*** ENTERING PROGRAM ***

Given the following list:

1.  FRIENDS
2.  ROMANS
3.  COUNTRYMEN
4.  LEND
5.  ME
6.  YOUR
7.  EARS
8.  I
9.  COME
10.  TO
11.  BURY
12.  CAESAR
13.  NOT
14.  TO
15.  PRAISE
16.  HIM
17.  THE
18.  EVIL
19.  THAT
20.  MEN

We seek the 19th. string.

We need to break this array into groups of five and, using brute
force, find the median of each group.

We need to find the median of the following strings:  
1.  FRIENDS
2.  ROMANS
3.  COUNTRYMEN
4.  LEND
5.  ME
The median is: LEND

We need to find the median of the following strings:  
1.  YOUR
2.  EARS
3.  I
4.  COME
5.  TO
The median is: I

We need to find the median of the following strings:  
1.  BURY
2.  CAESAR
3.  NOT
4.  TO
5.  PRAISE
The median is: NOT

We need to find the median of the following strings:  
1.  HIM
2.  THE
3.  EVIL
4.  THAT
5.  MEN
The median is: MEN

Having built an array of brute force medians,
we now need to compute the EXACT median of this list.
We will use recursion to do this.

*** ENTERING RECURSION LEVEL 1

Given the following list:

1.  LEND
2.  I
3.  NOT
4.  MEN

We seek the 2nd. string.

We need to break this array into groups of five and, using brute
force, find the median of each group.

We need to find the median of the following strings:  
1.  LEND
2.  I
3.  NOT
4.  MEN
The median is: LEND

Having built an array of brute force medians,
we now need to compute the EXACT median of this list.
We will use recursion to do this.

*** ENTERING RECURSION LEVEL 2

Given the following list:

1.  LEND

We seek the 1st. string.

Since there is only one string in this list, no work is necessary.
The desired string is: LEND

*** EXITING RECURSION LEVEL 2

REMINDER:  The above list was a list of brute force medians.
The EXACT median of that list is: LEND
The original list looks like this:

1.  LEND
2.  I
3.  NOT
4.  MEN

We will now pivot our ORIGINAL array around the median of medians.

The BEFORE list is:

1.  I

The EQUAL list is:

1.  LEND

The AFTER list is:

1.  NOT
2.  MEN

Since there are 1 items in the BEFORE list,
and 1 items in the EQUAL list,
and we seek the 2nd. item, the item must be the 1st. item 
of the EQUAL list.
There is no need to recursively scan the EQUAL list.
So, given the original list:

1.  LEND
2.  I
3.  NOT
4.  MEN

The 2nd. string is:  LEND

*** EXITING RECURSION LEVEL 1

REMINDER:  The above list was a list of brute force medians.
The EXACT median of that list is: LEND
The original list looks like this:

1.  FRIENDS
2.  ROMANS
3.  COUNTRYMEN
4.  LEND
5.  ME
6.  YOUR
7.  EARS
8.  I
9.  COME
10.  TO
11.  BURY
12.  CAESAR
13.  NOT
14.  TO
15.  PRAISE
16.  HIM
17.  THE
18.  EVIL
19.  THAT
20.  MEN

We will now pivot our ORIGINAL array around the median of medians.

The BEFORE list is:

1.  FRIENDS
2.  COUNTRYMEN
3.  EARS
4.  I
5.  COME
6.  BURY
7.  CAESAR
8.  HIM
9.  EVIL

The EQUAL list is:

1.  LEND

The AFTER list is:

1.  ROMANS
2.  ME
3.  YOUR
4.  TO
5.  NOT
6.  TO
7.  PRAISE
8.  THE
9.  THAT
10.  MEN

Since there are 9 items in the BEFORE list,
and 1 items in the EQUAL list,
and we seek the 19th. item, the item must be the 9th. item 
of the AFTER list.
We will therefore use recursion on the AFTER list.

*** ENTERING RECURSION LEVEL 1

Given the following list:

1.  ROMANS
2.  ME
3.  YOUR
4.  TO
5.  NOT
6.  TO
7.  PRAISE
8.  THE
9.  THAT
10.  MEN

We seek the 9th. string.

We need to break this array into groups of five and, using brute
force, find the median of each group.

We need to find the median of the following strings:  
1.  ROMANS
2.  ME
3.  YOUR
4.  TO
5.  NOT
The median is: ROMANS

We need to find the median of the following strings:  
1.  TO
2.  PRAISE
3.  THE
4.  THAT
5.  MEN
The median is: THAT

Having built an array of brute force medians,
we now need to compute the EXACT median of this list.
We will use recursion to do this.

