425_D. Sereja and Squares
Problem Description
Sereja has painted n distinct points on the plane. The coordinates of each point are integers. Now he is wondering: how many squares are there with sides parallel to the coordinate axes and with points painted in all its four vertexes? Help him, calculate this number.
Input
The first line contains integer n (1 ≤ n ≤ 105). Each of the next n lines contains two integers xi, yi (0 ≤ xi, yi ≤ 105), the integers represent the coordinates of the i-th point. It is guaranteed that all the given points are distinct.
Output
In a single line print the required number of squares.
Examples
Input
5 0 0 0 2 2 0 2 2 1 1
Output
1
Input
9 0 0 1 1 2 2 0 1 1 0 0 2 2 0 1 2 2 1
Output
5
Contest Information
- Contest ID: 425
- Problem Index: D
- Points: 2000.0
- Rating: 2300
- Tags: binary search, data structures, hashing
- Time Limit: {'seconds': 2, 'nanos': 0} seconds
- Memory Limit: 512000000 bytes
Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.