CF39B 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 $ a_{1} $ billion bourles, in $ 2002 $ — to $ a_{2} $ 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 $ y_{1} $ , $ y_{2} $ , ..., $ y_{k} $ ,so that in the year $ y_{1} $ the company income amounted to $ 1 $ billion bourles, in the year $ y_{2} $ — $ 2 $ billion bourles etc., in accordance with the perfect growth dynamics. Help him to choose the longest such sequence.

The first line contains an integer $ n $ ( $ 1

Output $ k $ — the maximum possible length of a perfect sequence. In the next line output the sequence of years $ y_{1} $ , $ y_{2} $ , ..., $ y_{k} $ . Separate the numbers by spaces. If the answer is not unique, output any. If no solution exist, output one number $ 0 $ .