Toppling Dominoes (Small)

$N$ dominoes stand in a row on a number line. Domino $i$ stands at position $X_i$ with height $H_i$, and no two dominoes share a position.

Hongjun can pick one domino and push it over to the left or to the right. When a domino of height $h$ at position $x$ falls to the left, every domino whose position is at least $x-h$ and at most $x$ falls to the left. When it falls to the right, every domino whose position is at least $x$ and at most $x+h$ falls to the right. A domino knocked over this way keeps the same direction and topples the dominoes around it in turn, and the chain continues until nothing is left to fall.

Hongjun wants every domino on the ground with as few pushes of his hand as possible. Write a program that computes how many pushes he needs.

The first line contains the number of dominoes $N$. ($1 \le N \le 300$)

Each of the next $N$ lines contains two integers $X_i$ and $H_i$, the position and the height of one domino, separated by a space. ($1 \le X_i, H_i \le 2\,000\,000\,000$)

The dominoes are not necessarily given in order of position.

Print on the first line the minimum number of pushes needed to topple every domino.