CMSC 250
Discrete Structures
Counting
Counting Elements in a List

How many integers in the list from 1 to 10?

How many integers in the list from m to n?
(assuming m  n)
–n–m+1
– Can you prove this?
27 June 2016
Counting
2
Prove: # elements in list

Base case (List of size 1, x=y)
– y – x + 1 = y – y + 1 (by substitution) = 1

IH (generic x, y=k [where x  k])
– Assume size of list x to k, is k – x + 1

IS
– Show size of list x to k + 1, is (k + 1) – x + 1
– Prove
 Split into two lists …
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Counting
3
How many in list divisible by something

How many positive three digit integers are there?
– (this means only the ones that require 3 digits)
– 999 – 100 + 1 = 900

How many three digit integers are divisible by 5?
– think about the definition of divisible by
x | y   k Z, y = kx and then count the k’s that work
100, 101, 102, 103, 104, 105, 106,… 994, 995, 996, 997, 998, 999
20*5
21*5
…
199*5
– count the integers between 20 and 199
– 199 – 20 + 1 = 180
27 June 2016
Counting
4
Probability
likelihood of a specific event
Sample Space = set of all possible outcomes
 Random = outcome of trial is unknown
 Event = subset of sample space
 Equal Probability Formula:

– Given a finite sample space S where all outcomes are
equally likely
– Select an event E from the sample space S
– The probability of event E from sample space S:
n( E )
P( E ) 
n( S )
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Counting
5
Flipping Two Coins

Sample Space = {(H,H), (H,T), (T,H), (T,T)}

What do the following events represent?
– Probability of no heads
– Probability of at least one head
– Probability of same sides on the two coins

Compute the above probabilities

If flip two coins 100 times will you get 25-50-25?
– Probability & actual outcomes often differ
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Counting
6
Standard Playing Cards
Values: 2,3,4,5,6,7,8,9,10,J,Q,K,A
 Suits: D(), H(), S(), C()

Probability
 Probability
 Probability
 Probability

27 June 2016
of
of
of
of
drawing
drawing
drawing
drawing
Counting
the Ace of Spades
a Spade
a face card
a red face card
7
Rolling Two Six-Sided Dice

Sample Space
– Ordered pairs
{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),
…
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
– Simplified
{11,12,13,14,15,16,
21,22,23,24,25,26,
…
61,62,63,64,65,66}


Set representing rolling a 10?
The probability of rolling a 10?

Set representing rolling a pair?
Probability of rolling a pair?

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Counting
8
Multi-level Probability
If I toss a coin once – the probability of
Head = ½
 If I toss that coin 5 times

– The probability of all heads
1 1 1 1 1
1
     5
2 2 2 2 2 2
– The probability of exactly 4 heads
5
5
2
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Counting
9
Combination Examples

Breakfast
– Main
– Fruit

Red, White, Blue marbles
– How can you arrange 10 of them
– __ __ __ __ __ __ __ __ __ __
– 3  3  3  3  3  3  3  3  3  3 = 310
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Counting
10
Multiplication Rule

1st step can be performed n1 ways
2nd step can be performed n2 ways
…
Kth step can be performed nk ways
Operation can be performed n1* n2 *…* nk ways

Cartesian product n(A)=3, n(B)=2, n(C)=4




– n(AxBxC) = 24
– n(AxB) = 6, n((AxB)xC) = 24
27 June 2016
Counting
11
Tournament Play
Team A and Team B in “Best of 3” Tournament
 Where they each have an equal likelihood of
winning each game

– Do leaves add up to 1?
– Do we have to play 3 games?
– Do A and B have an equal chance of winning?
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Counting
12
What if A wins 2 of every 3 games?
Each line for A must have a 2/3
 Each line for B must have a 1/3

How likely is A to win the tournament?
 How likely is B to win the tournament?

27 June 2016
Counting
13
Permutation Example

How many ways to take a picture?
–
–
–
–
–

With
With
With
With
With
1
2
3
4
5
person?
people?
people?
people?
people?
Number of ways to arrange n objects
– n!
– 10n < n!
27 June 2016
Counting
14
Permutation Example
How many ways to rewrite CAT?
 3! = 6
 cat, cta, act, atc, tca, tac

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Counting
15
Multiplication Rule

If there are n steps to a decision, each
step having c(k) choices, the total number
of choices is:
n
c
(
i
)

i 1
27 June 2016
Counting
16
Examples

Choose a PIN from a {0,1,2,3,4,A,B,C} keyboard
with PIN length 3
= 8  8  8 = 83 = 512

Choose a PIN of the form #L# where
– #  {0,1,2,…,9}
– L  {0,1,2,…,9}
= 10  26  10

Choose a 3-value PIN of digits and letters
= 36  36  36
– Without repeats
= 36  35  34
27 June 2016
Counting
17
Permutation Example

Hexadecimal numbers are made using digits:
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F with subscript 16.

How many 5-digit long begin with a digit 3
through B, and end with a digit 5 through F?
– 9  16  16  16  11 = 405,504

How many 6-digit long begin with one of 4
through D, and end with a digit 2 through E?
– 10  16  16  16  16  13 = 8,519,680
27 June 2016
Counting
18
Probabilities with PINs

Number of 4 digit PINs of (0,1,2,.)
– With repetition allowed = 4  4  4  4 = 256
– With no repetition allowed = 4  3  2  1 = 24
What is the probability that your 4 digit PIN
has no repeated characters?
 What is the probability that your 4 digit PIN
does have repeated characters?


Probability of the complement of an event
P(E’) = P(Ec) = 1 – P(E)
27 June 2016
Counting
19
Permutation Example

Consider strings of length n over the set {a,b,c,d}.

How many strings contain at least one pair of
adjacent characters that are the same?
– Total number of length n is 4n
– No two adjacent = 4  3  3  3 = 4  3n-1
– So 4n – 4  3n-1

What is the probability that a random string of
length 10 contains at least one pair of adjacent
characters that are the same?
9
10
9
4  43
3

 1     92.5%
10
4
4
27 June 2016
Counting
20
Difference Rule Formally

If A is a finite set and BA, then
n(A – B) = n(A) – n(B)

One application:
probability of the complement of an event
P(E’) = P(Ec) = 1 - P(E)
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Counting
21
PINs with less specified length
Addition Rule
Assume it can be a 2, 3 or 4 length PIN
 Partition the problem

– Number of 2 length PINs w/rep allowed: 4  4 = 16
– Number of 3 length PINs w/rep allowed: 4  4  4 = 64
– Number of 4 length PINs w/rep allowed: 4  4  4  4 = 256

Number PINs if allowing length of 2, 3 or 4 = 336
27 June 2016
Counting
22
Addition Rule Formally

If A1 A2  A3  …  Ak =A
and A1, A2 , A3,…,Ak are pairwise disjoint
(i.e. if these subsets form a partition of A)

n(A) = n(A1) + n(A2) + n(A3) + … + n(Ak)
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Counting
23
Another example for
Multiplication Rule and Addition Rule

How many 3 digit integers are divisible by 5?
– How many end in a 0? 9  10  1 = 90
– How many end in a 5? 9  10  1 = 90
– These form a partition with the set of numbers
divisible by 5 so
 90 + 90 = 180
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Counting
24
Where Multiplication Rule Doesn’t Work
People = {Angel, Bob, Carol, Dan}
 Need to be appointed as

– President, vice-president, and treasurer
– Nobody can hold more than one office
– Angel doesn’t want to be president
– Only Bob and Dan want to be vice-president

Draw tree …
27 June 2016
Counting
25
Where Multiplication Rule Doesn’t Work
P1 picks a card and doesn’t look at it
 P2 picks a card


What are the chances P2 picked a red face
card?

Draw tree …
27 June 2016
Counting
26
Inclusion/Exclusion Rule

If there are two sets:
n(A  B) = n(A) + n(B) – n(A  B)

If there are three sets:
n(A  B  C) = n(A) + n(B) + n(C)
– n(A  B) – n(A  C) – n(B  C)
+ n(A  B  C)
27 June 2016
Counting
27
Inclusion/Exclusion Example
How many integers from 1 to 1000 are multiples
of 3, 5, or 8?
 Sets

–A=3
–B=5
–C=5

n(A B C) =
n(A) + n(B) + n(C)
– n(A  B) – n(A  C) – n(B  C)
– n(A  B  C)
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Counting
28
Permutation Example
How many ways to rewrite COMPUTER?
 8! = 40320

computer, computre, compuetr, compuert, compurte, compuret, comptuer, compture, compteur,
compteru, comptrue, comptreu, compeutr, compeurt, competur, competru, comperut, compertu,
comprute, compruet, comprtue, comprteu, compreut, compretu, comupter, comuptre, comupetr,
comupert, comuprte, comupret, comutper, comutpre, comutepr, comuterp, comutrpe, comutrep,
comueptr, comueprt, comuetpr, comuetrp, comuerpt, comuertp, comurpte, comurpet, comurtpe,
comurtep, comurept, comuretp, comtpuer, comtpure, comtpeur, comtperu, comtprue, comtpreu,
comtuper, comtupre, comtuepr, comtuerp, comturpe, comturep, comtepur, comtepru, comteupr,
comteurp, comterpu, comterup, comtrpue, comtrpeu, comtrupe, comtruep, comtrepu, comtreup,
comeputr, comepurt, comeptur, comeptru, comeprut, comeprtu, comeuptr, comeuprt, comeutpr,
comeutrp, comeurpt, comeurtp, cometpur, cometpru, cometupr, cometurp, cometrpu, cometrup,
comerput, comerptu, comerupt, comerutp, comertpu, comertup, comrpute, comrpuet, comrptue,
comrpteu, comrpeut, comrpetu, comrupte, comrupet, comrutpe, comrutep, comruept, comruetp,
comrtpue, comrtpeu, comrtupe, comrtuep, comrtepu, comrteup, comreput, comreptu, comreupt,
comreutp, comretpu, comretup, copmuter, copmutre, copmuetr, copmuert, copmurte, copmuret,
copmtuer, copmture, copmteur, copmteru, copmtrue, copmtreu, copmeutr, copmeurt, copmetur,
copmetru, copmerut, copmertu, copmrute, copmruet, copmrtue, copmrteu, copmreut, copmretu,
copumter, copumtre, copumetr, copumert, copumrte, copumret, coputmer, coputmre, …
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Counting
29
Permutation Example
How many to rewrite CO-M-P-U-T-E-R?
 7! = 5040



