Tulip Bouquet

Lieke, inspired by a visit to one of the world's largest gardens, decided to create a beautiful bouquet using wild roadside tulips. However, she must comply with the Dutch Tulip Protection Act. There are N tulips arranged along a road from left to right, numbered from 0 to N-1. Each tulip i is assigned two integers \(l_i\) and \(r_i\). If tulip i is included in the bouquet, then the l_i tulips immediately to its left and the r_i tulips immediately to its right (even if fewer exist) cannot be included in the bouquet.

In other words, if you select a tulip i, then for the chosen set of indices \(i_1 < i_2 < \cdots < i_k\), for every consecutive pair \(i_j\) and \(i_{j+1}\) the following conditions must hold:

• \(i_{j+1} \ge i_j + r_{i_j} + 1\) (tulip i_j forbids the next \(r_{i_j}\) tulips) and
• \(i_{j+1} \ge i_j + l_{i_{j+1}} + 1\) (tulip i_{j+1}'s left neighbors must be clear).

Your task is to help Lieke by computing the maximum number of tulips that she can collect to form a legal bouquet.

inputFormat

The first line contains a single integer N (the number of tulips).
Each of the following N lines contains two integers l_i and r_i, describing the exclusion counts for the tulip with index i.

outputFormat

Print a single integer denoting the maximum number of tulips that can be collected while obeying the protection law.

sample

5
0 0
0 0
0 0
0 0
0 0

5