#include<bits/stdc++.h>

using namespace std;

#define ll  long long
#define ld  double

#define sz(x)   (int)x.size()
#define all(x)  x.begin(),x.end()

#define pb  emplace_back
#define X   first
#define Y   second

const int   N   = 2e3 + 10;

typedef pair<ll,int>    ii;

struct Edge {
    int v, c;
    ll  cost;

    Edge(int _v,int _c,ll  _cost) : v(_v), c(_c), cost(_cost)   {}
};

vector<int>  g[N];
vector<Edge> E;

void addEdge(int u,int v,int c,ll cost) {
    g[u].pb(sz(E));     E.pb(v,c, cost);
    g[v].pb(sz(E));     E.pb(u,0,-cost);
}

int S, T;
int p[N];
ll  d[N];

bool inc()  {
    for(int i = 0 ; i <= T ; ++i)
        d[i] = 1e18,
        p[i] = -1;

    d[S] = 0;
    p[S] = 1e9;

    vector<bool> inq(T + 1,0);
    queue<int>   qu;

    qu.push(S);

    while (qu.size())   {
        int u = qu.front(); qu.pop();
        inq[u] = 0;

        for(int i : g[u])   {
            int v = E[i].v;
            int C = E[i].cost;

            if (d[v] > d[u] + C && E[i].c > 0)  {
                d[v] = d[u] + C;
                p[v] = i;
                if(!inq[v]) {
                    inq[v] = 1;
                    qu.push(v);
                }
            }
        }
    }
    return  p[T] >= 0;
}
ll  MCMF()  {
    static int Flow = 0;
    static ll  Cost = 0;

    while (inc())   {
        int F = 1e9;
        for(int u = T ; u != S ;)   {
            int i = p[u];
            F = min(E[i].c,F);
            u = E[i ^ 1].v;
        }
        for(int u = T ; u != S ;)   {
            int i = p[u];
            E[i].c -= F;    i ^= 1;
            E[i].c += F;    u = E[i].v;
        }

        Flow += F;
        Cost += d[T] * F;
    }
    return  Cost;
}

int main()  {
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);

    int n;  cin >> n;

    S = 0;
    T = 5 + n +n;

    int tot = 4;

    for(int i = 0 ; i < n ; ++i)    {
        int x;  cin >> x;
        int y;  cin >> y;
        int c;  cin >> c;

        addEdge(S,++tot,c,0);

        for(int j = 0 ; j < 4 ; ++j)    {
            ll  C = 0;
            if (j & 1)  C -= x;
            else        C += x;
            if (j & 2)  C -= y;
            else        C += y;

            addEdge(tot,j + 1,c,C);
        }
    }
    for(int i = 0 ; i < n ; ++i)    {
        int x;  cin >> x;
        int y;  cin >> y;
        int c;  cin >> c;

        addEdge(++tot,T,c,0);

        for(int j = 0 ; j < 4 ; ++j)    {
            ll  C = 0;
            if (j & 1)  C += x;
            else        C -= x;
            if (j & 2)  C += y;
            else        C -= y;

            addEdge(j + 1,tot,c,C);
        }
    }
    cout << -MCMF() << endl;
}
### Prompt

Generate 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>

using namespace std;

#define ll  long long
#define ld  double

#define sz(x)   (int)x.size()
#define all(x)  x.begin(),x.end()

#define pb  emplace_back
#define X   first
#define Y   second

const int   N   = 2e3 + 10;

typedef pair<ll,int>    ii;

struct Edge {
    int v, c;
    ll  cost;

    Edge(int _v,int _c,ll  _cost) : v(_v), c(_c), cost(_cost)   {}
};

vector<int>  g[N];
vector<Edge> E;

void addEdge(int u,int v,int c,ll cost) {
    g[u].pb(sz(E));     E.pb(v,c, cost);
    g[v].pb(sz(E));     E.pb(u,0,-cost);
}

int S, T;
int p[N];
ll  d[N];

bool inc()  {
    for(int i = 0 ; i <= T ; ++i)
        d[i] = 1e18,
        p[i] = -1;

    d[S] = 0;
    p[S] = 1e9;

    vector<bool> inq(T + 1,0);
    queue<int>   qu;

    qu.push(S);

    while (qu.size())   {
        int u = qu.front(); qu.pop();
        inq[u] = 0;

        for(int i : g[u])   {
            int v = E[i].v;
            int C = E[i].cost;

            if (d[v] > d[u] + C && E[i].c > 0)  {
                d[v] = d[u] + C;
                p[v] = i;
                if(!inq[v]) {
                    inq[v] = 1;
                    qu.push(v);
                }
            }
        }
    }
    return  p[T] >= 0;
}
ll  MCMF()  {
    static int Flow = 0;
    static ll  Cost = 0;

    while (inc())   {
        int F = 1e9;
        for(int u = T ; u != S ;)   {
            int i = p[u];
            F = min(E[i].c,F);
            u = E[i ^ 1].v;
        }
        for(int u = T ; u != S ;)   {
            int i = p[u];
            E[i].c -= F;    i ^= 1;
            E[i].c += F;    u = E[i].v;
        }

        Flow += F;
        Cost += d[T] * F;
    }
    return  Cost;
}

int main()  {
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);

    int n;  cin >> n;

    S = 0;
    T = 5 + n +n;

    int tot = 4;

    for(int i = 0 ; i < n ; ++i)    {
        int x;  cin >> x;
        int y;  cin >> y;
        int c;  cin >> c;

        addEdge(S,++tot,c,0);

        for(int j = 0 ; j < 4 ; ++j)    {
            ll  C = 0;
            if (j & 1)  C -= x;
            else        C += x;
            if (j & 2)  C -= y;
            else        C += y;

            addEdge(tot,j + 1,c,C);
        }
    }
    for(int i = 0 ; i < n ; ++i)    {
        int x;  cin >> x;
        int y;  cin >> y;
        int c;  cin >> c;

        addEdge(++tot,T,c,0);

        for(int j = 0 ; j < 4 ; ++j)    {
            ll  C = 0;
            if (j & 1)  C += x;
            else        C -= x;
            if (j & 2)  C += y;
            else        C -= y;

            addEdge(j + 1,tot,c,C);
        }
    }
    cout << -MCMF() << endl;
}
```