After seeing Jaime Lannister in Winterfell, Bran gives him a problem. If Jaime can solve the problem then he can enter in Winterfell otherwise not.
There are n trees located (in winterfell) along the road at points with coordinates x1, x2, ..., xn. Each tree has its height hi. Woodcutters can cut down a tree and fell it to the left or to the right. After that it occupies one of the segments [xi - hi, xi] or [xi;xi + hi]. The tree that is not cut down occupies a single point with coordinate xi. Woodcutters can fell a tree if the segment to be occupied by the fallen tree doesn't contain any occupied point. The woodcutters want to process as many trees as possible. What is the maximum number of trees to fell.
Input:
The first line contains integer n (1 ≤ n ≤ 105) — the number of trees.
Next n lines contain pairs of integers xi, hi (1 ≤ xi, hi ≤ 109) — the coordinate and the height of the і-th tree.
The pairs are given in the order of ascending xi. No two trees are located at the point with the same coordinate.
Output:
Print a single number — the maximum number of trees that you can cut down by the given rules.
You can fell the trees like that: