcmf::AddEdge(i+n,T,bc[i],0);
        for(int d=0;d<4;d++){
            mcmf::AddEdge(i,T+d+1,INT_MAX,+dx[d]*rx[i]+dy[d]*ry[i]);
            mcmf::AddEdge(T+d+1,i+n,INT_MAX,-dx[d]*bx[i]-dy[d]*by[i]);
        }
    }
    cout<<-mcmf::mcmf(S,T).second<<"\n";
    return 0;
}
```