| # 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. |