Drawing Arrows

On a line, $N$ points are given, and each point has one of $N$ colors. For convenience, colors are represented by numbers from 1 to $N$, and all point coordinates are distinct.

For each point $p$, we want to connect it to another point $q$ using a straight arrow that starts at $p$. Here, $q$ must be the point of the same color as $p$ that is closest to $p$. If two or more points are tied for closest, choose any one of them.

For each point $p$, draw a single arrow $\vec{\ell_{p}}$ going to the $q$ that satisfies the condition above. In particular, if no other point of the same color exists, then $\left|\vec{\ell_{p}}\right|=0$. Here $\left|\vec{\ell_{p}}\right|$ denotes the length of arrow $\vec{\ell_{p}}$.

For example, representing points as ordered pairs (coordinate, color), let $p_1$ = (0, 1), $p_2$ = (1, 2), $p_3$ = (3, 1), $p_4$ = (4, 1). The arrow of point $p_1$, $\left|\vec{\ell_{p_1}}\right|$, connects $p_1\rightarrow p_3$. The arrows of points $p_3$ and $p_4$, $\left|\vec{\ell_{p_3}}\right|$ and $\left|\vec{\ell_{p_4}}\right|$, connect $p_3\rightarrow p_4$ and $p_4\rightarrow p_3$ respectively. For point $p_2$, no other point of the same color exists. Therefore the sum of all arrow lengths is $\left|\vec{\ell_{p_1}}\right|+\left|\vec{\ell_{p_2}}\right|+\left|\vec{\ell_{p_3}}\right|+\left|\vec{\ell_{p_4}}\right|=3+0+1+1=5$.

Given the coordinates and colors of the points, write a program that prints the sum of the lengths of the arrows starting at all points, that is, $\displaystyle\sum_{p}\left|\vec{\ell_{p}}\right|$.

The standard input provides the following information. The first line contains an integer $N$, the number of points. Each of the next $N$ lines contains two integers $x$ and $y$, representing the coordinate and color of a point.

Print the sum of the lengths of the arrows starting at all points to standard output.

In every subtask, the coordinate $x$ and color $y$ of a point satisfy 0 ≤ $x$ ≤ 109 and 1 ≤ $y$ ≤ $N$ respectively.