Sereja and Squares

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

inputFormat

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.

outputFormat

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

样例

5
0 0
0 2
2 0
2 2
1 1

1

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