Company Income Growth

Petya works as a PR manager for a successful Berland company BerSoft. He needs to prepare a presentation on the company income growth since 2001 (the year of its founding) till now. Petya knows that in 2001 the company income amounted to a₁ billion bourles, in 2002 — to a₂ billion, ..., and in the current (2000 + n)-th year — a_n billion bourles. On the base of the information Petya decided to show in his presentation the linear progress history which is in his opinion perfect. According to a graph Petya has already made, in the first year BerSoft company income must amount to 1 billion bourles, in the second year — 2 billion bourles etc., each following year the income increases by 1 billion bourles. Unfortunately, the real numbers are different from the perfect ones. Among the numbers a_i can even occur negative ones that are a sign of the company’s losses in some years. That is why Petya wants to ignore some data, in other words, cross some numbers a_i from the sequence and leave only some subsequence that has perfect growth.

Thus Petya has to choose a sequence of years y₁, y₂, ..., y_k,so that in the year y₁ the company income amounted to 1 billion bourles, in the year y₂ — 2 billion bourles etc., in accordance with the perfect growth dynamics. Help him to choose the longest such sequence.