COMPUTER, COMPUTRE, COMPUETR, COMPUERT, COMPURTE,
COMPURET, COMPTUER, COMPTURE, COMPTEUR, COMPTERU,
COMPTRUE, COMPTREU, COMPEUTR, COMPEURT, COMPETUR, …
COMPUTER, COMPUTRE, COMPUETR, COMPUERT, COMPURTE, COMPURET, COMPTUER, COMPTURE, COMPTEUR, COMPTERU, COMPTRUE, COMPTREU, COMPEUTR, COMPEURT, COMPETUR, COMPETRU, COMPERUT, COMPERTU, COMPRUTE, COMPRUET, COMPRTUE, COMPRTEU, COMPREUT, COMPRETU, COMUPTER, COMUPTRE, COMUPETR, COMUPERT, COMUPRTE, COMUPRET, COMUTPER, COMUTPRE, COMUTEPR, COMUTERP, COMUTRPE, COMUTREP, COMUEPTR, COMUEPRT, COMUETPR, COMUETRP, COMUERPT, COMUERTP, COMURPTE, COMURPET, COMURTPE, COMURTEP, COMUREPT, COMURETP, COMTPUER, COMTPURE, COMTPEUR, COMTPERU, COMTPRUE,
COMTPREU, COMTUPER, COMTUPRE, COMTUEPR, COMTUERP, COMTURPE, COMTUREP, COMTEPUR, COMTEPRU, COMTEUPR, COMTEURP, COMTERPU, COMTERUP, COMTRPUE, COMTRPEU, COMTRUPE, COMTRUEP, COMTREPU, COMTREUP, COMEPUTR, COMEPURT, COMEPTUR, COMEPTRU, COMEPRUT, COMEPRTU, COMEUPTR, COMEUPRT, COMEUTPR, COMEUTRP, COMEURPT, COMEURTP, COMETPUR, COMETPRU, COMETUPR, COMETURP, COMETRPU, COMETRUP, COMERPUT, COMERPTU, COMERUPT, COMERUTP, COMERTPU, COMERTUP, COMRPUTE, COMRPUET, COMRPTUE, COMRPTEU, COMRPEUT, COMRPETU, COMRUPTE, COMRUPET, COMRUTPE, COMRUTEP,
COMRUEPT, COMRUETP, COMRTPUE, COMRTPEU, COMRTUPE, COMRTUEP, COMRTEPU, COMRTEUP, COMREPUT, COMREPTU, COMREUPT, COMREUTP, COMRETPU, COMRETUP, COPMUTER, COPMUTRE, COPMUETR, COPMUERT, COPMURTE, COPMURET, COPMTUER, COPMTURE, COPMTEUR, COPMTERU, COPMTRUE, COPMTREU, COPMEUTR, COPMEURT, COPMETUR, COPMETRU, COPMERUT, COPMERTU, COPMRUTE, COPMRUET, COPMRTUE, COPMRTEU, COPMREUT, COPMRETU, COPUMTER, COPUMTRE, COPUMETR, COPUMERT, COPUMRTE, COPUMRET, COPUTMER, COPUTMRE, COPUTEMR, COPUTERM, COPUTRME, COPUTREM, COPUEMTR, COPUEMRT, COPUETMR,
COPUETRM, COPUERMT, COPUERTM, COPURMTE, COPURMET, COPURTME, COPURTEM, COPUREMT, COPURETM, COPTMUER, COPTMURE, COPTMEUR, COPTMERU, COPTMRUE, COPTMREU, COPTUMER, COPTUMRE, COPTUEMR, COPTUERM, COPTURME, COPTUREM, COPTEMUR, COPTEMRU, COPTEUMR, COPTEURM, COPTERMU, COPTERUM, COPTRMUE, COPTRMEU, COPTRUME, COPTRUEM, COPTREMU, COPTREUM, COPEMUTR, COPEMURT, COPEMTUR, COPEMTRU, COPEMRUT, COPEMRTU, COPEUMTR, COPEUMRT, COPEUTMR, COPEUTRM, COPEURMT, COPEURTM, COPETMUR, COPETMRU, COPETUMR, COPETURM, COPETRMU, COPETRUM, COPERMUT, COPERMTU,
COPERUMT, COPERUTM, COPERTMU, COPERTUM, COPRMUTE, COPRMUET, COPRMTUE, COPRMTEU, COPRMEUT, COPRMETU, COPRUMTE, COPRUMET, COPRUTME, COPRUTEM, COPRUEMT, COPRUETM, COPRTMUE, COPRTMEU, COPRTUME, COPRTUEM, COPRTEMU, COPRTEUM, COPREMUT, COPREMTU, COPREUMT, COPREUTM, COPRETMU, COPRETUM, COUMPTER, COUMPTRE, COUMPETR, COUMPERT, COUMPRTE, COUMPRET, COUMTPER, COUMTPRE, COUMTEPR, COUMTERP, COUMTRPE, COUMTREP, COUMEPTR, COUMEPRT, COUMETPR, COUMETRP, COUMERPT, COUMERTP, COUMRPTE, COUMRPET, COUMRTPE, COUMRTEP, COUMREPT, COUMRETP, COUPMTER,
COUPMTRE, COUPMETR, COUPMERT, COUPMRTE, COUPMRET, COUPTMER, COUPTMRE, COUPTEMR, COUPTERM, COUPTRME, COUPTREM, COUPEMTR, COUPEMRT, COUPETMR, COUPETRM, COUPERMT, COUPERTM, COUPRMTE, COUPRMET, COUPRTME, COUPRTEM, COUPREMT, COUPRETM, COUTMPER, COUTMPRE, COUTMEPR, COUTMERP, COUTMRPE, COUTMREP, COUTPMER, COUTPMRE, COUTPEMR, COUTPERM, COUTPRME, COUTPREM, COUTEMPR, COUTEMRP, COUTEPMR, COUTEPRM, COUTERMP, COUTERPM, COUTRMPE, COUTRMEP, COUTRPME, COUTRPEM, COUTREMP, COUTREPM, COUEMPTR, COUEMPRT, COUEMTPR, COUEMTRP, COUEMRPT, COUEMRTP,
COUEPMTR, COUEPMRT, COUEPTMR, COUEPTRM, COUEPRMT, COUEPRTM, COUETMPR, COUETMRP, COUETPMR, COUETPRM, COUETRMP, COUETRPM, COUERMPT, COUERMTP, COUERPMT, COUERPTM, COUERTMP, COUERTPM, COURMPTE, COURMPET, COURMTPE, COURMTEP, COURMEPT, COURMETP, COURPMTE, COURPMET, COURPTME, COURPTEM, COURPEMT, COURPETM, COURTMPE, COURTMEP, COURTPME, COURTPEM, COURTEMP, COURTEPM, COUREMPT, COUREMTP, COUREPMT, COUREPTM, COURETMP, COURETPM, COTMPUER, COTMPURE, COTMPEUR, COTMPERU, COTMPRUE, COTMPREU, COTMUPER, COTMUPRE, COTMUEPR, COTMUERP, COTMURPE,
COTMUREP, COTMEPUR, COTMEPRU, COTMEUPR, COTMEURP, COTMERPU, COTMERUP, COTMRPUE, COTMRPEU, COTMRUPE, COTMRUEP, COTMREPU, COTMREUP, COTPMUER, COTPMURE, COTPMEUR, COTPMERU, COTPMRUE, COTPMREU, COTPUMER, COTPUMRE, COTPUEMR, COTPUERM, COTPURME, COTPUREM, COTPEMUR, COTPEMRU, COTPEUMR, COTPEURM, COTPERMU, COTPERUM, COTPRMUE, COTPRMEU, COTPRUME, COTPRUEM, COTPREMU, COTPREUM, COTUMPER, COTUMPRE, COTUMEPR, COTUMERP, COTUMRPE, COTUMREP, COTUPMER, COTUPMRE, COTUPEMR, COTUPERM, COTUPRME, COTUPREM, COTUEMPR, COTUEMRP, COTUEPMR, COTUEPRM,
COTUERMP, COTUERPM, COTURMPE, COTURMEP, COTURPME, COTURPEM, COTUREMP, COTUREPM, COTEMPUR, COTEMPRU, COTEMUPR, COTEMURP, COTEMRPU, COTEMRUP, COTEPMUR, COTEPMRU, COTEPUMR, COTEPURM, COTEPRMU, COTEPRUM, COTEUMPR, COTEUMRP, COTEUPMR, COTEUPRM, COTEURMP, COTEURPM, COTERMPU, COTERMUP, COTERPMU, COTERPUM, COTERUMP, COTERUPM, COTRMPUE, COTRMPEU, COTRMUPE, COTRMUEP, COTRMEPU, COTRMEUP, COTRPMUE, COTRPMEU, COTRPUME, COTRPUEM, COTRPEMU, COTRPEUM, COTRUMPE, COTRUMEP, COTRUPME, COTRUPEM, COTRUEMP, COTRUEPM, COTREMPU, COTREMUP, COTREPMU,
COTREPUM, COTREUMP, COTREUPM, COEMPUTR, COEMPURT, COEMPTUR, COEMPTRU, COEMPRUT, COEMPRTU, COEMUPTR, COEMUPRT, COEMUTPR, COEMUTRP, COEMURPT, COEMURTP, COEMTPUR, COEMTPRU, COEMTUPR, COEMTURP, COEMTRPU, COEMTRUP, COEMRPUT, COEMRPTU, COEMRUPT, COEMRUTP, COEMRTPU, COEMRTUP, COEPMUTR, COEPMURT, COEPMTUR, COEPMTRU, COEPMRUT, COEPMRTU, COEPUMTR, COEPUMRT, COEPUTMR, COEPUTRM, COEPURMT, COEPURTM, COEPTMUR, COEPTMRU, COEPTUMR, COEPTURM, COEPTRMU, COEPTRUM, COEPRMUT, COEPRMTU, COEPRUMT, COEPRUTM, COEPRTMU, COEPRTUM, COEUMPTR, COEUMPRT,
COEUMTPR, COEUMTRP, COEUMRPT, COEUMRTP, COEUPMTR, COEUPMRT, COEUPTMR, COEUPTRM, COEUPRMT, COEUPRTM, COEUTMPR, COEUTMRP, COEUTPMR, COEUTPRM, COEUTRMP, COEUTRPM, COEURMPT, COEURMTP, COEURPMT, COEURPTM, COEURTMP, COEURTPM, COETMPUR, COETMPRU, COETMUPR, COETMURP, COETMRPU, COETMRUP, COETPMUR, COETPMRU, COETPUMR, COETPURM, COETPRMU, COETPRUM, COETUMPR, COETUMRP, COETUPMR, COETUPRM, COETURMP, COETURPM, COETRMPU, COETRMUP, COETRPMU, COETRPUM, COETRUMP, COETRUPM, COERMPUT, COERMPTU, COERMUPT, COERMUTP, COERMTPU, COERMTUP, COERPMUT,
COERPMTU, COERPUMT, COERPUTM, COERPTMU, COERPTUM, COERUMPT, COERUMTP, COERUPMT, COERUPTM, COERUTMP, COERUTPM, COERTMPU, COERTMUP, COERTPMU, COERTPUM, COERTUMP, COERTUPM, CORMPUTE, CORMPUET, CORMPTUE, CORMPTEU, CORMPEUT, CORMPETU, CORMUPTE, CORMUPET, CORMUTPE, CORMUTEP, CORMUEPT, CORMUETP, CORMTPUE, CORMTPEU, CORMTUPE, CORMTUEP, CORMTEPU, CORMTEUP, CORMEPUT, CORMEPTU, CORMEUPT, CORMEUTP, CORMETPU, CORMETUP, CORPMUTE, CORPMUET, CORPMTUE, CORPMTEU, CORPMEUT, CORPMETU, CORPUMTE, CORPUMET, CORPUTME, CORPUTEM, CORPUEMT, CORPUETM,
CORPTMUE, CORPTMEU, CORPTUME, CORPTUEM, CORPTEMU, CORPTEUM, CORPEMUT, CORPEMTU, CORPEUMT, CORPEUTM, CORPETMU, CORPETUM, CORUMPTE, CORUMPET, CORUMTPE, CORUMTEP, CORUMEPT, CORUMETP, CORUPMTE, CORUPMET, CORUPTME, CORUPTEM, CORUPEMT, CORUPETM, CORUTMPE, CORUTMEP, CORUTPME, CORUTPEM, CORUTEMP, CORUTEPM, CORUEMPT, CORUEMTP, CORUEPMT, CORUEPTM, CORUETMP, CORUETPM, CORTMPUE, CORTMPEU, CORTMUPE, CORTMUEP, CORTMEPU, CORTMEUP, CORTPMUE, CORTPMEU, CORTPUME, CORTPUEM, CORTPEMU, CORTPEUM, CORTUMPE, CORTUMEP, CORTUPME, CORTUPEM, CORTUEMP,
CORTUEPM, CORTEMPU, CORTEMUP, CORTEPMU, CORTEPUM, CORTEUMP, CORTEUPM, COREMPUT, COREMPTU, COREMUPT, COREMUTP, COREMTPU, COREMTUP, COREPMUT, COREPMTU, COREPUMT, COREPUTM, COREPTMU, COREPTUM, COREUMPT, COREUMTP, COREUPMT, COREUPTM, COREUTMP, COREUTPM, CORETMPU, CORETMUP, CORETPMU, CORETPUM, CORETUMP, CORETUPM, MCOPUTER, MCOPUTRE, MCOPUETR, MCOPUERT, MCOPURTE, MCOPURET, MCOPTUER, MCOPTURE, MCOPTEUR, MCOPTERU, MCOPTRUE, MCOPTREU, MCOPEUTR, MCOPEURT, MCOPETUR, MCOPETRU, MCOPERUT, MCOPERTU, MCOPRUTE, MCOPRUET, MCOPRTUE, MCOPRTEU,
MCOPREUT, MCOPRETU, MCOUPTER, MCOUPTRE, MCOUPETR, MCOUPERT, MCOUPRTE, MCOUPRET, MCOUTPER, MCOUTPRE, MCOUTEPR, MCOUTERP, MCOUTRPE, MCOUTREP, MCOUEPTR, MCOUEPRT, MCOUETPR, MCOUETRP, MCOUERPT, MCOUERTP, MCOURPTE, MCOURPET, MCOURTPE, MCOURTEP, MCOUREPT, MCOURETP, MCOTPUER, MCOTPURE, MCOTPEUR, MCOTPERU, MCOTPRUE, MCOTPREU, MCOTUPER, MCOTUPRE, MCOTUEPR, MCOTUERP, MCOTURPE, MCOTUREP, MCOTEPUR, MCOTEPRU, MCOTEUPR, MCOTEURP, MCOTERPU, MCOTERUP, MCOTRPUE, MCOTRPEU, MCOTRUPE, MCOTRUEP, MCOTREPU, MCOTREUP, MCOEPUTR, MCOEPURT, MCOEPTUR,
MCOEPTRU, MCOEPRUT, MCOEPRTU, MCOEUPTR, MCOEUPRT, MCOEUTPR, MCOEUTRP, MCOEURPT, MCOEURTP, MCOETPUR, MCOETPRU, MCOETUPR, MCOETURP, MCOETRPU, MCOETRUP, MCOERPUT, MCOERPTU, MCOERUPT, MCOERUTP, MCOERTPU, MCOERTUP, MCORPUTE, MCORPUET, MCORPTUE, MCORPTEU, MCORPEUT, MCORPETU, MCORUPTE, MCORUPET, MCORUTPE, MCORUTEP, MCORUEPT, MCORUETP, MCORTPUE, MCORTPEU, MCORTUPE, MCORTUEP, MCORTEPU, MCORTEUP, MCOREPUT, MCOREPTU, MCOREUPT, MCOREUTP, MCORETPU, MCORETUP, MPCOUTER, MPCOUTRE, MPCOUETR, MPCOUERT, MPCOURTE, MPCOURET, MPCOTUER, MPCOTURE,
MPCOTEUR, MPCOTERU, MPCOTRUE, MPCOTREU, MPCOEUTR, MPCOEURT, MPCOETUR, MPCOETRU, MPCOERUT, MPCOERTU, MPCORUTE, MPCORUET, MPCORTUE, MPCORTEU, MPCOREUT, MPCORETU, MPUCOTER, MPUCOTRE, MPUCOETR, MPUCOERT, MPUCORTE, MPUCORET, MPUTCOER, MPUTCORE, MPUTECOR, MPUTERCO, MPUTRCOE, MPUTRECO, MPUECOTR, MPUECORT, MPUETCOR, MPUETRCO, MPUERCOT, MPUERTCO, MPURCOTE, MPURCOET, MPURTCOE, MPURTECO, MPURECOT, MPURETCO, MPTCOUER, MPTCOURE, MPTCOEUR, MPTCOERU, MPTCORUE, MPTCOREU, MPTUCOER, MPTUCORE, MPTUECOR, MPTUERCO, MPTURCOE, MPTURECO, MPTECOUR,
MPTECORU, MPTEUCOR, MPTEURCO, MPTERCOU, MPTERUCO, MPTRCOUE, MPTRCOEU, MPTRUCOE, MPTRUECO, MPTRECOU, MPTREUCO, MPECOUTR, MPECOURT, MPECOTUR, MPECOTRU, MPECORUT, MPECORTU, MPEUCOTR, MPEUCORT, MPEUTCOR, MPEUTRCO, MPEURCOT, MPEURTCO, MPETCOUR, MPETCORU, MPETUCOR, MPETURCO, MPETRCOU, MPETRUCO, MPERCOUT, MPERCOTU, MPERUCOT, MPERUTCO, MPERTCOU, MPERTUCO, MPRCOUTE, MPRCOUET, MPRCOTUE, MPRCOTEU, MPRCOEUT, MPRCOETU, MPRUCOTE, MPRUCOET, MPRUTCOE, MPRUTECO, MPRUECOT, MPRUETCO, MPRTCOUE, MPRTCOEU, MPRTUCOE, MPRTUECO, MPRTECOU, MPRTEUCO,
MPRECOUT, MPRECOTU, MPREUCOT, MPREUTCO, MPRETCOU, MPRETUCO, MUCOPTER, MUCOPTRE, MUCOPETR, MUCOPERT, MUCOPRTE, MUCOPRET, MUCOTPER, MUCOTPRE, MUCOTEPR, MUCOTERP, MUCOTRPE, MUCOTREP, MUCOEPTR, MUCOEPRT, MUCOETPR, MUCOETRP, MUCOERPT, MUCOERTP, MUCORPTE, MUCORPET, MUCORTPE, MUCORTEP, MUCOREPT, MUCORETP, MUPCOTER, MUPCOTRE, MUPCOETR, MUPCOERT, MUPCORTE, MUPCORET, MUPTCOER, MUPTCORE, MUPTECOR, MUPTERCO, MUPTRCOE, MUPTRECO, MUPECOTR, MUPECORT, MUPETCOR, MUPETRCO, MUPERCOT, MUPERTCO, MUPRCOTE, MUPRCOET, MUPRTCOE, MUPRTECO, MUPRECOT,
MUPRETCO, MUTCOPER, MUTCOPRE, MUTCOEPR, MUTCOERP, MUTCORPE, MUTCOREP, MUTPCOER, MUTPCORE, MUTPECOR, MUTPERCO, MUTPRCOE, MUTPRECO, MUTECOPR, MUTECORP, MUTEPCOR, MUTEPRCO, MUTERCOP, MUTERPCO, MUTRCOPE, MUTRCOEP, MUTRPCOE, MUTRPECO, MUTRECOP, MUTREPCO, MUECOPTR, MUECOPRT, MUECOTPR, MUECOTRP, MUECORPT, MUECORTP, MUEPCOTR, MUEPCORT, MUEPTCOR, MUEPTRCO, MUEPRCOT, MUEPRTCO, MUETCOPR, MUETCORP, MUETPCOR, MUETPRCO, MUETRCOP, MUETRPCO, MUERCOPT, MUERCOTP, MUERPCOT, MUERPTCO, MUERTCOP, MUERTPCO, MURCOPTE, MURCOPET, MURCOTPE, MURCOTEP,
MURCOEPT, MURCOETP, MURPCOTE, MURPCOET, MURPTCOE, MURPTECO, MURPECOT, MURPETCO, MURTCOPE, MURTCOEP, MURTPCOE, MURTPECO, MURTECOP, MURTEPCO, MURECOPT, MURECOTP, MUREPCOT, MUREPTCO, MURETCOP, MURETPCO, MTCOPUER, MTCOPURE, MTCOPEUR, MTCOPERU, MTCOPRUE, MTCOPREU, MTCOUPER, MTCOUPRE, MTCOUEPR, MTCOUERP, MTCOURPE, MTCOUREP, MTCOEPUR, MTCOEPRU, MTCOEUPR, MTCOEURP, MTCOERPU, MTCOERUP, MTCORPUE, MTCORPEU, MTCORUPE, MTCORUEP, MTCOREPU, MTCOREUP, MTPCOUER, MTPCOURE, MTPCOEUR, MTPCOERU, MTPCORUE, MTPCOREU, MTPUCOER, MTPUCORE, MTPUECOR,
