Cottage Village

## 题目描述 给定一个坐标轴，轴上有 $n$ 座房子，每座房子的位置是 $x_i$，边长是 $a_i$。有个人想要贴着其中一座房子建造一座他自己的边长为 $t$ 的房子，请输出共有多少种建造方法。 ## 输入格式 第一行输入两个正整数 $n,t$。 接下来 $n$ 行，每行输入两个以空格分隔的整数 $x_i,a_i$。 ## 输出格式 输出共 $1$ 行，输出边长为 $t$ 的房子有多少种建造方法。 ## 数据范围 $1\le n,t\le10^3$，$0\le|x_i|\le10^3$，$1\le a_i\le10^3$。 --- 译自[残阳如血](/user/726139)。

A new cottage village called «Flatville» is being built in Flatland. By now they have already built in «Flatville» $n$ square houses with the centres on the $Ox$ -axis. The houses' sides are parallel to the coordinate axes. It's known that no two houses overlap, but they can touch each other. The architect bureau, where Peter works, was commissioned to build a new house in «Flatville». The customer wants his future house to be on the $Ox$ -axis, to be square in shape, have a side $ t $ , and touch at least one of the already built houses. For sure, its sides should be parallel to the coordinate axes, its centre should be on the $ Ox $ -axis and it shouldn't overlap any of the houses in the village. Peter was given a list of all the houses in «Flatville». Would you help him find the amount of possible positions of the new house?

The first line of the input data contains numbers $ n $ and $ t $ ( $ 1<=n,t<=1000 $ ). Then there follow $ n $ lines, each of them contains two space-separated integer numbers: $ x_{i} $ $ a_{i} $ , where $ x_{i} $ — $ x $ -coordinate of the centre of the $ i $ -th house, and $ a_{i} $ — length of its side ( $ -1000<=x_{i}<=1000 $ , $ 1<=a_{i}<=1000 $ ).

Output the amount of possible positions of the new house.

2 2
0 4
6 2

4

2 2
0 4
5 2

3

2 3
0 4
5 2

2

It is possible for the $ x $ -coordinate of the new house to have non-integer value.