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: Accepted)

#include <iostream>
#include <stack>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <string>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <tuple>
#include <algorithm>
#include <functional>
#include <cstring>
#include <limits.h>
#define FOR(i,k,n)  for (int i=(k); i<(int)(n); ++i)
#define REP(i,n)    FOR(i,0,n)
#define FORIT(i,c)	for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)
#define SZ(i) ((int)i.size())
#define pb          push_back
#define mp          make_pair
#define mt          make_tuple
#define get0(x)     (get<0>(x))
#define get1(x)     (get<1>(x))
#define get2(x)     (get<2>(x))
#define ALL(X)      (X).begin(),(X).end()
#define LLMAX       9223372036854775807LL
#define LLMIN       -9223372036854775808LL
#define IMAX        2147483647
#define IMIN        -2147483648
typedef long long LL;
using namespace std;

class RangeAddRangeSum {
    public:
        int N;
        vector<int> dat, sum_dat;
        RangeAddRangeSum(int n) {
            N = 1;
            while(N < n) N <<= 1;
            dat.assign(2*N-1, 0);
            sum_dat.assign(2*N-1, 0);
        }

        void add(int a, int b, int x) { add(a,b,x,0,0,N); }
        int add(int a, int b, int x, int k, int l, int r) {
            if(b <= l or r <= a) return dat[k];
            if(a <= l and r <= b) {
                sum_dat[k] += x;
                return dat[k] += x*(r-l);
            }
            const int m = (l+r)/2;
            return dat[k] = add(a,b,x,2*k+1,l,m)+add(a,b,x,2*k+2,m,r)+sum_dat[k]*(min(r,b)-max(l,a));
        }

        int sum(int a, int b) { return sum(a,b,0,0,N); }
        int sum(int a, int b, int k, int l, int r) {
            if(b <= l or r <= a) return 0;
            if(a <= l and r <= b) return dat[k];
            const int m = (l+r)/2;
            return sum(a,b,2*k+1,l,m)+sum(a,b,2*k+2,m,r)+sum_dat[k]*(min(r,b)-max(l,a));
        }
};

int main(void){
    int N;
    // cin>>N;
    scanf("%d",&N);
    vector<LL> ABC[3];
    REP(i,3){
        REP(j,N){
            LL x;
            // cin>>x;
            scanf("%lld",&x);
            ABC[i].pb(x);
        }
        sort(ALL(ABC[i]));
    }
    LL ans=0;
    // RangeAddRangeSum rsq(N);
    vector<LL> dat(N);
    REP(i,N){
        // rsq.add(i,i+1,ABC[2].end()-upper_bound(ALL(ABC[2]),ABC[1][i]));
        dat[i]=ABC[2].end()-upper_bound(ALL(ABC[2]),ABC[1][i]);
    }
    LL sum=0;
    LL index=N-1;
    // REP(i,N){
    for(int i=N-1;0<=i;i--){
        // ans+=rsq.sum(upper_bound(ALL(ABC[1]),ABC[0][i])-ABC[1].begin(),N);
        int j=upper_bound(ALL(ABC[1]),ABC[0][i])-ABC[1].begin();
        while(j<=index){
            sum+=dat[index];
            index--;
        }
        ans+=sum;
    }
    cout<<ans<<endl;
   return 0;
}