Codeforces Round #341 (Div. 2)B

B. Wet Shark and Bishops

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Today, Wet Shark is given n bishops on a 1000 by 1000 grid. Both rows and columns of the grid are numbered from 1 to 1000. Rows are numbered from top to bottom, while columns are numbered from left to right.

Wet Shark thinks that two bishops attack each other if they share the same diagonal. Note, that this is the only criteria, so two bishops may attack each other (according to Wet Shark) even if there is another bishop located between them. Now Wet Shark wants to count the number of pairs of bishops that attack each other.

Input

The first line of the input contains n (1 ≤ n ≤ 200 000) — the number of bishops.

Each of next n lines contains two space separated integers x_i and y_i (1 ≤ x_i, y_i ≤ 1000) — the number of row and the number of column where i-th bishop is positioned. It's guaranteed that no two bishops share the same position.

Output

Output one integer — the number of pairs of bishops which attack each other.

Sample test(s)

Input

5
1 1
1 5
3 3
5 1
5 5

Output

6

Input

3
1 1
2 3
3 5

Output

0

Note

In the first sample following pairs of bishops attack each other: (1, 3), (1, 5), (2, 3), (2, 4), (3, 4) and (3, 5). Pairs (1, 2), (1, 4), (2, 5) and (4, 5) do not attack each other because they do not share the same diagonal.

题意：棋盘上象可以互相攻击（象只能在斜率为1 -1上攻击）

输入n个象 判断有多少种攻击配对

题解： 斜率为1的 x-y的值相同

斜率为-1的x+y的值相同   （都在同一对角线上）

数组标记 或map标记

每条线上的配对数量 fun（）实现

#include<bits/stdc++.h>
using namespace std;
#define ll __int64
int flag[4005];
int flag1[4005];
ll fun(ll n,ll m)
{
    ll sum=1;
    for(ll i=1,j=n;i<=m;i++,j--)
        sum=sum*j/i;
    return sum;
}
int main()
{
    ll x,y,z,i;
    scanf("%I64d",&x);
    for(i=0;i<x;i++)
    {
        scanf("%I64d%I64d",&y,&z);
        flag[y+z]++;
        flag1[y-z+1000]++;
    }
    ll ans=0;
    for(i=0;i<=3000;i++)
    {
        if(flag[i])
        ans+=fun(flag[i],2);
        if(flag1[i])
        ans+=fun(flag1[i],2);
    }
    printf("%I64d\n",ans);
    return 0;
}