**********************************************************************
                           BRONZE PROBLEMS
**********************************************************************
                  Four problems numbered 11 through 14
**********************************************************************

Problem 11: Binary Numbers [Traditional, 2004]

Given a positive integer A (0 <= A <= 2,110,000,000), print its binary
(base two) representation (without extra leading zeroes, of course). Do not
use automatic conversion routines or automatic binary printing routines.

PROBLEM NAME: binnum

INPUT FORMAT:

* Line 1: An integer

SAMPLE INPUT (file binnum.in):

277309

OUTPUT FORMAT:

* Line 1: The binary representation of the input integer

SAMPLE OUTPUT (file binnum.out):

1000011101100111101

**********************************************************************

Problem 12: Bank Balance [Rob Kolstad, 2004]

Alice, Betsy, Corinne, and Debra have opened bank accounts. The
bank has kept a central ledger of their deposits (money into the
bank) and withdrawals (money out of the bank). They are good financial
citizens and never withdraw more money than they have.

Given the ledger (see format below), print the amount of money each
has in the bank after the ledger's transactions are completed. The
initial balance for each is, of course, 0. All numbers fit into 32 bit
integers.

PROBLEM NAME: bankbal

INPUT FORMAT:

* Line 1: A single integer N, the number of transactions

* Lines 2..N+1: Each line contains a single transaction with two
        fields. The first field is    the name of the person
        performing the transaction. The second field is a number: if
        positive, the number is a deposit; if negative, the number is
        a withdrawal.

SAMPLE INPUT (file bankbal.in):

6
Alice +100
Corinne +100
Betsy +200
Alice -10
Debra +10
Betsy -100

INPUT DETAILS:

Alice deposits 100; so does Corrinne. Betsy deposits 200.  Alice takes out
10; Debra puts in 10.  Betsy takes out 100. The input never contains names
other than 'Alice', 'Betsy', 'Corinne', and 'Debra'.

OUTPUT FORMAT:

* Lines 1..4: Each line tells the name and balance of one of the
        depositors. The depositors are listed in alphabetical order.

SAMPLE OUTPUT (file bankbal.out):

Alice 90
Betsy 100
Corinne 100
Debra 10

**********************************************************************

Problem 13: Satellite Photo [Brian Dean, 2004]

Farmer John always wanted a good map of his farm, so he purchased
a satellite photograph of his land which is represented by R (1 <=
R <= 75) rows and C (1 <= C <= 75) columns in the photo.  One part
of a photo looks something like this:

..................
..#####.......##..
..#####......##...
..................
#.......###.....#.
#.....#####.......
      
In trying to interpret the photo, he figures that every connected
shape is either a barn or a cow.  A "connected shape" is a set of
one or more #'s that are adjacent to each other either vertically
or horizontally. The following would be two distinct "connected
shapes":

....
.#..
..#.
....

FJ claims that a connected shape is a barn if it is a filled-in
rectangle whose four sides are parallel to the x and y axes. In the
first photo above, there are three barns (sizes 2x1, 2x5, and 1x1)
and two cows (you'd be surprised at the size of some of FJ's cows!).
Count the number of barns and cows in his satellite photo.

A cow never completely encircles another cow or barn.

PROBLEM NAME: satel

INPUT FORMAT:

* Line 1: Two space-separated integers: R and C.

* Lines 2..R+1: Line i+1 represents row i of the photograph and
        contains C characters (and no spaces).

SAMPLE INPUT (file satel.in):

5 8
#####..#
#####.##
......#.
.###...#
.###..##

INPUT DETAILS:

The photo consists of 5 lines, each of which is 8 characters long.

OUTPUT FORMAT:

* Line 1: The number of barns in the photo.

* Line 2: The number of cows in the photo.

SAMPLE OUTPUT (file satel.out):

2
2

OUTPUT DETAILS:

The photo has 2 barns (the shapes on the left) and 2 cows (on the right).

**********************************************************************

Problem 14: Plate Stacking [Rob Kolstad, 2005]

The cows want to be on TV. They've decided their best chance is to
demonstrate their prowess in stacking plates as high as they possibly
can.  They hope to maximize entertainment value by stacking certain
plates that are thrown from stage left toward stage center.

Of course, plates can only be stacked when a strictly smaller plate
is stacked upon a larger plate. Thus, some plates might be discarded.

Given the sequence of integer of N (1 <= N <= 5,000) plate thrown
from the side of the stage, calculate the height (in plates) of the
tallest possible plate-stacking structure that can be build.  Sizes
are integers in the range 1..1,000,000.

If the plates were thrown on this order:

     7 10 7 8 9 7 8 6 4

Then the tallest possible stack would be 10, 9, 8, 6, 4 whose height is 5.

Solve this problem perfectly to earn an invitation to the Silver division.

PROBLEM NAME: plates

INPUT FORMAT:

* Line 1: A single integer, N

* Lines 2..N+1: Line i+1 describes the i_th plate tossed from the side
        of the stage.

SAMPLE INPUT (file plates.in):

9
7
10
7
8
9
7
8
6
4

OUTPUT FORMAT:

* Line 1: A single line with the maximum height of plates that can be
        stacked.

SAMPLE OUTPUT (file plates.out):

5

**********************************************************************