MTPUERCO, MTPURCOE, MTPURECO, MTPECOUR, MTPECORU, MTPEUCOR, MTPEURCO, MTPERCOU, MTPERUCO, MTPRCOUE, MTPRCOEU, MTPRUCOE, MTPRUECO, MTPRECOU, MTPREUCO, MTUCOPER, MTUCOPRE, MTUCOEPR, MTUCOERP, MTUCORPE, MTUCOREP, MTUPCOER, MTUPCORE, MTUPECOR, MTUPERCO, MTUPRCOE, MTUPRECO, MTUECOPR, MTUECORP, MTUEPCOR, MTUEPRCO, MTUERCOP, MTUERPCO, MTURCOPE, MTURCOEP, MTURPCOE, MTURPECO, MTURECOP, MTUREPCO, MTECOPUR, MTECOPRU, MTECOUPR, MTECOURP, MTECORPU, MTECORUP, MTEPCOUR, MTEPCORU, MTEPUCOR, MTEPURCO, MTEPRCOU, MTEPRUCO, MTEUCOPR, MTEUCORP,
MTEUPCOR, MTEUPRCO, MTEURCOP, MTEURPCO, MTERCOPU, MTERCOUP, MTERPCOU, MTERPUCO, MTERUCOP, MTERUPCO, MTRCOPUE, MTRCOPEU, MTRCOUPE, MTRCOUEP, MTRCOEPU, MTRCOEUP, MTRPCOUE, MTRPCOEU, MTRPUCOE, MTRPUECO, MTRPECOU, MTRPEUCO, MTRUCOPE, MTRUCOEP, MTRUPCOE, MTRUPECO, MTRUECOP, MTRUEPCO, MTRECOPU, MTRECOUP, MTREPCOU, MTREPUCO, MTREUCOP, MTREUPCO, MECOPUTR, MECOPURT, MECOPTUR, MECOPTRU, MECOPRUT, MECOPRTU, MECOUPTR, MECOUPRT, MECOUTPR, MECOUTRP, MECOURPT, MECOURTP, MECOTPUR, MECOTPRU, MECOTUPR, MECOTURP, MECOTRPU, MECOTRUP, MECORPUT,
MECORPTU, MECORUPT, MECORUTP, MECORTPU, MECORTUP, MEPCOUTR, MEPCOURT, MEPCOTUR, MEPCOTRU, MEPCORUT, MEPCORTU, MEPUCOTR, MEPUCORT, MEPUTCOR, MEPUTRCO, MEPURCOT, MEPURTCO, MEPTCOUR, MEPTCORU, MEPTUCOR, MEPTURCO, MEPTRCOU, MEPTRUCO, MEPRCOUT, MEPRCOTU, MEPRUCOT, MEPRUTCO, MEPRTCOU, MEPRTUCO, MEUCOPTR, MEUCOPRT, MEUCOTPR, MEUCOTRP, MEUCORPT, MEUCORTP, MEUPCOTR, MEUPCORT, MEUPTCOR, MEUPTRCO, MEUPRCOT, MEUPRTCO, MEUTCOPR, MEUTCORP, MEUTPCOR, MEUTPRCO, MEUTRCOP, MEUTRPCO, MEURCOPT, MEURCOTP, MEURPCOT, MEURPTCO, MEURTCOP, MEURTPCO,
METCOPUR, METCOPRU, METCOUPR, METCOURP, METCORPU, METCORUP, METPCOUR, METPCORU, METPUCOR, METPURCO, METPRCOU, METPRUCO, METUCOPR, METUCORP, METUPCOR, METUPRCO, METURCOP, METURPCO, METRCOPU, METRCOUP, METRPCOU, METRPUCO, METRUCOP, METRUPCO, MERCOPUT, MERCOPTU, MERCOUPT, MERCOUTP, MERCOTPU, MERCOTUP, MERPCOUT, MERPCOTU, MERPUCOT, MERPUTCO, MERPTCOU, MERPTUCO, MERUCOPT, MERUCOTP, MERUPCOT, MERUPTCO, MERUTCOP, MERUTPCO, MERTCOPU, MERTCOUP, MERTPCOU, MERTPUCO, MERTUCOP, MERTUPCO, MRCOPUTE, MRCOPUET, MRCOPTUE, MRCOPTEU, MRCOPEUT,
MRCOPETU, MRCOUPTE, MRCOUPET, MRCOUTPE, MRCOUTEP, MRCOUEPT, MRCOUETP, MRCOTPUE, MRCOTPEU, MRCOTUPE, MRCOTUEP, MRCOTEPU, MRCOTEUP, MRCOEPUT, MRCOEPTU, MRCOEUPT, MRCOEUTP, MRCOETPU, MRCOETUP, MRPCOUTE, MRPCOUET, MRPCOTUE, MRPCOTEU, MRPCOEUT, MRPCOETU, MRPUCOTE, MRPUCOET, MRPUTCOE, MRPUTECO, MRPUECOT, MRPUETCO, MRPTCOUE, MRPTCOEU, MRPTUCOE, MRPTUECO, MRPTECOU, MRPTEUCO, MRPECOUT, MRPECOTU, MRPEUCOT, MRPEUTCO, MRPETCOU, MRPETUCO, MRUCOPTE, MRUCOPET, MRUCOTPE, MRUCOTEP, MRUCOEPT, MRUCOETP, MRUPCOTE, MRUPCOET, MRUPTCOE, MRUPTECO,
MRUPECOT, MRUPETCO, MRUTCOPE, MRUTCOEP, MRUTPCOE, MRUTPECO, MRUTECOP, MRUTEPCO, MRUECOPT, MRUECOTP, MRUEPCOT, MRUEPTCO, MRUETCOP, MRUETPCO, MRTCOPUE, MRTCOPEU, MRTCOUPE, MRTCOUEP, MRTCOEPU, MRTCOEUP, MRTPCOUE, MRTPCOEU, MRTPUCOE, MRTPUECO, MRTPECOU, MRTPEUCO, MRTUCOPE, MRTUCOEP, MRTUPCOE, MRTUPECO, MRTUECOP, MRTUEPCO, MRTECOPU, MRTECOUP, MRTEPCOU, MRTEPUCO, MRTEUCOP, MRTEUPCO, MRECOPUT, MRECOPTU, MRECOUPT, MRECOUTP, MRECOTPU, MRECOTUP, MREPCOUT, MREPCOTU, MREPUCOT, MREPUTCO, MREPTCOU, MREPTUCO, MREUCOPT, MREUCOTP, MREUPCOT,
MREUPTCO, MREUTCOP, MREUTPCO, MRETCOPU, MRETCOUP, MRETPCOU, MRETPUCO, MRETUCOP, MRETUPCO, PCOMUTER, PCOMUTRE, PCOMUETR, PCOMUERT, PCOMURTE, PCOMURET, PCOMTUER, PCOMTURE, PCOMTEUR, PCOMTERU, PCOMTRUE, PCOMTREU, PCOMEUTR, PCOMEURT, PCOMETUR, PCOMETRU, PCOMERUT, PCOMERTU, PCOMRUTE, PCOMRUET, PCOMRTUE, PCOMRTEU, PCOMREUT, PCOMRETU, PCOUMTER, PCOUMTRE, PCOUMETR, PCOUMERT, PCOUMRTE, PCOUMRET, PCOUTMER, PCOUTMRE, PCOUTEMR, PCOUTERM, PCOUTRME, PCOUTREM, PCOUEMTR, PCOUEMRT, PCOUETMR, PCOUETRM, PCOUERMT, PCOUERTM, PCOURMTE, PCOURMET,
PCOURTME, PCOURTEM, PCOUREMT, PCOURETM, PCOTMUER, PCOTMURE, PCOTMEUR, PCOTMERU, PCOTMRUE, PCOTMREU, PCOTUMER, PCOTUMRE, PCOTUEMR, PCOTUERM, PCOTURME, PCOTUREM, PCOTEMUR, PCOTEMRU, PCOTEUMR, PCOTEURM, PCOTERMU, PCOTERUM, PCOTRMUE, PCOTRMEU, PCOTRUME, PCOTRUEM, PCOTREMU, PCOTREUM, PCOEMUTR, PCOEMURT, PCOEMTUR, PCOEMTRU, PCOEMRUT, PCOEMRTU, PCOEUMTR, PCOEUMRT, PCOEUTMR, PCOEUTRM, PCOEURMT, PCOEURTM, PCOETMUR, PCOETMRU, PCOETUMR, PCOETURM, PCOETRMU, PCOETRUM, PCOERMUT, PCOERMTU, PCOERUMT, PCOERUTM, PCOERTMU, PCOERTUM, PCORMUTE,
PCORMUET, PCORMTUE, PCORMTEU, PCORMEUT, PCORMETU, PCORUMTE, PCORUMET, PCORUTME, PCORUTEM, PCORUEMT, PCORUETM, PCORTMUE, PCORTMEU, PCORTUME, PCORTUEM, PCORTEMU, PCORTEUM, PCOREMUT, PCOREMTU, PCOREUMT, PCOREUTM, PCORETMU, PCORETUM, PMCOUTER, PMCOUTRE, PMCOUETR, PMCOUERT, PMCOURTE, PMCOURET, PMCOTUER, PMCOTURE, PMCOTEUR, PMCOTERU, PMCOTRUE, PMCOTREU, PMCOEUTR, PMCOEURT, PMCOETUR, PMCOETRU, PMCOERUT, PMCOERTU, PMCORUTE, PMCORUET, PMCORTUE, PMCORTEU, PMCOREUT, PMCORETU, PMUCOTER, PMUCOTRE, PMUCOETR, PMUCOERT, PMUCORTE, PMUCORET,
PMUTCOER, PMUTCORE, PMUTECOR, PMUTERCO, PMUTRCOE, PMUTRECO, PMUECOTR, PMUECORT, PMUETCOR, PMUETRCO, PMUERCOT, PMUERTCO, PMURCOTE, PMURCOET, PMURTCOE, PMURTECO, PMURECOT, PMURETCO, PMTCOUER, PMTCOURE, PMTCOEUR, PMTCOERU, PMTCORUE, PMTCOREU, PMTUCOER, PMTUCORE, PMTUECOR, PMTUERCO, PMTURCOE, PMTURECO, PMTECOUR, PMTECORU, PMTEUCOR, PMTEURCO, PMTERCOU, PMTERUCO, PMTRCOUE, PMTRCOEU, PMTRUCOE, PMTRUECO, PMTRECOU, PMTREUCO, PMECOUTR, PMECOURT, PMECOTUR, PMECOTRU, PMECORUT, PMECORTU, PMEUCOTR, PMEUCORT, PMEUTCOR, PMEUTRCO, PMEURCOT,
