四维偏序

CDQ套CDQ或者CDQ套树套树
前者快于后者然而我写了后者

# include <stdio.h>
# include <stdlib.h>
# include <iostream>
# include <algorithm>
# include <string.h>
# define IL inline
# define RG register
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;

IL ll Read(){
    RG char c = getchar(); RG ll x = 0, z = 1;
    for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
    for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + c - '0';
    return x * z;
}

const int MAXN(50010);
int n, k, ans, cnt;
struct Point{
    int a, b, c, d;
    IL bool operator <(RG Point B) const{
        if(a != B.a) return a < B.a;
        if(b != B.b) return b < B.b;
        if(c != B.c) return c < B.c;
        return d < B.d;
    }
} p[MAXN];
struct Treap{
    int key, fix, size, num;
    Treap *ch[2];
    IL Treap(int x){  
        num = size = 1;  
        fix = rand();  
        key = x;  
        ch[0] = ch[1] = NULL;  
    }
} *root[MAXN << 1];

IL void Updata(Treap *x){
    x -> size = x -> num;
    if(x -> ch[0] != NULL) x -> size += x -> ch[0] -> size;
    if(x -> ch[1] != NULL) x -> size += x -> ch[1] -> size;
}

IL void Rot(Treap *&x, int c){
    Treap *y = x -> ch[!c];
    x -> ch[!c] = y -> ch[c];
    y -> ch[c] = x;
    Updata(x); Updata(y);
    x = y;
}

IL void Insert(Treap *&x, int val){
    if(x == NULL) x = new Treap(val);
    else if(x -> key == val) x -> num++;
    else{
        int c = val > x -> key;
        Insert(x -> ch[c], val);
        if(x -> ch[c] -> fix > x -> fix)
            Rot(x, c ^ 1);
    }
    Updata(x);
}

IL void Delete(Treap *&x, int val){
    if(val == x -> key){
        Treap *tmp = x;
        if(x -> num > 1) x -> num--;
        else if(x -> ch[0] == NULL){
            x = x -> ch[1];
            delete tmp;
        }
        else if(x -> ch[1] == NULL){
            x = x -> ch[0];
            delete tmp;
        }
        else{
            int c = x -> ch[0] -> fix > x -> ch[1] -> fix;
            Rot(x, c);
            Delete(x -> ch[c], val);
        }
    }
    else{
        int c = val > x -> key;
        Delete(x -> ch[c], val);
    }
    if(x != NULL) Updata(x);
}

IL void Rank(Treap *x, int val){
    if(x == NULL) return;
    if(val < x -> key) Rank(x -> ch[0], val);   
    else{
        if(x -> ch[0] != NULL) cnt += x -> ch[0] -> size;
        if(x -> key == val) return;
        cnt += x -> num;
        Rank(x -> ch[1], val);
    }
}

IL void Add(RG int x, RG int y){  for(; x <= n; x += x & -x) Insert(root[x], y);  }

IL int Query(RG int x, RG int y){  cnt = 0; for(; x; x -= x & -x) Rank(root[x], y); return cnt;  } 

IL void Del(RG int x, RG int y){  for(; x <= n; x += x & -x) Delete(root[x], y);  }

IL void CDQ(RG int l, RG int r){
    if(l == r) return;
    RG int mid = (l + r) >> 1; CDQ(l, mid); CDQ(mid + 1, r);
    sort(p + l, p + r + 1);//可以归并排序
    for(RG int i = l; i <= r; i++)
        if(p[i].d <= mid) Add(p[i].b, p[i].c);
        else ans += Query(p[i].b, p[i].c);
    for(RG int i = l; i <= r; i++)
        if(p[i].d <= mid) Del(p[i].b, p[i].c);
}

int main(RG int argc, RG char* argv[]){
    n = Read();
    for(RG int i = 1; i <= n; i++) p[i].a = Read();
    for(RG int i = 1; i <= n; i++) p[i].b = Read();
    for(RG int i = 1; i <= n; i++) p[i].c = Read();
    for(RG int i = 1; i <= n; i++) p[i].d = i;
    CDQ(1, n);
    printf("%d
", ans);
    return 0;
}