#include<bits/stdc++.h>

#define pb push_back
#define mp make_pair
#define taskname "A"

using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair<int,int> ii;
const int maxn = 2e3 + 10;
const int inf = 1e6;
const ll C = 2e9;

struct edge{
    int u , v , c;
    ll cost;
    edge(){};edge(int u , int v , int c , ll cost):u(u),v(v),c(c),cost(cost){};
}e[maxn * 20];

vector<int> adj[maxn * 2];
int s , t;
int nTime = 0;

void add_edge(int u , int v , int c , ll cost){
    e[nTime * 2] = edge(u,v,c,cost);
    e[nTime * 2 + 1] = edge(v,u,0,-cost);
    adj[u].pb(nTime * 2);adj[v].pb(nTime*2+1);
    ++nTime;
}

ll d[maxn];
int trace[maxn];
int vis[maxn];
bool spfa(){
    queue<int> q;
    fill_n(d,maxn,1e18);fill_n(trace,maxn,-1);
    q.push(s);
    d[s] = 0;
    while(q.size()){
        auto u = q.front();q.pop();vis[u] = 0;
//        cout << u << " " << d[u] << endl;
        for(int c : adj[u]){
            if(e[c].c > 0 && d[e[c].v] > d[u] + e[c].cost){
                d[e[c].v] = d[u] + e[c].cost;
                trace[e[c].v] = c;
                if(vis[e[c].v] == 0){
                    vis[e[c].v] = 1;
                    q.push(e[c].v);
                }
            }
        }
    }
    return d[t] != 1e18;
}
int n;

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    if(fopen(taskname".INP" , "r"))
        freopen(taskname".INP","r",stdin),
        freopen(taskname".OUT","w",stdout);
    cin >> n;
    int sum = 0;s = 0 , t = maxn - 1;
    for(int i = 1 ; i <= n ; ++i){
        int x , y , c;cin >> x >> y >> c;
        sum += c;add_edge(s,i,c,0);
        for(int j = 0 ; j < 4 ; ++j){
            ll tmp = C + ((j & 1) ? -x : x) + ((j & 2) ? -y : y);
            add_edge(i,t-j-1,c,tmp);
        }
    }
    for(int i = 1 ; i <= n ; ++i){
        int x , y , c;cin >> x >> y >> c;
        add_edge(i+n,t,c,0);
        for(int j = 0 ; j < 4 ; ++j){
            ll tmp = C + ((j & 1) ? x : -x) + ((j & 2) ? y : -y);
            add_edge(t-j-1,i+n,c,tmp);
        }
    }
    ll res = 0;
    while(spfa()){
        int delta = 1e9;
        for(int u = t ; u != s ; u = e[trace[u]].u){
            delta = min(delta,e[trace[u]].c);
        }
        for(int u = t ; u != s ; u = e[trace[u]].u){
            e[trace[u]].c -= delta;e[trace[u]^1].c+=delta;
        }
        res += d[t] * delta;
//        cout << d[t] << " " << delta << endl;
    }
    res = 2 * sum * C - res;
//    res -= C * sum;
    cout << res;
}

### Prompt

Your challenge is to write 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>

#define pb push_back
#define mp make_pair
#define taskname "A"

using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair<int,int> ii;
const int maxn = 2e3 + 10;
const int inf = 1e6;
const ll C = 2e9;

struct edge{
    int u , v , c;
    ll cost;
    edge(){};edge(int u , int v , int c , ll cost):u(u),v(v),c(c),cost(cost){};
}e[maxn * 20];

vector<int> adj[maxn * 2];
int s , t;
int nTime = 0;

void add_edge(int u , int v , int c , ll cost){
    e[nTime * 2] = edge(u,v,c,cost);
    e[nTime * 2 + 1] = edge(v,u,0,-cost);
    adj[u].pb(nTime * 2);adj[v].pb(nTime*2+1);
    ++nTime;
}

ll d[maxn];
int trace[maxn];
int vis[maxn];
bool spfa(){
    queue<int> q;
    fill_n(d,maxn,1e18);fill_n(trace,maxn,-1);
    q.push(s);
    d[s] = 0;
    while(q.size()){
        auto u = q.front();q.pop();vis[u] = 0;
//        cout << u << " " << d[u] << endl;
        for(int c : adj[u]){
            if(e[c].c > 0 && d[e[c].v] > d[u] + e[c].cost){
                d[e[c].v] = d[u] + e[c].cost;
                trace[e[c].v] = c;
                if(vis[e[c].v] == 0){
                    vis[e[c].v] = 1;
                    q.push(e[c].v);
                }
            }
        }
    }
    return d[t] != 1e18;
}
int n;

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    if(fopen(taskname".INP" , "r"))
        freopen(taskname".INP","r",stdin),
        freopen(taskname".OUT","w",stdout);
    cin >> n;
    int sum = 0;s = 0 , t = maxn - 1;
    for(int i = 1 ; i <= n ; ++i){
        int x , y , c;cin >> x >> y >> c;
        sum += c;add_edge(s,i,c,0);
        for(int j = 0 ; j < 4 ; ++j){
            ll tmp = C + ((j & 1) ? -x : x) + ((j & 2) ? -y : y);
            add_edge(i,t-j-1,c,tmp);
        }
    }
    for(int i = 1 ; i <= n ; ++i){
        int x , y , c;cin >> x >> y >> c;
        add_edge(i+n,t,c,0);
        for(int j = 0 ; j < 4 ; ++j){
            ll tmp = C + ((j & 1) ? x : -x) + ((j & 2) ? y : -y);
            add_edge(t-j-1,i+n,c,tmp);
        }
    }
    ll res = 0;
    while(spfa()){
        int delta = 1e9;
        for(int u = t ; u != s ; u = e[trace[u]].u){
            delta = min(delta,e[trace[u]].c);
        }
        for(int u = t ; u != s ; u = e[trace[u]].u){
            e[trace[u]].c -= delta;e[trace[u]^1].c+=delta;
        }
        res += d[t] * delta;
//        cout << d[t] << " " << delta << endl;
    }
    res = 2 * sum * C - res;
//    res -= C * sum;
    cout << res;
}

```