B"You are a paparazzi working in Manhattan. Manhattan has r south-to-north streets, denoted by numbers 1, 2, ldots, r in order from west to east, and r west-to-east streets, denoted by numbers 1,2, ldots,r in order from south to north. Each of the r south-to-north streets intersects each of the r west-to-east streets; the intersection between the x -th south-to-north street and the y -th west-to-east street is denoted by (x, y) . In order to move from the intersection (x,y) to the intersection (x', y') you need |x-x'|+|y-y'| minutes. You know about the presence of n celebrities in the city and you want to take photos of as many of them as possible. More precisely, for each i=1, ... , n , you know that the i -th celebrity will be at the intersection (x_i, y_i) in exactly t_i minutes from now (and he will stay there for a very short time, so you may take a photo of him only if at the t_i -th minute from now you are at the intersection (x_i, y_i) ). You are very good at your job, so you are able to take photos instantaneously. You know that t_i < t_{i+1} for any i=1,2, ldots, n-1 . Currently you are at your office, which is located at the intersection (1, 1) . If you plan your working day optimally, what is the maximum number of celebrities you can take a photo of? The first line of the input contains two positive integers r, n ( 1 <= r <= 500 , 1 <= n <= 100,000 ) xe2 x80 x93 the number of south-to-north/west-to-east streets and the number of celebrities. Then n lines follow, each describing the appearance of a celebrity. The i -th of these lines contains 3 positive integers t_i, x_i, y_i ( 1 <= t_i <= 1,000,000 , 1 <= x_i, y_i <= r ) -- denoting that the i -th celebrity will appear at the intersection (x_i, y_i) in t_i minutes from now. It is guaranteed that t_i<t_{i+1} for "...