#include <cstdio>
#include <iostream>
#include <queue>
#include <cstring>
using namespace std;
typedef long long ll;
const int maxn = 2000,maxm = 20005;
const ll inf = 1e11;

struct Edge{
    Edge() {}
    Edge(int a,int b,ll c,int d){v = a;f = b;w = c;nxt = d;}
    int v,f,w,nxt;
};

int n,lmt;
int g[maxn + 10];
Edge e[maxm + 10];
int nume = 1;
int src,sink;

void addedge(int u,int v,int c,ll w){
    e[++nume] = Edge(v,c,w,g[u]);
    g[u] = nume;
    e[++nume] = Edge(u,0,-w,g[v]);
    g[v] = nume;
}

queue<int> que;
bool inq[maxn + 10];
ll dist[maxn + 10];
int prv[maxn + 10],pree[maxn + 10];

bool findpath(){
    while(!que.empty()) que.pop();
    que.push(src);
    memset(dist,63,sizeof dist);
    //for(int i = 0;i < maxn; ++i) dist[i] = inf;
    dist[src] = 0;
    inq[src] = true;
    while(!que.empty()){
        int u = que.front();que.pop();
        for(int i = g[u];i;i = e[i].nxt){
            if(e[i].f > 0 && dist[u] + e[i].w < dist[e[i].v]){
                dist[e[i].v] = dist[u] + e[i].w;
                prv[e[i].v] = u;
                pree[e[i].v] = i;
                if(!inq[e[i].v]){
                    inq[e[i].v] = true;
                    que.push(e[i].v);
                }
            }
        }
        inq[u] = false;
    }
    if(dist[sink] < inf) return true;
    else return false;
}

ll augment(){
    int u = sink;
    ll delta = inf;
    while(u != src){
        if(e[pree[u]].f < delta) delta = e[pree[u]].f;
        u = prv[u];
    }
    u = sink;
    while(u != src){
        e[pree[u]].f -= delta;
        e[pree[u] ^ 1].f += delta;
        u = prv[u];
    }
    return dist[sink] * delta;
}

ll mincostflow(){
    ll cur = 0,ans = 0;
    while(findpath()){
        cur += augment();
        if(cur < ans) ans = cur;
    }
    return ans;
}

int main(){
    scanf("%d",&n);
    src = 2 * n + 1,sink = 2 * n + 2;
    for(int i = 1;i <= n; ++i){
        int x,y,c;scanf("%d%d%d",&x,&y,&c);
        addedge(2 * n + 1,i,c,0);
        addedge(i,2 * n + 3,c,x + y);
        addedge(i,2 * n + 4,c,x - y);
        addedge(i,2 * n + 5,c,-x + y);
        addedge(i,2 * n + 6,c,-x - y);
    }
    for(int i = 1;i <= n; ++i){
        int x,y,c;scanf("%d%d%d",&x,&y,&c);
        addedge(n + i,2 * n + 2,c,0);
        addedge(2 * n + 3,n + i,c,-x - y);
        addedge(2 * n + 4,n + i,c,-x + y);
        addedge(2 * n + 5,n + i,c,x - y);
        addedge(2 * n + 6,n + i,c,x + y);
    }

    ll res = mincostflow();
    printf("%lld",-res);
    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 <cstdio>
#include <iostream>
#include <queue>
#include <cstring>
using namespace std;
typedef long long ll;
const int maxn = 2000,maxm = 20005;
const ll inf = 1e11;

struct Edge{
    Edge() {}
    Edge(int a,int b,ll c,int d){v = a;f = b;w = c;nxt = d;}
    int v,f,w,nxt;
};

int n,lmt;
int g[maxn + 10];
Edge e[maxm + 10];
int nume = 1;
int src,sink;

void addedge(int u,int v,int c,ll w){
    e[++nume] = Edge(v,c,w,g[u]);
    g[u] = nume;
    e[++nume] = Edge(u,0,-w,g[v]);
    g[v] = nume;
}

queue<int> que;
bool inq[maxn + 10];
ll dist[maxn + 10];
int prv[maxn + 10],pree[maxn + 10];

bool findpath(){
    while(!que.empty()) que.pop();
    que.push(src);
    memset(dist,63,sizeof dist);
    //for(int i = 0;i < maxn; ++i) dist[i] = inf;
    dist[src] = 0;
    inq[src] = true;
    while(!que.empty()){
        int u = que.front();que.pop();
        for(int i = g[u];i;i = e[i].nxt){
            if(e[i].f > 0 && dist[u] + e[i].w < dist[e[i].v]){
                dist[e[i].v] = dist[u] + e[i].w;
                prv[e[i].v] = u;
                pree[e[i].v] = i;
                if(!inq[e[i].v]){
                    inq[e[i].v] = true;
                    que.push(e[i].v);
                }
            }
        }
        inq[u] = false;
    }
    if(dist[sink] < inf) return true;
    else return false;
}

ll augment(){
    int u = sink;
    ll delta = inf;
    while(u != src){
        if(e[pree[u]].f < delta) delta = e[pree[u]].f;
        u = prv[u];
    }
    u = sink;
    while(u != src){
        e[pree[u]].f -= delta;
        e[pree[u] ^ 1].f += delta;
        u = prv[u];
    }
    return dist[sink] * delta;
}

ll mincostflow(){
    ll cur = 0,ans = 0;
    while(findpath()){
        cur += augment();
        if(cur < ans) ans = cur;
    }
    return ans;
}

int main(){
    scanf("%d",&n);
    src = 2 * n + 1,sink = 2 * n + 2;
    for(int i = 1;i <= n; ++i){
        int x,y,c;scanf("%d%d%d",&x,&y,&c);
        addedge(2 * n + 1,i,c,0);
        addedge(i,2 * n + 3,c,x + y);
        addedge(i,2 * n + 4,c,x - y);
        addedge(i,2 * n + 5,c,-x + y);
        addedge(i,2 * n + 6,c,-x - y);
    }
    for(int i = 1;i <= n; ++i){
        int x,y,c;scanf("%d%d%d",&x,&y,&c);
        addedge(n + i,2 * n + 2,c,0);
        addedge(2 * n + 3,n + i,c,-x - y);
        addedge(2 * n + 4,n + i,c,-x + y);
        addedge(2 * n + 5,n + i,c,x - y);
        addedge(2 * n + 6,n + i,c,x + y);
    }

    ll res = mincostflow();
    printf("%lld",-res);
    return 0;
}



```