/*



*/
#include <bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define pb push_back
#define ll long long
typedef pair<ll,int> pii;
const int maxn=2e3+10;
struct edge{
    int a,b,flow,cap;
    ll cost;
};
int parent[maxn],source,sink,mflow,maxflow,n;
ll dp[maxn],pot[maxn],rez;
vector<edge>e;
vector<int>vect[maxn];
int inf=1e9;
ll offset=1e10;
void add_edge(int a,int b,int cap,ll cost){

    cost=-cost;
    cost+=offset;

    vect[a].pb(e.size());
    e.pb({a,b,0,cap,cost});

    vect[b].pb(e.size());
    e.pb({b,a,cap,cap,-cost});
}
ll flow(){

    memset(parent,-1,sizeof(parent));
    for(int i=source;i<=sink+4;i++)dp[i]=1e18;

    set<pii>st;
    st.insert({0,source});
    dp[source]=0;
    while(st.size()){

        int x=(*st.begin()).ss;
        st.erase(st.begin());

        for(int i=0;i<vect[x].size();i++){
            int id=vect[x][i];
            ll w=pot[x]+e[id].cost-pot[e[id].b];
            if(e[id].flow>=e[id].cap || dp[x]+w>=dp[e[id].b])continue;

            int id2=e[id].b;
            st.erase({dp[id2],id2});
            dp[id2]=dp[x]+w;
            parent[id2]=id;
            st.insert({dp[id2],id2});
        }

    }

    for(int i=source;i<=sink+4;i++)pot[i]=dp[i];

    int x=sink;
    int flow=1e9;
    while(x!=source){
        int id=parent[x];
        flow=min(flow,e[id].cap-e[id].flow);
        x=e[id].a;

        ///printf("%d %d %d X\n",x,e[id].a,e[id].b);
    }

    mflow+=flow;

    x=sink;
    ll cost=0;
    while(x!=source){
        int id=parent[x];
        cost+=e[id].cost;
        x=e[id].a;

        e[id].flow+=flow;
        e[id^1].flow-=flow;
    }

    cost-=4*offset;
    cost=-cost;
    cost*=(ll)flow;

    ///printf("%lld AA COST\n",cost);

    return cost;
}
void go(){

    while(mflow<maxflow)
        rez+=flow();

}
int main(){

    ///freopen("test.txt","r",stdin);

    scanf("%d",&n);
    source=0;
    sink=2*n+1;
    for(int i=1;i<=n;i++){
        ll x,y,w;
        scanf("%lld %lld %lld",&x,&y,&w);

        maxflow+=(int)w;

        add_edge(source,i,w,0);
        add_edge(i,sink+1,inf,x+y);
        add_edge(i,sink+2,inf,x-y);
        add_edge(i,sink+3,inf,-x+y);
        add_edge(i,sink+4,inf,-x-y);
    }
    for(int i=1;i<=n;i++){
        ll x,y,w;
        scanf("%lld %lld %lld",&x,&y,&w);

        add_edge(i+n,sink,w,0);
        add_edge(sink+1,i+n,inf,-x-y);
        add_edge(sink+2,i+n,inf,-x+y);
        add_edge(sink+3,i+n,inf,x-y);
        add_edge(sink+4,i+n,inf,x+y);
    }

    go();

    printf("%lld\n",rez);

	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>
using namespace std;
#define ff first
#define ss second
#define pb push_back
#define ll long long
typedef pair<ll,int> pii;
const int maxn=2e3+10;
struct edge{
    int a,b,flow,cap;
    ll cost;
};
int parent[maxn],source,sink,mflow,maxflow,n;
ll dp[maxn],pot[maxn],rez;
vector<edge>e;
vector<int>vect[maxn];
int inf=1e9;
ll offset=1e10;
void add_edge(int a,int b,int cap,ll cost){

    cost=-cost;
    cost+=offset;

    vect[a].pb(e.size());
    e.pb({a,b,0,cap,cost});

    vect[b].pb(e.size());
    e.pb({b,a,cap,cap,-cost});
}
ll flow(){

    memset(parent,-1,sizeof(parent));
    for(int i=source;i<=sink+4;i++)dp[i]=1e18;

    set<pii>st;
    st.insert({0,source});
    dp[source]=0;
    while(st.size()){

        int x=(*st.begin()).ss;
        st.erase(st.begin());

        for(int i=0;i<vect[x].size();i++){
            int id=vect[x][i];
            ll w=pot[x]+e[id].cost-pot[e[id].b];
            if(e[id].flow>=e[id].cap || dp[x]+w>=dp[e[id].b])continue;

            int id2=e[id].b;
            st.erase({dp[id2],id2});
            dp[id2]=dp[x]+w;
            parent[id2]=id;
            st.insert({dp[id2],id2});
        }

    }

    for(int i=source;i<=sink+4;i++)pot[i]=dp[i];

    int x=sink;
    int flow=1e9;
    while(x!=source){
        int id=parent[x];
        flow=min(flow,e[id].cap-e[id].flow);
        x=e[id].a;

        ///printf("%d %d %d X\n",x,e[id].a,e[id].b);
    }

    mflow+=flow;

    x=sink;
    ll cost=0;
    while(x!=source){
        int id=parent[x];
        cost+=e[id].cost;
        x=e[id].a;

        e[id].flow+=flow;
        e[id^1].flow-=flow;
    }

    cost-=4*offset;
    cost=-cost;
    cost*=(ll)flow;

    ///printf("%lld AA COST\n",cost);

    return cost;
}
void go(){

    while(mflow<maxflow)
        rez+=flow();

}
int main(){

    ///freopen("test.txt","r",stdin);

    scanf("%d",&n);
    source=0;
    sink=2*n+1;
    for(int i=1;i<=n;i++){
        ll x,y,w;
        scanf("%lld %lld %lld",&x,&y,&w);

        maxflow+=(int)w;

        add_edge(source,i,w,0);
        add_edge(i,sink+1,inf,x+y);
        add_edge(i,sink+2,inf,x-y);
        add_edge(i,sink+3,inf,-x+y);
        add_edge(i,sink+4,inf,-x-y);
    }
    for(int i=1;i<=n;i++){
        ll x,y,w;
        scanf("%lld %lld %lld",&x,&y,&w);

        add_edge(i+n,sink,w,0);
        add_edge(sink+1,i+n,inf,-x-y);
        add_edge(sink+2,i+n,inf,-x+y);
        add_edge(sink+3,i+n,inf,x-y);
        add_edge(sink+4,i+n,inf,x+y);
    }

    go();

    printf("%lld\n",rez);

	return 0;
}

```