B. Company Income Growth
time limit per test
2 seconds
memory limit per test
64 megabytes
input
standard input
output
standard output

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 22 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