Problem:
Score : 300 points

Problem Statement

The season for Snuke Festival has come again this year. First of all, Ringo will perform a ritual to summon Snuke. For the ritual, he needs an altar, which consists of three parts, one in each of the three categories: upper, middle and lower.

He has N parts for each of the three categories. The size of the i-th upper part is A_i, the size of the i-th middle part is B_i, and the size of the i-th lower part is C_i.

To build an altar, the size of the middle part must be strictly greater than that of the upper part, and the size of the lower part must be strictly greater than that of the middle part. On the other hand, any three parts that satisfy these conditions can be combined to form an altar.

How many different altars can Ringo build? Here, two altars are considered different when at least one of the three parts used is different.

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9(1\leq i\leq N)

1 \leq B_i \leq 10^9(1\leq i\leq N)

1 \leq C_i \leq 10^9(1\leq i\leq N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N
B_1 ... B_N
C_1 ... C_N

Output

Print the number of different altars that Ringo can build.

Sample Input 1

2
1 5
2 4
3 6

Sample Output 1

3

The following three altars can be built:

Upper: 1-st part, Middle: 1-st part, Lower: 1-st part

Upper: 1-st part, Middle: 1-st part, Lower: 2-nd part

Upper: 1-st part, Middle: 2-nd part, Lower: 2-nd part

Sample Input 2

3
1 1 1
2 2 2
3 3 3

Sample Output 2

27

Sample Input 3

6
3 14 159 2 6 53
58 9 79 323 84 6
2643 383 2 79 50 288

Sample Output 3

87

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

//  Created by conan1024hao in 2019.
//  Copyright © 2019 conan1024hao. All rights reserved.
//  専用ライブラリです、自由にコピーして構いません。
//  感谢看我的代码！Wechat:conan1024hao QQ:810396815
#pragma GCC optimize ("O3")
#include <iostream>
#include <iomanip>
#include <istream>
#include <ostream>
#include <sstream>
#include <iterator>
#include <vector>
#include <algorithm>
#include <queue>
#include <deque>
#include <list>
#include <stack>
#include <map>
#include <set>
#include <utility>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <string>
#include <ctime>
#include <cctype>
#include <cstdlib>
#define INF 10e16
#define MOD 1000000007
#define rep(i, a, n) for (ll i = a; i < (ll)(n); i++)
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define mmax(x,y)(x>y?x:y)
#define mmin(x,y)(x<y?x:y)
#define chmax(x,y) x=mmax(x,y)
#define chmin(x,y) x=mmin(x,y)
#define all(x) (x).begin(),(x).end()
#define siz(x) (ll)(x).size()
#define PI acos(-1.0)
using namespace std;
//using Int=int_fast64_t;
typedef long long int ll;
typedef pair<ll,ll>Pll;
typedef pair<int,int>Pin;
long long GCD(long long a, long long b) { return b ? GCD(b, a%b) : a; }
long long LCM(long long a, long long b)  {return a/GCD(a,b)*b;}
int dx[8]={-1,0,1,0,1,1,-1,-1};
int dy[8]={0,-1,0,1,1,-1,1,-1};
char dir[4]={'u','l','d','r'};
ll cmp1(pair<ll,string>a,pair<ll,string> b){
        if(a.fi!=b.fi)
        return a.fi<b.fi;
        else
        return a.se<b.se;
}
//--------------------------------------------------------------------------
int n;double ans=0;
int cnt=0;
void dfs(double t,int m1,int m2,int m3){
    if(m1==0&&m2==0&&m3==0){
        ans+=t;
        cnt++;
        return;
    }
    t+=(double)n/(m1+m2+m3);
    //cout<<t<<endl;
    
   
        if(m1)
        dfs(t,m1-1,m2,m3);
        if(m2)
        dfs(t,m1+1,m2-1,m3);
        if(m3)
        dfs(t,m1,m2+1,m3-1);
    
}
//---------------------------------------------------------------------------
int main(){//問題をちゃんと見ろ!!!!!!!!!!!!!!!!!      llか??????????        memset()!!!!!!!!!!!!
    cin.tie(0);
    ios::sync_with_stdio(false);
    //-------------------------------
    int n;cin>>n;
    vector<ll>a(n);for(int i=0;i<n;i++)cin>>a[i];
    vector<ll>b(n);for(int i=0;i<n;i++)cin>>b[i];
    vector<ll>c(n);for(int i=0;i<n;i++)cin>>c[i];
    sort(all(a));sort(all(b));sort(all(c));
    ll ans=0;
    ll cob[100001];
    ll sb[100001];
    memset(cob,0,sizeof(cob));
    memset(sb,0,sizeof(sb));
    int nc=0;
    for(int i=0;i<n;i++){
        for(nc;nc<n;){
            while(c[nc]<=b[i])
                nc++;
            cob[i]=n-nc;
            break;
        }
    }
    sb[n-1]=cob[n-1];
    for(int i=n-2;i>=0;i--){
        sb[i]=sb[i+1]+cob[i];
    }
    vector<ll>::iterator nowb=b.begin();
    for(int i=0;i<n;i++){
        auto m=upper_bound(nowb,b.end(),a[i]);
        ans+=sb[m-b.begin()];
        nowb=m;
    }
    cout<<ans<<endl;
    //-------------------------------
    return 0;
}
//---------------------------------------------------------------------------