Shooting section#9066
After Atreus successfully mastered archery with the "Claw" bow, Faye decided not to stop there and opened an entire archery club.
At the first session of the club, students showed up. Faye numbered them with integers from to . At the beginning of the session, the students lined up along a coordinate line, which had been drawn on the floor in advance. The -th student stood at the point with coordinate x_i. The coordinates of the students strictly increase, that is, x_i < x_{i+1} for all from to n - 1.
Each student has a magical bow characterized by a range r_i and a strength c_i — both parameters are positive integers. When a student fires an arrow, the magical projectile begins to move along the coordinate line in the direction of increasing coordinates. The strength of the projectile is initially equal to c_i, and every time it travels r_i units of distance, its strength decreases by one. The projectile continues flying as long as its strength remains positive.
If a projectile reaches the next student in order along the line, it immediately stops, and the student who was hit by the projectile instantly fires their own shot — even if the projectile reached them with strength zero.
Faye wants each student to fire at least once. To achieve this, she may personally instruct some of the students to shoot — which may trigger a chain reaction of other students shooting as a result.
Help Faye determine the minimum number of students she needs to command to shoot so that, eventually, every student fires at least once.
The first line contains a single integer n~(1 \le n \le 1000) — the number of students in Faye's club.
Each of the following lines contains three integers: x_i, r_i, and c_i~(1 \le x_i \le 10^9,~1 \le r_i, c_i \le 100) — the coordinate of the student, the range, and the strength of their bow.
It is guaranteed that the coordinates are strictly increasing: x_i < x_{i+1} for all from to n - 1.
Print a single integer — the minimum number of students Faye needs to command to shoot, so that in the end, every student fires at least once.
Example 1