CF842B.Gleb And Pizza

Gleb ordered pizza home. When the courier delivered the pizza, he was very upset, because several pieces of sausage lay on the crust, and he does not really like the crust.

The pizza is a circle of radius r and center at the origin. Pizza consists of the main part — circle of radius r - d with center at the origin, and crust around the main part of the width d. Pieces of sausage are also circles. The radius of the i -th piece of the sausage is r__i, and the center is given as a pair (x__i, y__i).

Gleb asks you to help determine the number of pieces of sausage caught on the crust. A piece of sausage got on the crust, if it completely lies on the crust.

格列布在家订购了披萨。当快递员将披萨送到时，他非常不高兴，因为几片香肠落在了披萨的饼边（crust）上，而他其实并不喜欢饼边。

披萨是一个以原点为圆心、半径为 $r$ 的圆形。披萨由主体部分和围绕主体的饼边组成：主体部分是以原点为圆心、半径为 $r - d$ 的圆形；饼边是围绕主体部分、宽度为 $d$ 的环形区域。香肠片也是圆形。第 $i$ 片香肠的半径为 $r_i$，其中心坐标为 $(x_i, y_i)$。

格列布请你帮忙计算有多少片香肠完全落在饼边上。一片香肠“落在饼边上”，当且仅当该香肠片完全位于饼边区域内。

First string contains two integer numbers r and d (0 ≤ d < r ≤ 500) — the radius of pizza and the width of crust.

Next line contains one integer number n — the number of pieces of sausage (1 ≤ n ≤ 105).

Each of next n lines contains three integer numbers x__i, y__i and r__i ( - 500 ≤ x__i, y__i ≤ 500, 0 ≤ r__i ≤ 500), where x__i and y__i are coordinates of the center of i-th peace of sausage, r__i — radius of i-th peace of sausage.

第一行包含两个整数 $r$ 和 $d$（$0 \leq d < r \leq 500$）——分别为披萨的半径和饼边（crust）的宽度。

下一行包含一个整数 $n$——香肠片的数量（$1 \leq n \leq 10^5$）。

接下来的 $n$ 行中，每行包含三个整数 $x_i$、$y_i$ 和 $r_i$（$-500 \leq x_i, y_i \leq 500$，$0 \leq r_i \leq 500$），其中 $x_i$ 和 $y_i$ 是第 $i$ 片香肠中心的坐标，$r_i$ 是第 $i$ 片香肠的半径。

Output the number of pieces of sausage that lay on the crust.

输出位于披萨饼边上的香肠片数量。

Below is a picture explaining the first example. Circles of green color denote pieces of sausage lying on the crust.

下图解释了第一个示例。绿色圆圈表示位于披萨饼皮上的香肠片。