#include <bits/stdc++.h>

#define rep(i, a, b) for (ll i = (a); i < (b); i++)
typedef uint64_t ull;
typedef int64_t ll;
typedef std::pair<ll, ll> PLL;
using namespace std;

class MinCostFlow {
 private:
  typedef std::pair<ll, ll> P;
  struct Edge { ll to, cap, cost, rev; };
  const ll V;
  std::vector<std::vector<Edge>> G;
  std::vector<ll> h, dist, prevv, preve;

 public:
  explicit MinCostFlow(ll v) : V(v), G(v), h(v), dist(v), prevv(v), preve(v) {}

  void addEdge(ll from, ll to, ll cap, ll cost) {
    G[from].push_back({to, cap, cost, static_cast<ll>(G[to].size())});
    G[to].push_back({from, 0, -cost, static_cast<ll>(G[from].size())-1});
  }

  ll minCostFlow(ll s, ll t, ll f) {
    ll res = 0;
    for (ll i = 0; i < V; ++i) h[i] = 0;
    while (f > 0) {
      std::priority_queue<P, std::vector<P>, std::greater<P>> q;
      for (ll i = 0; i < V; ++i) dist[i] = 1e18;
      dist[s] = 0;
      q.push(P(0, s));
      while (!q.empty()) {
        P p = q.top(); q.pop();
        ll v = p.second;
        if (dist[v] < p.first) continue;
        for (ll i = 0; i < G[v].size(); ++i) {
          auto& e = G[v][i];
          if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
            dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
            prevv[e.to] = v;
            preve[e.to] = i;
            q.push(P(dist[e.to], e.to));
          }
        }
      }
      if (dist[t] == 1e18) return -1;
      for (ll v = 0; v < V; ++v) h[v] += dist[v];
      ll d = f;
      for (ll v = t; v != s; v = prevv[v]) {
        d = std::min(d, G[prevv[v]][preve[v]].cap);
      }
      f -= d;
      res += d * h[t];
      for (ll v = t; v != s; v = prevv[v]) {
        Edge& e = G[prevv[v]][preve[v]];
        e.cap -= d;
        G[v][e.rev].cap += d;
      }
    }
    return res;
  }
};

const ll INF    = 1e11;
const ll OFFSET = 1e11;

vector<PLL> reds, blues;

signed main() {
  ll N, t=0;
  cin>>N;

  auto m = MinCostFlow(300000);
  rep(i,0,N) {
    ll x,y,c;
    cin>>x>>y>>c;
    m.addEdge(2*N, i, c, 0);
    m.addEdge(i, 2*N+2, INF, OFFSET - ( x+y));
    m.addEdge(i, 2*N+3, INF, OFFSET - (-x+y));
    m.addEdge(i, 2*N+4, INF, OFFSET - ( x-y));
    m.addEdge(i, 2*N+5, INF, OFFSET - (-x-y));
    t += c;
  }
  rep(i,0,N) {
    ll x,y,c;
    cin>>x>>y>>c;
    m.addEdge(N+i, 2*N+1, c, 0);
    m.addEdge(2*N+2, N+i, INF, OFFSET - (-x-y));
    m.addEdge(2*N+3, N+i, INF, OFFSET - ( x-y));
    m.addEdge(2*N+4, N+i, INF, OFFSET - (-x+y));
    m.addEdge(2*N+5, N+i, INF, OFFSET - ( x+y));
  }

  cout<<-1 * (m.minCostFlow(2*N, 2*N+1, t) - OFFSET*2*t)<<endl;
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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 rep(i, a, b) for (ll i = (a); i < (b); i++)
typedef uint64_t ull;
typedef int64_t ll;
typedef std::pair<ll, ll> PLL;
using namespace std;

class MinCostFlow {
 private:
  typedef std::pair<ll, ll> P;
  struct Edge { ll to, cap, cost, rev; };
  const ll V;
  std::vector<std::vector<Edge>> G;
  std::vector<ll> h, dist, prevv, preve;

 public:
  explicit MinCostFlow(ll v) : V(v), G(v), h(v), dist(v), prevv(v), preve(v) {}

  void addEdge(ll from, ll to, ll cap, ll cost) {
    G[from].push_back({to, cap, cost, static_cast<ll>(G[to].size())});
    G[to].push_back({from, 0, -cost, static_cast<ll>(G[from].size())-1});
  }

  ll minCostFlow(ll s, ll t, ll f) {
    ll res = 0;
    for (ll i = 0; i < V; ++i) h[i] = 0;
    while (f > 0) {
      std::priority_queue<P, std::vector<P>, std::greater<P>> q;
      for (ll i = 0; i < V; ++i) dist[i] = 1e18;
      dist[s] = 0;
      q.push(P(0, s));
      while (!q.empty()) {
        P p = q.top(); q.pop();
        ll v = p.second;
        if (dist[v] < p.first) continue;
        for (ll i = 0; i < G[v].size(); ++i) {
          auto& e = G[v][i];
          if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
            dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
            prevv[e.to] = v;
            preve[e.to] = i;
            q.push(P(dist[e.to], e.to));
          }
        }
      }
      if (dist[t] == 1e18) return -1;
      for (ll v = 0; v < V; ++v) h[v] += dist[v];
      ll d = f;
      for (ll v = t; v != s; v = prevv[v]) {
        d = std::min(d, G[prevv[v]][preve[v]].cap);
      }
      f -= d;
      res += d * h[t];
      for (ll v = t; v != s; v = prevv[v]) {
        Edge& e = G[prevv[v]][preve[v]];
        e.cap -= d;
        G[v][e.rev].cap += d;
      }
    }
    return res;
  }
};

const ll INF    = 1e11;
const ll OFFSET = 1e11;

vector<PLL> reds, blues;

signed main() {
  ll N, t=0;
  cin>>N;

  auto m = MinCostFlow(300000);
  rep(i,0,N) {
    ll x,y,c;
    cin>>x>>y>>c;
    m.addEdge(2*N, i, c, 0);
    m.addEdge(i, 2*N+2, INF, OFFSET - ( x+y));
    m.addEdge(i, 2*N+3, INF, OFFSET - (-x+y));
    m.addEdge(i, 2*N+4, INF, OFFSET - ( x-y));
    m.addEdge(i, 2*N+5, INF, OFFSET - (-x-y));
    t += c;
  }
  rep(i,0,N) {
    ll x,y,c;
    cin>>x>>y>>c;
    m.addEdge(N+i, 2*N+1, c, 0);
    m.addEdge(2*N+2, N+i, INF, OFFSET - (-x-y));
    m.addEdge(2*N+3, N+i, INF, OFFSET - ( x-y));
    m.addEdge(2*N+4, N+i, INF, OFFSET - (-x+y));
    m.addEdge(2*N+5, N+i, INF, OFFSET - ( x+y));
  }

  cout<<-1 * (m.minCostFlow(2*N, 2*N+1, t) - OFFSET*2*t)<<endl;
  return 0;
}

```