PMEURTCO, PMETCOUR, PMETCORU, PMETUCOR, PMETURCO, PMETRCOU, PMETRUCO, PMERCOUT, PMERCOTU, PMERUCOT, PMERUTCO, PMERTCOU, PMERTUCO, PMRCOUTE, PMRCOUET, PMRCOTUE, PMRCOTEU, PMRCOEUT, PMRCOETU, PMRUCOTE, PMRUCOET, PMRUTCOE, PMRUTECO, PMRUECOT, PMRUETCO, PMRTCOUE, PMRTCOEU, PMRTUCOE, PMRTUECO, PMRTECOU, PMRTEUCO, PMRECOUT, PMRECOTU, PMREUCOT, PMREUTCO, PMRETCOU, PMRETUCO, PUCOMTER, PUCOMTRE, PUCOMETR, PUCOMERT, PUCOMRTE, PUCOMRET, PUCOTMER, PUCOTMRE, PUCOTEMR, PUCOTERM, PUCOTRME, PUCOTREM, PUCOEMTR, PUCOEMRT, PUCOETMR, PUCOETRM,
PUCOERMT, PUCOERTM, PUCORMTE, PUCORMET, PUCORTME, PUCORTEM, PUCOREMT, PUCORETM, PUMCOTER, PUMCOTRE, PUMCOETR, PUMCOERT, PUMCORTE, PUMCORET, PUMTCOER, PUMTCORE, PUMTECOR, PUMTERCO, PUMTRCOE, PUMTRECO, PUMECOTR, PUMECORT, PUMETCOR, PUMETRCO, PUMERCOT, PUMERTCO, PUMRCOTE, PUMRCOET, PUMRTCOE, PUMRTECO, PUMRECOT, PUMRETCO, PUTCOMER, PUTCOMRE, PUTCOEMR, PUTCOERM, PUTCORME, PUTCOREM, PUTMCOER, PUTMCORE, PUTMECOR, PUTMERCO, PUTMRCOE, PUTMRECO, PUTECOMR, PUTECORM, PUTEMCOR, PUTEMRCO, PUTERCOM, PUTERMCO, PUTRCOME, PUTRCOEM, PUTRMCOE,
PUTRMECO, PUTRECOM, PUTREMCO, PUECOMTR, PUECOMRT, PUECOTMR, PUECOTRM, PUECORMT, PUECORTM, PUEMCOTR, PUEMCORT, PUEMTCOR, PUEMTRCO, PUEMRCOT, PUEMRTCO, PUETCOMR, PUETCORM, PUETMCOR, PUETMRCO, PUETRCOM, PUETRMCO, PUERCOMT, PUERCOTM, PUERMCOT, PUERMTCO, PUERTCOM, PUERTMCO, PURCOMTE, PURCOMET, PURCOTME, PURCOTEM, PURCOEMT, PURCOETM, PURMCOTE, PURMCOET, PURMTCOE, PURMTECO, PURMECOT, PURMETCO, PURTCOME, PURTCOEM, PURTMCOE, PURTMECO, PURTECOM, PURTEMCO, PURECOMT, PURECOTM, PUREMCOT, PUREMTCO, PURETCOM, PURETMCO, PTCOMUER, PTCOMURE,
PTCOMEUR, PTCOMERU, PTCOMRUE, PTCOMREU, PTCOUMER, PTCOUMRE, PTCOUEMR, PTCOUERM, PTCOURME, PTCOUREM, PTCOEMUR, PTCOEMRU, PTCOEUMR, PTCOEURM, PTCOERMU, PTCOERUM, PTCORMUE, PTCORMEU, PTCORUME, PTCORUEM, PTCOREMU, PTCOREUM, PTMCOUER, PTMCOURE, PTMCOEUR, PTMCOERU, PTMCORUE, PTMCOREU, PTMUCOER, PTMUCORE, PTMUECOR, PTMUERCO, PTMURCOE, PTMURECO, PTMECOUR, PTMECORU, PTMEUCOR, PTMEURCO, PTMERCOU, PTMERUCO, PTMRCOUE, PTMRCOEU, PTMRUCOE, PTMRUECO, PTMRECOU, PTMREUCO, PTUCOMER, PTUCOMRE, PTUCOEMR, PTUCOERM, PTUCORME, PTUCOREM, PTUMCOER,
PTUMCORE, PTUMECOR, PTUMERCO, PTUMRCOE, PTUMRECO, PTUECOMR, PTUECORM, PTUEMCOR, PTUEMRCO, PTUERCOM, PTUERMCO, PTURCOME, PTURCOEM, PTURMCOE, PTURMECO, PTURECOM, PTUREMCO, PTECOMUR, PTECOMRU, PTECOUMR, PTECOURM, PTECORMU, PTECORUM, PTEMCOUR, PTEMCORU, PTEMUCOR, PTEMURCO, PTEMRCOU, PTEMRUCO, PTEUCOMR, PTEUCORM, PTEUMCOR, PTEUMRCO, PTEURCOM, PTEURMCO, PTERCOMU, PTERCOUM, PTERMCOU, PTERMUCO, PTERUCOM, PTERUMCO, PTRCOMUE, PTRCOMEU, PTRCOUME, PTRCOUEM, PTRCOEMU, PTRCOEUM, PTRMCOUE, PTRMCOEU, PTRMUCOE, PTRMUECO, PTRMECOU, PTRMEUCO,
PTRUCOME, PTRUCOEM, PTRUMCOE, PTRUMECO, PTRUECOM, PTRUEMCO, PTRECOMU, PTRECOUM, PTREMCOU, PTREMUCO, PTREUCOM, PTREUMCO, PECOMUTR, PECOMURT, PECOMTUR, PECOMTRU, PECOMRUT, PECOMRTU, PECOUMTR, PECOUMRT, PECOUTMR, PECOUTRM, PECOURMT, PECOURTM, PECOTMUR, PECOTMRU, PECOTUMR, PECOTURM, PECOTRMU, PECOTRUM, PECORMUT, PECORMTU, PECORUMT, PECORUTM, PECORTMU, PECORTUM, PEMCOUTR, PEMCOURT, PEMCOTUR, PEMCOTRU, PEMCORUT, PEMCORTU, PEMUCOTR, PEMUCORT, PEMUTCOR, PEMUTRCO, PEMURCOT, PEMURTCO, PEMTCOUR, PEMTCORU, PEMTUCOR, PEMTURCO, PEMTRCOU,
PEMTRUCO, PEMRCOUT, PEMRCOTU, PEMRUCOT, PEMRUTCO, PEMRTCOU, PEMRTUCO, PEUCOMTR, PEUCOMRT, PEUCOTMR, PEUCOTRM, PEUCORMT, PEUCORTM, PEUMCOTR, PEUMCORT, PEUMTCOR, PEUMTRCO, PEUMRCOT, PEUMRTCO, PEUTCOMR, PEUTCORM, PEUTMCOR, PEUTMRCO, PEUTRCOM, PEUTRMCO, PEURCOMT, PEURCOTM, PEURMCOT, PEURMTCO, PEURTCOM, PEURTMCO, PETCOMUR, PETCOMRU, PETCOUMR, PETCOURM, PETCORMU, PETCORUM, PETMCOUR, PETMCORU, PETMUCOR, PETMURCO, PETMRCOU, PETMRUCO, PETUCOMR, PETUCORM, PETUMCOR, PETUMRCO, PETURCOM, PETURMCO, PETRCOMU, PETRCOUM, PETRMCOU, PETRMUCO,
PETRUCOM, PETRUMCO, PERCOMUT, PERCOMTU, PERCOUMT, PERCOUTM, PERCOTMU, PERCOTUM, PERMCOUT, PERMCOTU, PERMUCOT, PERMUTCO, PERMTCOU, PERMTUCO, PERUCOMT, PERUCOTM, PERUMCOT, PERUMTCO, PERUTCOM, PERUTMCO, PERTCOMU, PERTCOUM, PERTMCOU, PERTMUCO, PERTUCOM, PERTUMCO, PRCOMUTE, PRCOMUET, PRCOMTUE, PRCOMTEU, PRCOMEUT, PRCOMETU, PRCOUMTE, PRCOUMET, PRCOUTME, PRCOUTEM, PRCOUEMT, PRCOUETM, PRCOTMUE, PRCOTMEU, PRCOTUME, PRCOTUEM, PRCOTEMU, PRCOTEUM, PRCOEMUT, PRCOEMTU, PRCOEUMT, PRCOEUTM, PRCOETMU, PRCOETUM, PRMCOUTE, PRMCOUET, PRMCOTUE,
PRMCOTEU, PRMCOEUT, PRMCOETU, PRMUCOTE, PRMUCOET, PRMUTCOE, PRMUTECO, PRMUECOT, PRMUETCO, PRMTCOUE, PRMTCOEU, PRMTUCOE, PRMTUECO, PRMTECOU, PRMTEUCO, PRMECOUT, PRMECOTU, PRMEUCOT, PRMEUTCO, PRMETCOU, PRMETUCO, PRUCOMTE, PRUCOMET, PRUCOTME, PRUCOTEM, PRUCOEMT, PRUCOETM, PRUMCOTE, PRUMCOET, PRUMTCOE, PRUMTECO, PRUMECOT, PRUMETCO, PRUTCOME, PRUTCOEM, PRUTMCOE, PRUTMECO, PRUTECOM, PRUTEMCO, PRUECOMT, PRUECOTM, PRUEMCOT, PRUEMTCO, PRUETCOM, PRUETMCO, PRTCOMUE, PRTCOMEU, PRTCOUME, PRTCOUEM, PRTCOEMU, PRTCOEUM, PRTMCOUE, PRTMCOEU,
PRTMUCOE, PRTMUECO, PRTMECOU, PRTMEUCO, PRTUCOME, PRTUCOEM, PRTUMCOE, PRTUMECO, PRTUECOM, PRTUEMCO, PRTECOMU, PRTECOUM, PRTEMCOU, PRTEMUCO, PRTEUCOM, PRTEUMCO, PRECOMUT, PRECOMTU, PRECOUMT, PRECOUTM, PRECOTMU, PRECOTUM, PREMCOUT, PREMCOTU, PREMUCOT, PREMUTCO, PREMTCOU, PREMTUCO, PREUCOMT, PREUCOTM, PREUMCOT, PREUMTCO, PREUTCOM, PREUTMCO, PRETCOMU, PRETCOUM, PRETMCOU, PRETMUCO, PRETUCOM, PRETUMCO, UCOMPTER, UCOMPTRE, UCOMPETR, UCOMPERT, UCOMPRTE, UCOMPRET, UCOMTPER, UCOMTPRE, UCOMTEPR, UCOMTERP, UCOMTRPE, UCOMTREP, UCOMEPTR,
