There are only two directions in Perpendicularia: vertical and horizontal. Perpendicularia government are going to build a new secret service facility. They have some proposed facility plans and want to calculate total secured perimeter for each of them.</p>

The total secured perimeter is calculated as the total length of the facility walls invisible for the perpendicularly-looking outside observer. The figure below shows one of the proposed plans and corresponding secured perimeter.

Write a program that calculates the total secured perimeter for the given plan of the secret service facility.

입력 형식

The plan of the secret service facility is specified as a polygon.</p>

The first line of the input contains one integer n — the number of vertices of the polygon (4 ≤ n ≤ 1000). Each of the following n lines contains two integers x_i and y_i – the coordinates of the i-th vertex (−10⁶ ≤ x_i, y_i ≤ 10⁶). Vertices are listed in the consecutive order.

All polygon vertices are distinct and none of them lie at the polygon’s edge. All polygon edges are either vertical (x_i = x_i+1 or horizontal (y_i = y_i+1) and none of them intersect each other.

출력 형식

Output a single integer — the total secured perimeter of the secret service facility.

예제 입력

10
1 1
6 1
6 4
3 4
3 3
5 3
5 2
2 2
2 3
1 3

예제 출력

6