The Climbing Wall   climbing.X

One of the most popular attractions at the county fair is the
climbing wall. Bessie wants to plan her trip up the wall in advance
and needs your help.

The wall is 30,000 millimeters wide and H (1001 <= H <= 30,000)
millimeters high and has F (1 <= F <= 10,000) hoof-holds at unique
X,Y coordinates expressed in millimeters. 0,0 is at the ground level
on the left side of the wall. Hoof-holds are separated by at least
300 millimeters since no cow can use them if they are spaced
closer than that! Bessie knows there is at least one way up.

Bessie, through techniques only she knows, uses successive single
hoof-holds to climb the wall. She can only move from one hoof-hold
to another if they are no more than one meter apart. She can, of
course, move up, down, right, left or some combination of these in
each move. Similarly, once she gets to a hoof-hold that is at least
(H-1000) millimeters above the ground, she can nimbly climb from there
onto the platform atop the wall. Bessie can start at any X location
that has a Y location <= 1000 millimeters.

Given the height of the wall and the locations of the hoof-holds,
determine the smallest number of hoof-holds Bessie should use to
reach the top.

PROBLEM NAME: climbing.X

INPUT FORMAT:

* Line 1: Two space-separated integers, H and F.

* Lines 2..F+1: Each line contains two space-separated integers
        (respectively X and Y) that describe a hoof-hold. X is the
        distance from the left edge of the climbing wall; Y is the
        distance from the ground.

SAMPLE INPUT:

3000 5
600 800
1600 1800
100 1300
300 2100
1600 2300

INPUT DETAILS:

The wall is three meters high with 5 hoof-holds.

OUTPUT FORMAT:

* Line 1: A single integer that is the smallest number of hoof-holds
        Bessie must use to reach the top of the climbing wall.

SAMPLE OUTPUT:

3

OUTPUT DETAILS:

Bessie can start on the ground, move to the hoof-hold at (600,800), move
from there to (100,1300), move from there to (300,2100), and from that high
height can hop onto the platform. This trip requires three hoof-holds. 
There is no shorter path that Bessie can take.