UCOMEPRT, UCOMETPR, UCOMETRP, UCOMERPT, UCOMERTP, UCOMRPTE, UCOMRPET, UCOMRTPE, UCOMRTEP, UCOMREPT, UCOMRETP, UCOPMTER, UCOPMTRE, UCOPMETR, UCOPMERT, UCOPMRTE, UCOPMRET, UCOPTMER, UCOPTMRE, UCOPTEMR, UCOPTERM, UCOPTRME, UCOPTREM, UCOPEMTR, UCOPEMRT, UCOPETMR, UCOPETRM, UCOPERMT, UCOPERTM, UCOPRMTE, UCOPRMET, UCOPRTME, UCOPRTEM, UCOPREMT, UCOPRETM, UCOTMPER, UCOTMPRE, UCOTMEPR, UCOTMERP, UCOTMRPE, UCOTMREP, UCOTPMER, UCOTPMRE, UCOTPEMR, UCOTPERM, UCOTPRME, UCOTPREM, UCOTEMPR, UCOTEMRP, UCOTEPMR, UCOTEPRM, UCOTERMP, UCOTERPM,
UCOTRMPE, UCOTRMEP, UCOTRPME, UCOTRPEM, UCOTREMP, UCOTREPM, UCOEMPTR, UCOEMPRT, UCOEMTPR, UCOEMTRP, UCOEMRPT, UCOEMRTP, UCOEPMTR, UCOEPMRT, UCOEPTMR, UCOEPTRM, UCOEPRMT, UCOEPRTM, UCOETMPR, UCOETMRP, UCOETPMR, UCOETPRM, UCOETRMP, UCOETRPM, UCOERMPT, UCOERMTP, UCOERPMT, UCOERPTM, UCOERTMP, UCOERTPM, UCORMPTE, UCORMPET, UCORMTPE, UCORMTEP, UCORMEPT, UCORMETP, UCORPMTE, UCORPMET, UCORPTME, UCORPTEM, UCORPEMT, UCORPETM, UCORTMPE, UCORTMEP, UCORTPME, UCORTPEM, UCORTEMP, UCORTEPM, UCOREMPT, UCOREMTP, UCOREPMT, UCOREPTM, UCORETMP,
UCORETPM, UMCOPTER, UMCOPTRE, UMCOPETR, UMCOPERT, UMCOPRTE, UMCOPRET, UMCOTPER, UMCOTPRE, UMCOTEPR, UMCOTERP, UMCOTRPE, UMCOTREP, UMCOEPTR, UMCOEPRT, UMCOETPR, UMCOETRP, UMCOERPT, UMCOERTP, UMCORPTE, UMCORPET, UMCORTPE, UMCORTEP, UMCOREPT, UMCORETP, UMPCOTER, UMPCOTRE, UMPCOETR, UMPCOERT, UMPCORTE, UMPCORET, UMPTCOER, UMPTCORE, UMPTECOR, UMPTERCO, UMPTRCOE, UMPTRECO, UMPECOTR, UMPECORT, UMPETCOR, UMPETRCO, UMPERCOT, UMPERTCO, UMPRCOTE, UMPRCOET, UMPRTCOE, UMPRTECO, UMPRECOT, UMPRETCO, UMTCOPER, UMTCOPRE, UMTCOEPR, UMTCOERP,
UMTCORPE, UMTCOREP, UMTPCOER, UMTPCORE, UMTPECOR, UMTPERCO, UMTPRCOE, UMTPRECO, UMTECOPR, UMTECORP, UMTEPCOR, UMTEPRCO, UMTERCOP, UMTERPCO, UMTRCOPE, UMTRCOEP, UMTRPCOE, UMTRPECO, UMTRECOP, UMTREPCO, UMECOPTR, UMECOPRT, UMECOTPR, UMECOTRP, UMECORPT, UMECORTP, UMEPCOTR, UMEPCORT, UMEPTCOR, UMEPTRCO, UMEPRCOT, UMEPRTCO, UMETCOPR, UMETCORP, UMETPCOR, UMETPRCO, UMETRCOP, UMETRPCO, UMERCOPT, UMERCOTP, UMERPCOT, UMERPTCO, UMERTCOP, UMERTPCO, UMRCOPTE, UMRCOPET, UMRCOTPE, UMRCOTEP, UMRCOEPT, UMRCOETP, UMRPCOTE, UMRPCOET, UMRPTCOE,
UMRPTECO, UMRPECOT, UMRPETCO, UMRTCOPE, UMRTCOEP, UMRTPCOE, UMRTPECO, UMRTECOP, UMRTEPCO, UMRECOPT, UMRECOTP, UMREPCOT, UMREPTCO, UMRETCOP, UMRETPCO, UPCOMTER, UPCOMTRE, UPCOMETR, UPCOMERT, UPCOMRTE, UPCOMRET, UPCOTMER, UPCOTMRE, UPCOTEMR, UPCOTERM, UPCOTRME, UPCOTREM, UPCOEMTR, UPCOEMRT, UPCOETMR, UPCOETRM, UPCOERMT, UPCOERTM, UPCORMTE, UPCORMET, UPCORTME, UPCORTEM, UPCOREMT, UPCORETM, UPMCOTER, UPMCOTRE, UPMCOETR, UPMCOERT, UPMCORTE, UPMCORET, UPMTCOER, UPMTCORE, UPMTECOR, UPMTERCO, UPMTRCOE, UPMTRECO, UPMECOTR, UPMECORT,
UPMETCOR, UPMETRCO, UPMERCOT, UPMERTCO, UPMRCOTE, UPMRCOET, UPMRTCOE, UPMRTECO, UPMRECOT, UPMRETCO, UPTCOMER, UPTCOMRE, UPTCOEMR, UPTCOERM, UPTCORME, UPTCOREM, UPTMCOER, UPTMCORE, UPTMECOR, UPTMERCO, UPTMRCOE, UPTMRECO, UPTECOMR, UPTECORM, UPTEMCOR, UPTEMRCO, UPTERCOM, UPTERMCO, UPTRCOME, UPTRCOEM, UPTRMCOE, UPTRMECO, UPTRECOM, UPTREMCO, UPECOMTR, UPECOMRT, UPECOTMR, UPECOTRM, UPECORMT, UPECORTM, UPEMCOTR, UPEMCORT, UPEMTCOR, UPEMTRCO, UPEMRCOT, UPEMRTCO, UPETCOMR, UPETCORM, UPETMCOR, UPETMRCO, UPETRCOM, UPETRMCO, UPERCOMT,
UPERCOTM, UPERMCOT, UPERMTCO, UPERTCOM, UPERTMCO, UPRCOMTE, UPRCOMET, UPRCOTME, UPRCOTEM, UPRCOEMT, UPRCOETM, UPRMCOTE, UPRMCOET, UPRMTCOE, UPRMTECO, UPRMECOT, UPRMETCO, UPRTCOME, UPRTCOEM, UPRTMCOE, UPRTMECO, UPRTECOM, UPRTEMCO, UPRECOMT, UPRECOTM, UPREMCOT, UPREMTCO, UPRETCOM, UPRETMCO, UTCOMPER, UTCOMPRE, UTCOMEPR, UTCOMERP, UTCOMRPE, UTCOMREP, UTCOPMER, UTCOPMRE, UTCOPEMR, UTCOPERM, UTCOPRME, UTCOPREM, UTCOEMPR, UTCOEMRP, UTCOEPMR, UTCOEPRM, UTCOERMP, UTCOERPM, UTCORMPE, UTCORMEP, UTCORPME, UTCORPEM, UTCOREMP, UTCOREPM,
UTMCOPER, UTMCOPRE, UTMCOEPR, UTMCOERP, UTMCORPE, UTMCOREP, UTMPCOER, UTMPCORE, UTMPECOR, UTMPERCO, UTMPRCOE, UTMPRECO, UTMECOPR, UTMECORP, UTMEPCOR, UTMEPRCO, UTMERCOP, UTMERPCO, UTMRCOPE, UTMRCOEP, UTMRPCOE, UTMRPECO, UTMRECOP, UTMREPCO, UTPCOMER, UTPCOMRE, UTPCOEMR, UTPCOERM, UTPCORME, UTPCOREM, UTPMCOER, UTPMCORE, UTPMECOR, UTPMERCO, UTPMRCOE, UTPMRECO, UTPECOMR, UTPECORM, UTPEMCOR, UTPEMRCO, UTPERCOM, UTPERMCO, UTPRCOME, UTPRCOEM, UTPRMCOE, UTPRMECO, UTPRECOM, UTPREMCO, UTECOMPR, UTECOMRP, UTECOPMR, UTECOPRM, UTECORMP,
UTECORPM, UTEMCOPR, UTEMCORP, UTEMPCOR, UTEMPRCO, UTEMRCOP, UTEMRPCO, UTEPCOMR, UTEPCORM, UTEPMCOR, UTEPMRCO, UTEPRCOM, UTEPRMCO, UTERCOMP, UTERCOPM, UTERMCOP, UTERMPCO, UTERPCOM, UTERPMCO, UTRCOMPE, UTRCOMEP, UTRCOPME, UTRCOPEM, UTRCOEMP, UTRCOEPM, UTRMCOPE, UTRMCOEP, UTRMPCOE, UTRMPECO, UTRMECOP, UTRMEPCO, UTRPCOME, UTRPCOEM, UTRPMCOE, UTRPMECO, UTRPECOM, UTRPEMCO, UTRECOMP, UTRECOPM, UTREMCOP, UTREMPCO, UTREPCOM, UTREPMCO, UECOMPTR, UECOMPRT, UECOMTPR, UECOMTRP, UECOMRPT, UECOMRTP, UECOPMTR, UECOPMRT, UECOPTMR, UECOPTRM,
UECOPRMT, UECOPRTM, UECOTMPR, UECOTMRP, UECOTPMR, UECOTPRM, UECOTRMP, UECOTRPM, UECORMPT, UECORMTP, UECORPMT, UECORPTM, UECORTMP, UECORTPM, UEMCOPTR, UEMCOPRT, UEMCOTPR, UEMCOTRP, UEMCORPT, UEMCORTP, UEMPCOTR, UEMPCORT, UEMPTCOR, UEMPTRCO, UEMPRCOT, UEMPRTCO, UEMTCOPR, UEMTCORP, UEMTPCOR, UEMTPRCO, UEMTRCOP, UEMTRPCO, UEMRCOPT, UEMRCOTP, UEMRPCOT, UEMRPTCO, UEMRTCOP, UEMRTPCO, UEPCOMTR, UEPCOMRT, UEPCOTMR, UEPCOTRM, UEPCORMT, UEPCORTM, UEPMCOTR, UEPMCORT, UEPMTCOR, UEPMTRCO, UEPMRCOT, UEPMRTCO, UEPTCOMR, UEPTCORM, UEPTMCOR,
UEPTMRCO, UEPTRCOM, UEPTRMCO, UEPRCOMT, UEPRCOTM, UEPRMCOT, UEPRMTCO, UEPRTCOM, UEPRTMCO, UETCOMPR, UETCOMRP, UETCOPMR, UETCOPRM, UETCORMP, UETCORPM, UETMCOPR, UETMCORP, UETMPCOR, UETMPRCO, UETMRCOP, UETMRPCO, UETPCOMR, UETPCORM, UETPMCOR, UETPMRCO, UETPRCOM, UETPRMCO, UETRCOMP, UETRCOPM, UETRMCOP, UETRMPCO, UETRPCOM, UETRPMCO, UERCOMPT, UERCOMTP, UERCOPMT, UERCOPTM, UERCOTMP, UERCOTPM, UERMCOPT, UERMCOTP, UERMPCOT, UERMPTCO, UERMTCOP, UERMTPCO, UERPCOMT, UERPCOTM, UERPMCOT, UERPMTCO, UERPTCOM, UERPTMCO, UERTCOMP, UERTCOPM,
