Disks |
Solution |
Tests |

Consider N floating point numbers
**N** representing the radii of **N** disks. We fix a disk in the *xOy*
system, if we position it at a positive coordinate x (big enough), tangential
to the **0x** axis and above it and after that we push it to **0y** until
it becomes tangent to **0y** or to the first disk that it meets on the way.
In the configuration that results by fixing in order all the given disks, some
of them can be considered as being **dispensible, **because, if we eliminate
them, the total width of the configuration is the same, which means that there
is no disk that can be moved to the left.

Task

Identify all the indispensible disks for a given configuration.

Input format

The input file DISCURI.IN* *has
the following structure:

– the first line contains N, the number of disks;

– the next N* *lines contain
N* * real numbers representing the radii of the disks, in the order they
are fixed in the configuration.

Output format

The output file **DISCURI.OUT**
will have the following
structure:

- the first line will contain an integer K, representing the number of dispensable disks;
- each of the next K lines will contain the order number of the dispensable disks.

Constraints

- N<=10000

**Example: **(in the
configuration from above; the gray disks are dispensible)

DISCURI.IN 7 4 0.1 0.5 3 0.5 4 1 |
DISCURI.OUT 3 2 3 5 |

**Time limit:**
1 second/test