#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 1000;
const int maxm = 8e3;
const ll inf = 1e18;
const ll mx = 3e9;
struct edge
{
    int to;
    ll c;
    ll f;
    ll w;
    int nxt;
}e[31000];
int head[maxm + 10];
int tot;
int n;
int S,T;
void addedge(int u,int v,ll w,ll c)
{
    //cout<<u << v << w<< c<<endl;
    e[tot].to = v;
    e[tot].w = w;
    e[tot].c = c;
    e[tot].nxt = head[u];
    head[u] = tot++;

    e[tot].to = u;
    e[tot].w = -w;
    e[tot].c = 0;
    e[tot].nxt = head[v];
    head[v] = tot++;

}

ll dis[maxm+10];
bool vis[maxm+10];
int pre[maxm+10];
bool spfa()
{
    for(int i=0;i<=T;i++)
        dis[i] = inf;
    //memset(dis,inf,0,sizeof(dis));
    memset(pre,-1,sizeof(pre));
    memset(vis,false,sizeof(vis));
    dis[S] = 0;
    vis[S] = true;
    queue<int>q;
    q.push(S);
    while(!q.empty())
    {
        int u = q.front();
        q.pop();
        vis[u] = false;
        for(int i = head[u];i != -1;i = e[i].nxt)
        {
            int v = e[i].to;
            if(e[i].c)
            {
                if(dis[u] + e[i].w < dis[v])
                {
                    dis[v] = dis[u] + e[i].w;
                    pre[v] = i;
                    if(!vis[v])
                    {
                        vis[v] = true;
                        q.push(v);
                    }
                }
            }
        }
    }
    return dis[T] != inf;
}

ll MCMF()
{
    ll ret = 0;
    while(spfa())
    {
        ll flow = inf;
        for(int i = T;i != S;i = e[pre[i]^1].to)
        {
            flow = min(e[pre[i]].c,flow);
        }
        for(int i = T; i != S; i = e[pre[i]^1].to)
        {
            e[pre[i]].c -= flow;
            e[pre[i]^1].c += flow;
            ret += e[pre[i]].w * flow;
        }
    }
    return ret;
}

int main()
{
    while(~scanf("%d",&n))
    {
        tot = 0;
        memset(head,-1,sizeof(head));
        S = 1,T = S + 2*n + 5;
        for(int i=1;i<=n;i++)
        {
            int x,y,c;
            scanf("%d%d%d",&x,&y,&c);
            addedge(S,S+i,0,c);
            addedge(S+i,S+n+1,x+y,c);
            addedge(S+i,S+n+2,x-y,c);
            addedge(S+i,S+n+3,-x+y,c);
            addedge(S+i,S+n+4,-x-y,c);
        }

        for(int i=1;i<=n;i++)
        {
            int x,y,c;
            scanf("%d%d%d",&x,&y,&c);
            addedge(S+n+4+i,T,0,c);
            addedge(S+n+1,S+n+4+i,-x-y,c);
            addedge(S+n+2,S+n+4+i,-x+y,c);
            addedge(S+n+3,S+n+4+i,x-y,c);
            addedge(S+n+4,S+n+4+i,x+y,c);
        }

        printf("%lld\n",-MCMF());
    }
    return 0;
}

### Prompt

Create a solution in CPP for 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 = 1000;
const int maxm = 8e3;
const ll inf = 1e18;
const ll mx = 3e9;
struct edge
{
    int to;
    ll c;
    ll f;
    ll w;
    int nxt;
}e[31000];
int head[maxm + 10];
int tot;
int n;
int S,T;
void addedge(int u,int v,ll w,ll c)
{
    //cout<<u << v << w<< c<<endl;
    e[tot].to = v;
    e[tot].w = w;
    e[tot].c = c;
    e[tot].nxt = head[u];
    head[u] = tot++;

    e[tot].to = u;
    e[tot].w = -w;
    e[tot].c = 0;
    e[tot].nxt = head[v];
    head[v] = tot++;

}

ll dis[maxm+10];
bool vis[maxm+10];
int pre[maxm+10];
bool spfa()
{
    for(int i=0;i<=T;i++)
        dis[i] = inf;
    //memset(dis,inf,0,sizeof(dis));
    memset(pre,-1,sizeof(pre));
    memset(vis,false,sizeof(vis));
    dis[S] = 0;
    vis[S] = true;
    queue<int>q;
    q.push(S);
    while(!q.empty())
    {
        int u = q.front();
        q.pop();
        vis[u] = false;
        for(int i = head[u];i != -1;i = e[i].nxt)
        {
            int v = e[i].to;
            if(e[i].c)
            {
                if(dis[u] + e[i].w < dis[v])
                {
                    dis[v] = dis[u] + e[i].w;
                    pre[v] = i;
                    if(!vis[v])
                    {
                        vis[v] = true;
                        q.push(v);
                    }
                }
            }
        }
    }
    return dis[T] != inf;
}

ll MCMF()
{
    ll ret = 0;
    while(spfa())
    {
        ll flow = inf;
        for(int i = T;i != S;i = e[pre[i]^1].to)
        {
            flow = min(e[pre[i]].c,flow);
        }
        for(int i = T; i != S; i = e[pre[i]^1].to)
        {
            e[pre[i]].c -= flow;
            e[pre[i]^1].c += flow;
            ret += e[pre[i]].w * flow;
        }
    }
    return ret;
}

int main()
{
    while(~scanf("%d",&n))
    {
        tot = 0;
        memset(head,-1,sizeof(head));
        S = 1,T = S + 2*n + 5;
        for(int i=1;i<=n;i++)
        {
            int x,y,c;
            scanf("%d%d%d",&x,&y,&c);
            addedge(S,S+i,0,c);
            addedge(S+i,S+n+1,x+y,c);
            addedge(S+i,S+n+2,x-y,c);
            addedge(S+i,S+n+3,-x+y,c);
            addedge(S+i,S+n+4,-x-y,c);
        }

        for(int i=1;i<=n;i++)
        {
            int x,y,c;
            scanf("%d%d%d",&x,&y,&c);
            addedge(S+n+4+i,T,0,c);
            addedge(S+n+1,S+n+4+i,-x-y,c);
            addedge(S+n+2,S+n+4+i,-x+y,c);
            addedge(S+n+3,S+n+4+i,x-y,c);
            addedge(S+n+4,S+n+4+i,x+y,c);
        }

        printf("%lld\n",-MCMF());
    }
    return 0;
}

```