UERTMCOP, UERTMPCO, UERTPCOM, UERTPMCO, URCOMPTE, URCOMPET, URCOMTPE, URCOMTEP, URCOMEPT, URCOMETP, URCOPMTE, URCOPMET, URCOPTME, URCOPTEM, URCOPEMT, URCOPETM, URCOTMPE, URCOTMEP, URCOTPME, URCOTPEM, URCOTEMP, URCOTEPM, URCOEMPT, URCOEMTP, URCOEPMT, URCOEPTM, URCOETMP, URCOETPM, URMCOPTE, URMCOPET, URMCOTPE, URMCOTEP, URMCOEPT, URMCOETP, URMPCOTE, URMPCOET, URMPTCOE, URMPTECO, URMPECOT, URMPETCO, URMTCOPE, URMTCOEP, URMTPCOE, URMTPECO, URMTECOP, URMTEPCO, URMECOPT, URMECOTP, URMEPCOT, URMEPTCO, URMETCOP, URMETPCO, URPCOMTE,
URPCOMET, URPCOTME, URPCOTEM, URPCOEMT, URPCOETM, URPMCOTE, URPMCOET, URPMTCOE, URPMTECO, URPMECOT, URPMETCO, URPTCOME, URPTCOEM, URPTMCOE, URPTMECO, URPTECOM, URPTEMCO, URPECOMT, URPECOTM, URPEMCOT, URPEMTCO, URPETCOM, URPETMCO, URTCOMPE, URTCOMEP, URTCOPME, URTCOPEM, URTCOEMP, URTCOEPM, URTMCOPE, URTMCOEP, URTMPCOE, URTMPECO, URTMECOP, URTMEPCO, URTPCOME, URTPCOEM, URTPMCOE, URTPMECO, URTPECOM, URTPEMCO, URTECOMP, URTECOPM, URTEMCOP, URTEMPCO, URTEPCOM, URTEPMCO, URECOMPT, URECOMTP, URECOPMT, URECOPTM, URECOTMP, URECOTPM,
UREMCOPT, UREMCOTP, UREMPCOT, UREMPTCO, UREMTCOP, UREMTPCO, UREPCOMT, UREPCOTM, UREPMCOT, UREPMTCO, UREPTCOM, UREPTMCO, URETCOMP, URETCOPM, URETMCOP, URETMPCO, URETPCOM, URETPMCO, TCOMPUER, TCOMPURE, TCOMPEUR, TCOMPERU, TCOMPRUE, TCOMPREU, TCOMUPER, TCOMUPRE, TCOMUEPR, TCOMUERP, TCOMURPE, TCOMUREP, TCOMEPUR, TCOMEPRU, TCOMEUPR, TCOMEURP, TCOMERPU, TCOMERUP, TCOMRPUE, TCOMRPEU, TCOMRUPE, TCOMRUEP, TCOMREPU, TCOMREUP, TCOPMUER, TCOPMURE, TCOPMEUR, TCOPMERU, TCOPMRUE, TCOPMREU, TCOPUMER, TCOPUMRE, TCOPUEMR, TCOPUERM, TCOPURME,
TCOPUREM, TCOPEMUR, TCOPEMRU, TCOPEUMR, TCOPEURM, TCOPERMU, TCOPERUM, TCOPRMUE, TCOPRMEU, TCOPRUME, TCOPRUEM, TCOPREMU, TCOPREUM, TCOUMPER, TCOUMPRE, TCOUMEPR, TCOUMERP, TCOUMRPE, TCOUMREP, TCOUPMER, TCOUPMRE, TCOUPEMR, TCOUPERM, TCOUPRME, TCOUPREM, TCOUEMPR, TCOUEMRP, TCOUEPMR, TCOUEPRM, TCOUERMP, TCOUERPM, TCOURMPE, TCOURMEP, TCOURPME, TCOURPEM, TCOUREMP, TCOUREPM, TCOEMPUR, TCOEMPRU, TCOEMUPR, TCOEMURP, TCOEMRPU, TCOEMRUP, TCOEPMUR, TCOEPMRU, TCOEPUMR, TCOEPURM, TCOEPRMU, TCOEPRUM, TCOEUMPR, TCOEUMRP, TCOEUPMR, TCOEUPRM,
TCOEURMP, TCOEURPM, TCOERMPU, TCOERMUP, TCOERPMU, TCOERPUM, TCOERUMP, TCOERUPM, TCORMPUE, TCORMPEU, TCORMUPE, TCORMUEP, TCORMEPU, TCORMEUP, TCORPMUE, TCORPMEU, TCORPUME, TCORPUEM, TCORPEMU, TCORPEUM, TCORUMPE, TCORUMEP, TCORUPME, TCORUPEM, TCORUEMP, TCORUEPM, TCOREMPU, TCOREMUP, TCOREPMU, TCOREPUM, TCOREUMP, TCOREUPM, TMCOPUER, TMCOPURE, TMCOPEUR, TMCOPERU, TMCOPRUE, TMCOPREU, TMCOUPER, TMCOUPRE, TMCOUEPR, TMCOUERP, TMCOURPE, TMCOUREP, TMCOEPUR, TMCOEPRU, TMCOEUPR, TMCOEURP, TMCOERPU, TMCOERUP, TMCORPUE, TMCORPEU, TMCORUPE,
TMCORUEP, TMCOREPU, TMCOREUP, TMPCOUER, TMPCOURE, TMPCOEUR, TMPCOERU, TMPCORUE, TMPCOREU, TMPUCOER, TMPUCORE, TMPUECOR, TMPUERCO, TMPURCOE, TMPURECO, TMPECOUR, TMPECORU, TMPEUCOR, TMPEURCO, TMPERCOU, TMPERUCO, TMPRCOUE, TMPRCOEU, TMPRUCOE, TMPRUECO, TMPRECOU, TMPREUCO, TMUCOPER, TMUCOPRE, TMUCOEPR, TMUCOERP, TMUCORPE, TMUCOREP, TMUPCOER, TMUPCORE, TMUPECOR, TMUPERCO, TMUPRCOE, TMUPRECO, TMUECOPR, TMUECORP, TMUEPCOR, TMUEPRCO, TMUERCOP, TMUERPCO, TMURCOPE, TMURCOEP, TMURPCOE, TMURPECO, TMURECOP, TMUREPCO, TMECOPUR, TMECOPRU,
TMECOUPR, TMECOURP, TMECORPU, TMECORUP, TMEPCOUR, TMEPCORU, TMEPUCOR, TMEPURCO, TMEPRCOU, TMEPRUCO, TMEUCOPR, TMEUCORP, TMEUPCOR, TMEUPRCO, TMEURCOP, TMEURPCO, TMERCOPU, TMERCOUP, TMERPCOU, TMERPUCO, TMERUCOP, TMERUPCO, TMRCOPUE, TMRCOPEU, TMRCOUPE, TMRCOUEP, TMRCOEPU, TMRCOEUP, TMRPCOUE, TMRPCOEU, TMRPUCOE, TMRPUECO, TMRPECOU, TMRPEUCO, TMRUCOPE, TMRUCOEP, TMRUPCOE, TMRUPECO, TMRUECOP, TMRUEPCO, TMRECOPU, TMRECOUP, TMREPCOU, TMREPUCO, TMREUCOP, TMREUPCO, TPCOMUER, TPCOMURE, TPCOMEUR, TPCOMERU, TPCOMRUE, TPCOMREU, TPCOUMER,
TPCOUMRE, TPCOUEMR, TPCOUERM, TPCOURME, TPCOUREM, TPCOEMUR, TPCOEMRU, TPCOEUMR, TPCOEURM, TPCOERMU, TPCOERUM, TPCORMUE, TPCORMEU, TPCORUME, TPCORUEM, TPCOREMU, TPCOREUM, TPMCOUER, TPMCOURE, TPMCOEUR, TPMCOERU, TPMCORUE, TPMCOREU, TPMUCOER, TPMUCORE, TPMUECOR, TPMUERCO, TPMURCOE, TPMURECO, TPMECOUR, TPMECORU, TPMEUCOR, TPMEURCO, TPMERCOU, TPMERUCO, TPMRCOUE, TPMRCOEU, TPMRUCOE, TPMRUECO, TPMRECOU, TPMREUCO, TPUCOMER, TPUCOMRE, TPUCOEMR, TPUCOERM, TPUCORME, TPUCOREM, TPUMCOER, TPUMCORE, TPUMECOR, TPUMERCO, TPUMRCOE, TPUMRECO,
TPUECOMR, TPUECORM, TPUEMCOR, TPUEMRCO, TPUERCOM, TPUERMCO, TPURCOME, TPURCOEM, TPURMCOE, TPURMECO, TPURECOM, TPUREMCO, TPECOMUR, TPECOMRU, TPECOUMR, TPECOURM, TPECORMU, TPECORUM, TPEMCOUR, TPEMCORU, TPEMUCOR, TPEMURCO, TPEMRCOU, TPEMRUCO, TPEUCOMR, TPEUCORM, TPEUMCOR, TPEUMRCO, TPEURCOM, TPEURMCO, TPERCOMU, TPERCOUM, TPERMCOU, TPERMUCO, TPERUCOM, TPERUMCO, TPRCOMUE, TPRCOMEU, TPRCOUME, TPRCOUEM, TPRCOEMU, TPRCOEUM, TPRMCOUE, TPRMCOEU, TPRMUCOE, TPRMUECO, TPRMECOU, TPRMEUCO, TPRUCOME, TPRUCOEM, TPRUMCOE, TPRUMECO, TPRUECOM,
TPRUEMCO, TPRECOMU, TPRECOUM, TPREMCOU, TPREMUCO, TPREUCOM, TPREUMCO, TUCOMPER, TUCOMPRE, TUCOMEPR, TUCOMERP, TUCOMRPE, TUCOMREP, TUCOPMER, TUCOPMRE, TUCOPEMR, TUCOPERM, TUCOPRME, TUCOPREM, TUCOEMPR, TUCOEMRP, TUCOEPMR, TUCOEPRM, TUCOERMP, TUCOERPM, TUCORMPE, TUCORMEP, TUCORPME, TUCORPEM, TUCOREMP, TUCOREPM, TUMCOPER, TUMCOPRE, TUMCOEPR, TUMCOERP, TUMCORPE, TUMCOREP, TUMPCOER, TUMPCORE, TUMPECOR, TUMPERCO, TUMPRCOE, TUMPRECO, TUMECOPR, TUMECORP, TUMEPCOR, TUMEPRCO, TUMERCOP, TUMERPCO, TUMRCOPE, TUMRCOEP, TUMRPCOE, TUMRPECO,
