ACM Programming Contest
                            Problem 1
                                 
                                 
For this problem you are to write a program that  takes  as input
two numbers which are the base  and height  of  a rectangle, Your
program should print out the border of the rectangle using +, and
the inside using =. The base and the height will be at most 20.

Example:

	Input: 6 4
	Output:
	       ++++++
	       +====+
	       +====+
	       ++++++

	Input: 3 2
	Output:
	       +++
	       +++

  






                     ACM Programming Contest
                            Problem 2
                                 

Write a program which accepts as input a string of up to 40 lower
case letters and produces two lines of output. The first line has
all the vowels (a,e,i,o,u)  in the input string in the order they
appeared.  The second line has all the non-vowels in  the REVERSE
order to which they appeared.  The vowels appear forwards and the
consonants appear backwards. 

Example:
	INPUT:
	       naturally

	OUTPUT:
	
	       aua
	       yllrtn 



                     ACM-Programming Contest
                            Problem 3


A world  archery competition  has  commissioned  you  to  write a
scoring program.  The target computer reports the point of impact
as an (X,Y)  pair.  It also reports the coordinate for the center
of the target as an (X,Y) pair (not all of the targets re equally
aligned!). All X and Y will be between 0 and 50. 

The target has 5  concentric rings.  The bull's-eye has radius 10
and  each  successive  ring  increases  the  radius   by  5.  The
bull's-eye  scores 9  and  each  successive  ring  scores 2 less.
Missing the  target scores 0.  Assume that impacts on  a boundary
line between two rings score the lower of the two scores. 



Thus: 

	Input is what the target computer reports:

	center: X = 31, Y = 32
	impact point: X = 35, Y = 49

Your program , given this information, would print 

	"The score is 5."

Input for your program will be two lines with two  number on each
line.  The number on the first line  is the center point  and the
number on the second line is the impact point. 

Output is the score. 

Examples:

	INPUT:
	0 0
	5 12
	OUTPUT:
	The score is 7.

	INPUT:
	1 1
	40 40
	OUTPUT:
	The score is 0.

Recall that the square of the distance between two points (X1,Y1)
and (X2,Y2) is (X2-X1)(X2-X1)+(Y2-Y1)(Y2-Y1).



                     ACM Programming Contest
                            Problem 4
                                 

Describing Sequences

The following sequence  of  positive  integers is generated  by a
rule which tells how each number is determined  from the previous
number. The rule is not obvious and will be explained below.

	1
	11
	21
	1211
	111221
	312211
	13112221
	1113213211

	and so on.

To determine the next number in the sequence proceed as follows:

1.  Read the current  number as a string  of digits from  left to
right.

2.  Describe the string by writing down the number of consecutive
occurrences of an encountered digit followed by that digit.

3. Repeat step 2. as you read from left to right. 

For  example the first number  in  the  sequence  above  could be
anything but we chose 1.

Reading that first number from left to right we see  one 1. Hence
the second number is 11 (one 1).

Reading  that second number  from left to  right we  see two 1's.
Hence the third number is 21 (two 1's).

Reading the third number we see one 2  and then one 1.  Hence the
fourth number is 1211 (one 2 and one 1).

Reading that we see one 1,  one 2,  and two 1's. Remember that we
accumulate the last two 1's and don't  describe  them separately.
So the next number is 111221.

PROBLEM:

You are to write a program that accepts  as INPUT a  string of up
to 20 digits between 1 and 3 and having an even number of digits.
Your program is  to  produce as  OUTPUT  two  strings.  The first
should be the PREVIOUS string is the sequence  -  i.e. the string
described by the input string.  The  second output should  be the
NEXT string  in  the sequence  -  i.e.  the string describing the
input string. 


EXAMPLE:

	INPUT:
	       312211

	OUTPUT:

	       111221
	       13112221

Ask if you can't understand how the sequence is generated.   




                     ACM Programming Contest
                            Problem 5


Consider a two dimensional array of cells,  each of which  may be
either full or empty. Any group of full cells which are connected
horizontally  or  vertically  (but  NOT  diagonally)  is  said to
constitute  a "blob".  For  example,  in the  array shown bellow,
there are three blobs.

	                     -------------------
	                    | 1 |   |   |   |   | 
 		             -------------------
			    |   | 1 | 1 | 1 | 1 |
			     -------------------
			    | 1 |   | 1 |   | 1 |
			     -------------------
			    | 1 |   |   |   | 1 |
			     -------------------
			    |   | 1 | 1 | 1 | 1 |
			     -------------------

PROBLEM
-------

You are to write a program which inputs an N x N array  of binary
values and outputs the number of blobs in  that  array. The value
of N is also to be an input to the program.

Your program will first prompt the user for a value of N. You may
assume  that  N will  not exceed  50  for  the  purposes  of this
contest. After reading N, the program will input N lines of N 0's
or  1's that  represent the N x N  array.  The  0's  and  1's are
separated by spaces,  so the input for the example above would be
as follows:

	1 0 0 0 0 
	0 1 1 1 1
	1 0 1 0 1
	1 0 0 0 1
	0 1 1 1 1

All inputs will come from the keyboard.