Darko has a new imaginary extraterrestrial friend with a billion fingers. The extraterrestrial has soon taken hold of his guitar, found a simple melody online, and started playing it.

The guitar, as usual, has six strings denoted by numbers $1$ through $6$. Each string is divided into $P$ frets denoted by numbers $1$ through $P$.

A melody is a sequence of tones, where each tone is produced by picking a string pressed on a specific fret (e.g., $4^{\text{th}}$ string pressed on the $8^{\text{th}}$ fret). If a string is pressed on several frets, the produced tone will be the one corresponding to the highest of those frets.

For instance, if the $3^{\text{rd}}$ string is already pressed on the $5^{\text{th}}$ fret, and the tone which corresponds to the $7^{\text{th}}$ fret is to be produced, the string can be pressed on the $7^{\text{th}}$ fret and picked without releasing the $5^{\text{th}}$ fret, since only the highest one affects the tone produced ($7^{\text{th}}$ in this case). Similarly, if a tone that corresponds to the $2^{\text{nd}}$ fret on the same string is next to be produced, it is necessary to release both $5^{\text{th}}$ and $7^{\text{th}}$ frets.

Write a program which computes the minimum number of finger movements needed to produce the given melody. Note that press or release a single fret counts as one finger move. String picking does not count as a finger move, but rather a guitar pick move.

Input Specification

The first line of input contains two positive integers separated by a single space, $N$ $(N\le 500000)$ and $P$ $(2\le P\le 300000)$. They represent the number of tones in the melody and the number of frets, respectively.

The following $N$ lines describe the fields for the corresponding tones – the ordinal of the string and the ordinal of the fret, respectively, in the same order as the extraterrestrial plays them.

Output Specification

In a single line of output, print the minimum number of finger movements.

Sample Input 1

5 15
2 8
2 10
2 12
2 10
2 5

Sample Output 1

7

Explanation for Sample Output 1

All the tones played are produced by picking the $2^{\text{nd}}$ string. First, the frets $8$, $10$, $12$ are pressed, in order (three movements). Then, the ${12}^{\text{th}}$ fret is released to produce the second tone again (fourth movement). Finally, the $5^{\text{th}}$ fret is pressed followed by the release of frets $10$ and $12$ (a total of seven movements).

Sample Input 2

7 15
1 5
2 3
2 5
2 7
2 4
1 5
1 3

Sample Output 2

9

Explanation for Sample Output 2

$1$, $1$, $1$, $1$, $3$, $0$, $2$ finger movements are necessary, in the order of the seven tones produced.