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总和减去最小割即为答案

最小割删掉的边就是要减去的值,这样就可以最小化要减去的值,即答案最大化

那我们如何构造这张图呢?

  1. ST \xrightarrow{\text{选文科的值}} (i,j) \xrightarrow{\text{选理科的值}}ED

  2. ST \xrightarrow{\text{同时选文科的额外快乐}}new,new\rightarrow(i,j),new\rightarrow(i+1,j)(其他同理)

  3. (i,j)\rightarrow new,(i+1,j)\rightarrow new,new \xrightarrow{\text{同时选理科的额外快乐}}ED(其他同理)

每个点只能选择文科或理科,当某个点选择了文科,那么它向理科(ED)的边都应该要被断开。

它直接连向ED的边、它和别的点组合连向ED的边都要切断

这些边的权值就会从最终答案中减去

infinf同时选文科选理科选文科同时选理科infinf选理科选文科ST(i,j)ED(i+1,j)newnew'
#include<bits/stdc++.h>
namespace ZDY{
    #pragma GCC optimize(3)
    #define il __inline__ __attribute__ ((always_inline))
    #define register
    #define ll long long
    #define ull unsigned long long
    #define db double
    #define sht short
    #define MB template <class T>il
    #define Fur(i,x,y) for(int i(x);i<=y;++i)
    #define Fdr(i,x,y) for(int i(x);i>=y;--i)
    #define fl(i,x) for(int i(head[x]),to;to=e[i].to,i;i=e[i].nxt)
    #define clr(x,y) memset(x,y,sizeof(x))
    #define cpy(x,y) memcpy(x,y,sizeof(x))
    #define fin(s) freopen(s".in","r",stdin)
    #define fout(s) freopen(s".out","w",stdout)
    #define fcin ios::sync_with_stdio(false)
    #define l2(n) ((int)(log2(n)))
    #define inf (1<<30)
    MB T ABS(T x){return x>0?x:-x;}
    MB T MAX(T x,T y){return x>y?x:y;}
    MB T MIN(T x,T y){return x<y?x:y;}
    MB T GCD(T x,T y){return y?GCD(y,x%y):x;}
    MB void SWAP(T &x,T &y){T t=x;x=y;y=t;}
}using namespace ZDY;using namespace std;
namespace IO{const int str=1<<20;static char in_buf[str],*in_s,*in_t;bool __=0;il char gc(){return (in_s==in_t)&&(in_t=(in_s=in_buf)+fread(in_buf,1,str,stdin)),in_s==in_t?__=1,EOF:*in_s++;}il void in(string &ch){ch.clear();if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF){__=1;return;}ch+=c;while((c=gc())!=EOF&&!isspace(c))ch+=c;if(c==EOF)__=1;}il void in(char &ch){if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)__=1;else ch=c;}il void in(char *ch){*ch='\0';if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF){__=1;return;}*ch=c;ch++;while((c=gc())!=EOF&&!isspace(c))*ch=c,ch++;if(c==EOF)__=1;*ch='\0';}template<typename T>il void in(T &x){if(__)return;char c=gc();bool f=0;while(c!=EOF&&(c<'0'||c>'9'))f^=(c=='-'),c=gc();if(c==EOF){__=1;return;}x=0;while(c!=EOF&&'0'<=c&&c<='9')x=x*10+c-48,c=gc();if(c==EOF)__=1;if(f)x=-x;}template<typename T,typename ... arr>il void in(T &x,arr & ... y){in(x),in(y...);}const char ln='\n';static char out_buf[str],*out_s=out_buf,*out_t=out_buf+str;il void flush(){fwrite(out_buf,1,out_s-out_buf,stdout);out_s=out_buf;}il void pt(char c){(out_s==out_t)?(fwrite(out_s=out_buf,1,str,stdout),*out_s++=c):(*out_s++=c);}il void out(const char* s){while(*s)pt(*s++);}il void out(char* s){while(*s)pt(*s++);}il void out(char c){pt(c);}il void out(string s){for(int i=0;s[i];i++)pt(s[i]);}template<typename T>il void out(T x){if(!x){pt('0');return;}if(x<0)pt('-'),x=-x;char a[50],t=0;while(x)a[t++]=x%10,x/= 10;while(t--)pt(a[t]+'0');}template<typename T,typename ... arr>il void out(T x,arr & ... y){out(x),out(y...);}}using namespace IO;
const int N=100011,M=5000011;
int n,m,cnt=1,head[N],ST,ED,d[N],q[N];
struct edge{
    int to,nxt,w;
}e[M];
#define fl(i,x) for(int i=head[x],to;to=e[i].to,i;i=e[i].nxt)
void add(int x,int y,int w){
    e[++cnt].to=y;e[cnt].nxt=head[x];head[x]=cnt;e[cnt].w=w;
    e[++cnt].to=x;e[cnt].nxt=head[y];head[y]=cnt;e[cnt].w=0;
}
bool bfs(){
    int h=0,t=1,x;
    memset(d,0,sizeof d);
    q[h]=ST;d[ST]=1;
    while(h<t){
        x=q[h++];
        if(x==ED)return 1;
        fl(i,x)if(!d[to]&&e[i].w)
            d[to]=d[x]+1,q[t++]=to;
    }
    return 0;
}
int dfs(int x,int mf){
    if(x==ED)return mf;
    int us=0,w;
    fl(i,x)if(e[i].w&&d[to]==d[x]+1){
        w=dfs(to,min(mf-us,e[i].w));
        e[i].w-=w;
        e[i^1].w+=w;
        us+=w;
        if(us==mf)return mf;
    }
    if(!us)d[x]=-1;
    return us;
}
int id(int x,int y){
    return (x-1)*m+y;
}
int main(){
    in(n,m);
    ST=0,ED=n*m+2*(n-1)*m+2*n*(m-1)+1;
    int ans=0,w,tt=n*m;
    //选文科ST→(i,j)
    Fur(i,1,n)Fur(j,1,m)
        in(w),ans+=w,
        add(ST,id(i,j),w);
    //选理科(i,j)→ED
    Fur(i,1,n)Fur(j,1,m)
        in(w),ans+=w,
        add(id(i,j),ED,w);
    //ST→new,new→(i,j),new→(i+1,j)
    Fur(i,1,n-1)Fur(j,1,m)
        in(w),ans+=w,
        add(ST,++tt,w),
        add(tt,id(i,j),inf),
        add(tt,id(i+1,j),inf);
    //(i,j)→new,(i+1,j)→new,new→ED
    Fur(i,1,n-1)Fur(j,1,m)
        in(w),ans+=w,
        add(++tt,ED,w),
        add(id(i,j),tt,inf),
        add(id(i+1,j),tt,inf);
    //ST→new,new→(i,j),new→(i,j+1)
    Fur(i,1,n)Fur(j,1,m-1)
        in(w),ans+=w,
        add(ST,++tt,w),
        add(tt,id(i,j),inf),
        add(tt,id(i,j+1),inf);
    //(i,j)→new,(i,j+1)→new,new→ED
    Fur(i,1,n)Fur(j,1,m-1)
        in(w),ans+=w,
        add(++tt,ED,w),
        add(id(i,j),tt,inf),
        add(id(i,j+1),tt,inf);

    while(bfs())ans-=dfs(ST,inf);
    printf("%d\n",ans);
}
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