#include<bits/stdc++.h>
#define rep(i,a,b) for (int i = (a); i <= (b); ++i)
#define drep(i,a,b) for (int i = (a); i >= (b); --i)
#define grep(i,u) for (int i = head[u],v = e[i].v; i; v = e[i = e[i].nxt].v)
#define il inline
#define LL long long
#define ULL unsigned LL
#define pb push_back
#define mp make_pair
#define fi first
#define se second
using namespace std;
il LL read() {
	LL res = 0,f = 1; char ch = getchar(); while (!isdigit(ch)) {if (ch == '-') f = -f; ch = getchar();}
	while (isdigit(ch)) {res = res*10+ch-'0'; ch = getchar();} return res*f;
}
namespace qiqi {
	const int N = 5e4+5,INF = 0x3f3f3f3f; int n,ecnt = 1,head[N],s,t,p[4],dx[4] = {1,1,-1,-1},dy[4] = {1,-1,1,-1},pre[N],flow[N]; LL dis[N]; bool vis[N]; queue<int> q;
	struct Edge {int v,w,f,nxt;} e[N]; il void add(int u,int v,int f,int w) {e[++ecnt] = (Edge){v,w,f,head[u]}; head[u] = ecnt; e[++ecnt] = (Edge){u,-w,0,head[v]}; head[v] = ecnt;}
	il bool spfa(int s,int t) {
		memset(dis,flow[s] = INF,sizeof(dis)); dis[s] = pre[t] = 0; q.push(s);
		while (!q.empty()) {
			int u = q.front(); q.pop(); vis[u] = 0; grep(i,u) if (e[i].f && dis[v] > dis[u]+e[i].w) {
				pre[v] = i; dis[v] = dis[u]+e[i].w; flow[v] = min(flow[u],e[i].f); if (!vis[v]) {q.push(v); vis[v] = 1;}
			}
		}
		return pre[t];
	}
	il LL mcmf(int s,int t) {LL res = 0; while (spfa(s,t)) {res += 1LL*dis[t]*flow[t]; int x = t; while (x) {e[pre[x]].f -= flow[t]; e[pre[x]^1].f += flow[t]; x = e[pre[x]^1].v;}} return res;}
	void main() {
		n = read(); s = n*2+1; t = s+1; rep(i,0,3) p[i] = t+i+1;
		rep(i,1,n) {int x = read(),y = read(),k = read(); add(s,i,k,0); rep(j,0,3) add(i,p[j],INF,dx[j]*x+dy[j]*y);}
		rep(i,n+1,n*2) {int x = read(),y = read(),k = read(); add(i,t,k,0); rep(j,0,3) add(p[j],i,INF,-dx[j]*x-dy[j]*y);}
		printf("%lld\n",-mcmf(s,t));
	}
}
int main() {
	qiqi::main(); return 0;
}
### 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>
#define rep(i,a,b) for (int i = (a); i <= (b); ++i)
#define drep(i,a,b) for (int i = (a); i >= (b); --i)
#define grep(i,u) for (int i = head[u],v = e[i].v; i; v = e[i = e[i].nxt].v)
#define il inline
#define LL long long
#define ULL unsigned LL
#define pb push_back
#define mp make_pair
#define fi first
#define se second
using namespace std;
il LL read() {
	LL res = 0,f = 1; char ch = getchar(); while (!isdigit(ch)) {if (ch == '-') f = -f; ch = getchar();}
	while (isdigit(ch)) {res = res*10+ch-'0'; ch = getchar();} return res*f;
}
namespace qiqi {
	const int N = 5e4+5,INF = 0x3f3f3f3f; int n,ecnt = 1,head[N],s,t,p[4],dx[4] = {1,1,-1,-1},dy[4] = {1,-1,1,-1},pre[N],flow[N]; LL dis[N]; bool vis[N]; queue<int> q;
	struct Edge {int v,w,f,nxt;} e[N]; il void add(int u,int v,int f,int w) {e[++ecnt] = (Edge){v,w,f,head[u]}; head[u] = ecnt; e[++ecnt] = (Edge){u,-w,0,head[v]}; head[v] = ecnt;}
	il bool spfa(int s,int t) {
		memset(dis,flow[s] = INF,sizeof(dis)); dis[s] = pre[t] = 0; q.push(s);
		while (!q.empty()) {
			int u = q.front(); q.pop(); vis[u] = 0; grep(i,u) if (e[i].f && dis[v] > dis[u]+e[i].w) {
				pre[v] = i; dis[v] = dis[u]+e[i].w; flow[v] = min(flow[u],e[i].f); if (!vis[v]) {q.push(v); vis[v] = 1;}
			}
		}
		return pre[t];
	}
	il LL mcmf(int s,int t) {LL res = 0; while (spfa(s,t)) {res += 1LL*dis[t]*flow[t]; int x = t; while (x) {e[pre[x]].f -= flow[t]; e[pre[x]^1].f += flow[t]; x = e[pre[x]^1].v;}} return res;}
	void main() {
		n = read(); s = n*2+1; t = s+1; rep(i,0,3) p[i] = t+i+1;
		rep(i,1,n) {int x = read(),y = read(),k = read(); add(s,i,k,0); rep(j,0,3) add(i,p[j],INF,dx[j]*x+dy[j]*y);}
		rep(i,n+1,n*2) {int x = read(),y = read(),k = read(); add(i,t,k,0); rep(j,0,3) add(p[j],i,INF,-dx[j]*x-dy[j]*y);}
		printf("%lld\n",-mcmf(s,t));
	}
}
int main() {
	qiqi::main(); return 0;
}
```