//#define DEBUG
#include <cstdio>
#include <cstring>

using namespace std;

typedef long long ll;

const int maxn=10000, inf=0x7ffffff;

int min(int a, int b) {
	return a< b? a : b;
}

class Net {
	public:
		static const int maxm=10*maxn+3;
		int n, m=1, ind[2*maxn+7], link[2*maxm+1], to[2*maxm+1], val[2*maxm+1], cur[2*maxn+7];
		ll cost[2*maxm+1], dis[2*maxn+7], sumcost;

		void addSide(int x, int y, int u, ll v) {
			m++;
			to[m] = y;
			val[m] = u;
			cost[m] = v;
			link[m] = ind[x];
			ind[x] = m;
		}

		void add(int x, int y, int u, ll v) {
			addSide(x, y, u, v);
			addSide(y, x, 0, -v);
		}

		void spfa(int s) {
			static bool book[2*maxn+7];
			static int que[2*maxn+7];
			memset(dis, 200, sizeof dis);
			dis[s] = 0;
			book[1] = true;
			que[1] = s;
			for (int h=0, t=1; h!=t; ) {
				h = h%n+1;
				int x=que[h];
				book[x] = false;
				for (int i=ind[x]; i; i=link[i]) {
					if (val[i]) {
						int y=to[i];
						ll z=dis[x]+cost[i];
						if (z>dis[y]) {
							dis[y] = z;
							if (!book[y]) {
								book[y] = true;
								t = t%n+1;
								que[t] = y;
							}
						}
					}
				}
			}
		}

		int run(int o, int t, int flow) {
			static bool vis[2*maxn+7];
			if (o==t) {
				return flow;
			}
			vis[o] = true;
			int have=0;
			for (int i=cur[o]; i; i=link[i]) {
				if (!vis[to[i]] && val[i] && dis[to[i]]==dis[o]+cost[i]) {
					cur[o] = i;
					int temp=run(to[i], t, min(flow-have, val[i]));
					val[i]-=temp, val[i^1]+=temp, have+=temp, sumcost+=temp*cost[i];
					if (flow==have) break;
				}
			}
			vis[o] = false;
			return have;
		}

		bool init(int s, int t) {
			for (int i=1; i<=n; i++) {
				cur[i] = ind[i];
			}
			spfa(s);
			return dis[t]>0;
		}
};

int main() {
#ifdef DEBUG
	freopen("src.in", "r", stdin);
	freopen("src.out", "w", stdout);
#endif

	static Net g;
	int n;
	scanf("%d", &n);
	g.n = 2*n+6;
	for (int i=1; i<=n; i++) {
		int x, y, c;
		scanf("%d %d %d", &x, &y, &c);
		g.add(1, i+6, c, 0);
		g.add(i+6, 3, inf, -x-y);
		g.add(i+6, 4, inf, -x+y);
		g.add(i+6, 5, inf, x-y);
		g.add(i+6, 6, inf, x+y);
	}
	for (int i=1; i<=n; i++) {
		int x, y, c;
		scanf("%d %d %d", &x, &y, &c);
		g.add(n+i+6, 2, c, 0);
		g.add(3, n+i+6, inf, x+y);
		g.add(4, n+i+6, inf, x-y);
		g.add(5, n+i+6, inf, -x+y);
		g.add(6, n+i+6, inf, -x-y);
	}

	for (; g.init(1, 2); g.run(1, 2, inf));
	printf("%lld\n", g.sumcost);

	fclose(stdin);
	fclose(stdout);
	return 0;
}

### Prompt

Please formulate 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
//#define DEBUG
#include <cstdio>
#include <cstring>

using namespace std;

typedef long long ll;

const int maxn=10000, inf=0x7ffffff;

int min(int a, int b) {
	return a< b? a : b;
}

class Net {
	public:
		static const int maxm=10*maxn+3;
		int n, m=1, ind[2*maxn+7], link[2*maxm+1], to[2*maxm+1], val[2*maxm+1], cur[2*maxn+7];
		ll cost[2*maxm+1], dis[2*maxn+7], sumcost;

		void addSide(int x, int y, int u, ll v) {
			m++;
			to[m] = y;
			val[m] = u;
			cost[m] = v;
			link[m] = ind[x];
			ind[x] = m;
		}

		void add(int x, int y, int u, ll v) {
			addSide(x, y, u, v);
			addSide(y, x, 0, -v);
		}

		void spfa(int s) {
			static bool book[2*maxn+7];
			static int que[2*maxn+7];
			memset(dis, 200, sizeof dis);
			dis[s] = 0;
			book[1] = true;
			que[1] = s;
			for (int h=0, t=1; h!=t; ) {
				h = h%n+1;
				int x=que[h];
				book[x] = false;
				for (int i=ind[x]; i; i=link[i]) {
					if (val[i]) {
						int y=to[i];
						ll z=dis[x]+cost[i];
						if (z>dis[y]) {
							dis[y] = z;
							if (!book[y]) {
								book[y] = true;
								t = t%n+1;
								que[t] = y;
							}
						}
					}
				}
			}
		}

		int run(int o, int t, int flow) {
			static bool vis[2*maxn+7];
			if (o==t) {
				return flow;
			}
			vis[o] = true;
			int have=0;
			for (int i=cur[o]; i; i=link[i]) {
				if (!vis[to[i]] && val[i] && dis[to[i]]==dis[o]+cost[i]) {
					cur[o] = i;
					int temp=run(to[i], t, min(flow-have, val[i]));
					val[i]-=temp, val[i^1]+=temp, have+=temp, sumcost+=temp*cost[i];
					if (flow==have) break;
				}
			}
			vis[o] = false;
			return have;
		}

		bool init(int s, int t) {
			for (int i=1; i<=n; i++) {
				cur[i] = ind[i];
			}
			spfa(s);
			return dis[t]>0;
		}
};

int main() {
#ifdef DEBUG
	freopen("src.in", "r", stdin);
	freopen("src.out", "w", stdout);
#endif

	static Net g;
	int n;
	scanf("%d", &n);
	g.n = 2*n+6;
	for (int i=1; i<=n; i++) {
		int x, y, c;
		scanf("%d %d %d", &x, &y, &c);
		g.add(1, i+6, c, 0);
		g.add(i+6, 3, inf, -x-y);
		g.add(i+6, 4, inf, -x+y);
		g.add(i+6, 5, inf, x-y);
		g.add(i+6, 6, inf, x+y);
	}
	for (int i=1; i<=n; i++) {
		int x, y, c;
		scanf("%d %d %d", &x, &y, &c);
		g.add(n+i+6, 2, c, 0);
		g.add(3, n+i+6, inf, x+y);
		g.add(4, n+i+6, inf, x-y);
		g.add(5, n+i+6, inf, -x+y);
		g.add(6, n+i+6, inf, -x-y);
	}

	for (; g.init(1, 2); g.run(1, 2, inf));
	printf("%lld\n", g.sumcost);

	fclose(stdin);
	fclose(stdout);
	return 0;
}

```