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B. Company Income Growth

time limit per test

2 secondsmemory limit per test

64 megabytesinput

standard inputoutput

standard outputPetya 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.

Input

The first line contains an integer *n* (1 ≤ *n* ≤ 100). The next line contains *n* integers *a*_{i} ( - 100 ≤ *a*_{i} ≤ 100). The number *a*_{i} determines the income of BerSoft company in the (2000 + *i*)-th year. The numbers in the line are separated by spaces.

Output

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.

Examples

Input

10

-2 1 1 3 2 3 4 -10 -2 5

Output

5

2002 2005 2006 2007 2010

Input

3

-1 -2 -3

Output

0

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