*** ENTERING RECURSION LEVEL 2

Given the following list:

1.  ROMANS
2.  THAT

We seek the 1st. string.

We need to break this array into groups of five and, using brute
force, find the median of each group.

We need to find the median of the following strings:  
1.  ROMANS
2.  THAT
The median is: ROMANS

Having built an array of brute force medians,
we now need to compute the EXACT median of this list.
We will use recursion to do this.

*** ENTERING RECURSION LEVEL 3

Given the following list:

1.  ROMANS

We seek the 1st. string.

Since there is only one string in this list, no work is necessary.
The desired string is: ROMANS

*** EXITING RECURSION LEVEL 3

REMINDER:  The above list was a list of brute force medians.
The EXACT median of that list is: ROMANS
The original list looks like this:

1.  ROMANS
2.  THAT

We will now pivot our ORIGINAL array around the median of medians.

The BEFORE list is:


The EQUAL list is:

1.  ROMANS

The AFTER list is:

1.  THAT

Since there are 0 items in the BEFORE list,
and 1 items in the EQUAL list,
and we seek the 1st. item, the item must be the 1st. item 
of the EQUAL list.
There is no need to recursively scan the EQUAL list.
So, given the original list:

1.  ROMANS
2.  THAT

The 1st. string is:  ROMANS

*** EXITING RECURSION LEVEL 2

REMINDER:  The above list was a list of brute force medians.
The EXACT median of that list is: ROMANS
The original list looks like this:

1.  ROMANS
2.  ME
3.  YOUR
4.  TO
5.  NOT
6.  TO
7.  PRAISE
8.  THE
9.  THAT
10.  MEN

We will now pivot our ORIGINAL array around the median of medians.

The BEFORE list is:

1.  ME
2.  NOT
3.  PRAISE
4.  MEN

The EQUAL list is:

1.  ROMANS

The AFTER list is:

1.  YOUR
2.  TO
3.  TO
4.  THE
5.  THAT

Since there are 4 items in the BEFORE list,
and 1 items in the EQUAL list,
and we seek the 9th. item, the item must be the 4th. item 
of the AFTER list.
We will therefore use recursion on the AFTER list.

*** ENTERING RECURSION LEVEL 2

Given the following list:

1.  YOUR
2.  TO
3.  TO
4.  THE
5.  THAT

We seek the 4th. string.

We need to break this array into groups of five and, using brute
force, find the median of each group.

We need to find the median of the following strings:  
1.  YOUR
2.  TO
3.  TO
4.  THE
5.  THAT
The median is: TO

Having built an array of brute force medians,
we now need to compute the EXACT median of this list.
We will use recursion to do this.

*** ENTERING RECURSION LEVEL 3

Given the following list:

1.  TO

We seek the 1st. string.

Since there is only one string in this list, no work is necessary.
The desired string is: TO

*** EXITING RECURSION LEVEL 3

REMINDER:  The above list was a list of brute force medians.
The EXACT median of that list is: TO
The original list looks like this:

1.  YOUR
2.  TO
3.  TO
4.  THE
5.  THAT

We will now pivot our ORIGINAL array around the median of medians.

The BEFORE list is:

1.  THE
2.  THAT

The EQUAL list is:

1.  TO
2.  TO

The AFTER list is:

1.  YOUR

Since there are 2 items in the BEFORE list,
and 2 items in the EQUAL list,
and we seek the 4th. item, the item must be the 2nd. item 
of the EQUAL list.
There is no need to recursively scan the EQUAL list.
So, given the original list:

1.  YOUR
2.  TO
3.  TO
4.  THE
5.  THAT

The 4th. string is:  TO

*** EXITING RECURSION LEVEL 2

REMINDER:  The 4th. item of the AFTER list is the same as the
9th. item of the original list:

1.  ROMANS
2.  ME
3.  YOUR
4.  TO
5.  NOT
6.  TO
7.  PRAISE
8.  THE
9.  THAT
10.  MEN

The 9th. string is:  TO

*** EXITING RECURSION LEVEL 1

REMINDER:  The 9th. item of the AFTER list is the same as the
19th. item of the original list:

1.  FRIENDS
2.  ROMANS
3.  COUNTRYMEN
4.  LEND
5.  ME
6.  YOUR
7.  EARS
8.  I
9.  COME
10.  TO
11.  BURY
12.  CAESAR
13.  NOT
14.  TO
15.  PRAISE
16.  HIM
17.  THE
18.  EVIL
19.  THAT
20.  MEN

The 19th. string is:  TO


*** EXITING PROGRAM ***

The 19th. string is:  TO