D. Pair of Topics

D. Pair of Topics

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

The next lecture in a high school requires two topics to be discussed. The ii-th topic is interesting by aiai units for the teacher and by bibi units for the students.

The pair of topics ii and jj (i<ji<j) is called good if ai+aj>bi+bjai+aj>bi+bj (i.e. it is more interesting for the teacher).

Your task is to find the number of good pairs of topics.

Input

The first line of the input contains one integer nn (2≤n≤2⋅1052≤n≤2⋅105) — the number of topics.

The second line of the input contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤1091≤ai≤109), where aiai is the interestingness of the ii-th topic for the teacher.

The third line of the input contains nn integers b1,b2,…,bnb1,b2,…,bn (1≤bi≤1091≤bi≤109), where bibi is the interestingness of the ii-th topic for the students.

Output

Print one integer — the number of good pairs of topic.

Examples

input

Copy

5
4 8 2 6 2
4 5 4 1 3

output

Copy

7

input

Copy

4
1 3 2 4
1 3 2 4

output

Copy

0

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int main()
{
    ll n;
    scanf("%lld",&n);
    ll a[n];
    for(ll i=0; i<n; i++)
        scanf("%lld",&a[i]);
    for(ll i=0; i<n; i++)
    {
        ll x;
        scanf("%lld",&x);
        a[i]-=x;
    }
    sort(a,a+n);
    ll l=0;
    ll r=n-1;
    ll sum=0;
    while(l<r)
    {
       if(a[l]+a[r]>0)
       {
           sum+=r-l;
           r--;
       }
       else l++;
    }
    printf("%lld\n",sum);
    return 0;
}