CF15A.Cottage Village

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 Оx-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 Оx-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?

一座名为“Flatville”的新别墅区正在Flatland地区建设中。截至目前，Flatville 已建成 $n$ 座正方形房屋，所有房屋的中心均位于 $Ox$ 轴上，且房屋各边均与坐标轴平行。已知任意两座房屋不会重叠，但可以相互接触。

彼得所在的建筑设计事务所承接了在 Flatville 新建一座房屋的任务。客户希望其未来住宅也位于 $Ox$ 轴上、呈正方形、边长为 $t$，且至少与一座已建成的房屋相接触。当然，该房屋各边必须与坐标轴平行，其中心必须位于 $Ox$ 轴上，且不能与村中任何已有房屋重叠。

彼得已获得 Flatville 所有房屋的列表。您能否帮助他计算出新建房屋可能的位置数量？

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).

输入数据的第一行包含两个整数 $n$ 和 $t$（$1 \leq n, t \leq 1000$）。接下来有 $n$ 行，每行包含两个用空格分隔的整数 $x_i$ 和 $a_i$，其中 $x_i$ 表示第 $i$ 座房屋中心的 $x$ 坐标，$a_i$ 表示其边长（$-1000 \leq x_i \leq 1000$，$1 \leq a_i \leq 1000$）。

Output the amount of possible positions of the new house.

输出新房子可能的位置数量。

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

新房子的 x 坐标可以取非整数值。