TUMRECOP, TUMREPCO, TUPCOMER, TUPCOMRE, TUPCOEMR, TUPCOERM, TUPCORME, TUPCOREM, TUPMCOER, TUPMCORE, TUPMECOR, TUPMERCO, TUPMRCOE, TUPMRECO, TUPECOMR, TUPECORM, TUPEMCOR, TUPEMRCO, TUPERCOM, TUPERMCO, TUPRCOME, TUPRCOEM, TUPRMCOE, TUPRMECO, TUPRECOM, TUPREMCO, TUECOMPR, TUECOMRP, TUECOPMR, TUECOPRM, TUECORMP, TUECORPM, TUEMCOPR, TUEMCORP, TUEMPCOR, TUEMPRCO, TUEMRCOP, TUEMRPCO, TUEPCOMR, TUEPCORM, TUEPMCOR, TUEPMRCO, TUEPRCOM, TUEPRMCO, TUERCOMP, TUERCOPM, TUERMCOP, TUERMPCO, TUERPCOM, TUERPMCO, TURCOMPE, TURCOMEP, TURCOPME,
TURCOPEM, TURCOEMP, TURCOEPM, TURMCOPE, TURMCOEP, TURMPCOE, TURMPECO, TURMECOP, TURMEPCO, TURPCOME, TURPCOEM, TURPMCOE, TURPMECO, TURPECOM, TURPEMCO, TURECOMP, TURECOPM, TUREMCOP, TUREMPCO, TUREPCOM, TUREPMCO, TECOMPUR, TECOMPRU, TECOMUPR, TECOMURP, TECOMRPU, TECOMRUP, TECOPMUR, TECOPMRU, TECOPUMR, TECOPURM, TECOPRMU, TECOPRUM, TECOUMPR, TECOUMRP, TECOUPMR, TECOUPRM, TECOURMP, TECOURPM, TECORMPU, TECORMUP, TECORPMU, TECORPUM, TECORUMP, TECORUPM, TEMCOPUR, TEMCOPRU, TEMCOUPR, TEMCOURP, TEMCORPU, TEMCORUP, TEMPCOUR, TEMPCORU,
TEMPUCOR, TEMPURCO, TEMPRCOU, TEMPRUCO, TEMUCOPR, TEMUCORP, TEMUPCOR, TEMUPRCO, TEMURCOP, TEMURPCO, TEMRCOPU, TEMRCOUP, TEMRPCOU, TEMRPUCO, TEMRUCOP, TEMRUPCO, TEPCOMUR, TEPCOMRU, TEPCOUMR, TEPCOURM, TEPCORMU, TEPCORUM, TEPMCOUR, TEPMCORU, TEPMUCOR, TEPMURCO, TEPMRCOU, TEPMRUCO, TEPUCOMR, TEPUCORM, TEPUMCOR, TEPUMRCO, TEPURCOM, TEPURMCO, TEPRCOMU, TEPRCOUM, TEPRMCOU, TEPRMUCO, TEPRUCOM, TEPRUMCO, TEUCOMPR, TEUCOMRP, TEUCOPMR, TEUCOPRM, TEUCORMP, TEUCORPM, TEUMCOPR, TEUMCORP, TEUMPCOR, TEUMPRCO, TEUMRCOP, TEUMRPCO, TEUPCOMR,
TEUPCORM, TEUPMCOR, TEUPMRCO, TEUPRCOM, TEUPRMCO, TEURCOMP, TEURCOPM, TEURMCOP, TEURMPCO, TEURPCOM, TEURPMCO, TERCOMPU, TERCOMUP, TERCOPMU, TERCOPUM, TERCOUMP, TERCOUPM, TERMCOPU, TERMCOUP, TERMPCOU, TERMPUCO, TERMUCOP, TERMUPCO, TERPCOMU, TERPCOUM, TERPMCOU, TERPMUCO, TERPUCOM, TERPUMCO, TERUCOMP, TERUCOPM, TERUMCOP, TERUMPCO, TERUPCOM, TERUPMCO, TRCOMPUE, TRCOMPEU, TRCOMUPE, TRCOMUEP, TRCOMEPU, TRCOMEUP, TRCOPMUE, TRCOPMEU, TRCOPUME, TRCOPUEM, TRCOPEMU, TRCOPEUM, TRCOUMPE, TRCOUMEP, TRCOUPME, TRCOUPEM, TRCOUEMP, TRCOUEPM,
TRCOEMPU, TRCOEMUP, TRCOEPMU, TRCOEPUM, TRCOEUMP, TRCOEUPM, TRMCOPUE, TRMCOPEU, TRMCOUPE, TRMCOUEP, TRMCOEPU, TRMCOEUP, TRMPCOUE, TRMPCOEU, TRMPUCOE, TRMPUECO, TRMPECOU, TRMPEUCO, TRMUCOPE, TRMUCOEP, TRMUPCOE, TRMUPECO, TRMUECOP, TRMUEPCO, TRMECOPU, TRMECOUP, TRMEPCOU, TRMEPUCO, TRMEUCOP, TRMEUPCO, TRPCOMUE, TRPCOMEU, TRPCOUME, TRPCOUEM, TRPCOEMU, TRPCOEUM, TRPMCOUE, TRPMCOEU, TRPMUCOE, TRPMUECO, TRPMECOU, TRPMEUCO, TRPUCOME, TRPUCOEM, TRPUMCOE, TRPUMECO, TRPUECOM, TRPUEMCO, TRPECOMU, TRPECOUM, TRPEMCOU, TRPEMUCO, TRPEUCOM,
TRPEUMCO, TRUCOMPE, TRUCOMEP, TRUCOPME, TRUCOPEM, TRUCOEMP, TRUCOEPM, TRUMCOPE, TRUMCOEP, TRUMPCOE, TRUMPECO, TRUMECOP, TRUMEPCO, TRUPCOME, TRUPCOEM, TRUPMCOE, TRUPMECO, TRUPECOM, TRUPEMCO, TRUECOMP, TRUECOPM, TRUEMCOP, TRUEMPCO, TRUEPCOM, TRUEPMCO, TRECOMPU, TRECOMUP, TRECOPMU, TRECOPUM, TRECOUMP, TRECOUPM, TREMCOPU, TREMCOUP, TREMPCOU, TREMPUCO, TREMUCOP, TREMUPCO, TREPCOMU, TREPCOUM, TREPMCOU, TREPMUCO, TREPUCOM, TREPUMCO, TREUCOMP, TREUCOPM, TREUMCOP, TREUMPCO, TREUPCOM, TREUPMCO, ECOMPUTR, ECOMPURT, ECOMPTUR, ECOMPTRU,
ECOMPRUT, ECOMPRTU, ECOMUPTR, ECOMUPRT, ECOMUTPR, ECOMUTRP, ECOMURPT, ECOMURTP, ECOMTPUR, ECOMTPRU, ECOMTUPR, ECOMTURP, ECOMTRPU, ECOMTRUP, ECOMRPUT, ECOMRPTU, ECOMRUPT, ECOMRUTP, ECOMRTPU, ECOMRTUP, ECOPMUTR, ECOPMURT, ECOPMTUR, ECOPMTRU, ECOPMRUT, ECOPMRTU, ECOPUMTR, ECOPUMRT, ECOPUTMR, ECOPUTRM, ECOPURMT, ECOPURTM, ECOPTMUR, ECOPTMRU, ECOPTUMR, ECOPTURM, ECOPTRMU, ECOPTRUM, ECOPRMUT, ECOPRMTU, ECOPRUMT, ECOPRUTM, ECOPRTMU, ECOPRTUM, ECOUMPTR, ECOUMPRT, ECOUMTPR, ECOUMTRP, ECOUMRPT, ECOUMRTP, ECOUPMTR, ECOUPMRT, ECOUPTMR,
ECOUPTRM, ECOUPRMT, ECOUPRTM, ECOUTMPR, ECOUTMRP, ECOUTPMR, ECOUTPRM, ECOUTRMP, ECOUTRPM, ECOURMPT, ECOURMTP, ECOURPMT, ECOURPTM, ECOURTMP, ECOURTPM, ECOTMPUR, ECOTMPRU, ECOTMUPR, ECOTMURP, ECOTMRPU, ECOTMRUP, ECOTPMUR, ECOTPMRU, ECOTPUMR, ECOTPURM, ECOTPRMU, ECOTPRUM, ECOTUMPR, ECOTUMRP, ECOTUPMR, ECOTUPRM, ECOTURMP, ECOTURPM, ECOTRMPU, ECOTRMUP, ECOTRPMU, ECOTRPUM, ECOTRUMP, ECOTRUPM, ECORMPUT, ECORMPTU, ECORMUPT, ECORMUTP, ECORMTPU, ECORMTUP, ECORPMUT, ECORPMTU, ECORPUMT, ECORPUTM, ECORPTMU, ECORPTUM, ECORUMPT, ECORUMTP,
ECORUPMT, ECORUPTM, ECORUTMP, ECORUTPM, ECORTMPU, ECORTMUP, ECORTPMU, ECORTPUM, ECORTUMP, ECORTUPM, EMCOPUTR, EMCOPURT, EMCOPTUR, EMCOPTRU, EMCOPRUT, EMCOPRTU, EMCOUPTR, EMCOUPRT, EMCOUTPR, EMCOUTRP, EMCOURPT, EMCOURTP, EMCOTPUR, EMCOTPRU, EMCOTUPR, EMCOTURP, EMCOTRPU, EMCOTRUP, EMCORPUT, EMCORPTU, EMCORUPT, EMCORUTP, EMCORTPU, EMCORTUP, EMPCOUTR, EMPCOURT, EMPCOTUR, EMPCOTRU, EMPCORUT, EMPCORTU, EMPUCOTR, EMPUCORT, EMPUTCOR, EMPUTRCO, EMPURCOT, EMPURTCO, EMPTCOUR, EMPTCORU, EMPTUCOR, EMPTURCO, EMPTRCOU, EMPTRUCO, EMPRCOUT,
EMPRCOTU, EMPRUCOT, EMPRUTCO, EMPRTCOU, EMPRTUCO, EMUCOPTR, EMUCOPRT, EMUCOTPR, EMUCOTRP, EMUCORPT, EMUCORTP, EMUPCOTR, EMUPCORT, EMUPTCOR, EMUPTRCO, EMUPRCOT, EMUPRTCO, EMUTCOPR, EMUTCORP, EMUTPCOR, EMUTPRCO, EMUTRCOP, EMUTRPCO, EMURCOPT, EMURCOTP, EMURPCOT, EMURPTCO, EMURTCOP, EMURTPCO, EMTCOPUR, EMTCOPRU, EMTCOUPR, EMTCOURP, EMTCORPU, EMTCORUP, EMTPCOUR, EMTPCORU, EMTPUCOR, EMTPURCO, EMTPRCOU, EMTPRUCO, EMTUCOPR, EMTUCORP, EMTUPCOR, EMTUPRCO, EMTURCOP, EMTURPCO, EMTRCOPU, EMTRCOUP, EMTRPCOU, EMTRPUCO, EMTRUCOP, EMTRUPCO,
EMRCOPUT, EMRCOPTU, EMRCOUPT, EMRCOUTP, EMRCOTPU, EMRCOTUP, EMRPCOUT, EMRPCOTU, EMRPUCOT, EMRPUTCO, EMRPTCOU, EMRPTUCO, EMRUCOPT, EMRUCOTP, EMRUPCOT, EMRUPTCO, EMRUTCOP, EMRUTPCO, EMRTCOPU, EMRTCOUP, EMRTPCOU, EMRTPUCO, EMRTUCOP, EMRTUPCO, EPCOMUTR, EPCOMURT, EPCOMTUR, EPCOMTRU, EPCOMRUT, EPCOMRTU, EPCOUMTR, EPCOUMRT, EPCOUTMR, EPCOUTRM, EPCOURMT, EPCOURTM, EPCOTMUR, EPCOTMRU, EPCOTUMR, EPCOTURM, EPCOTRMU, EPCOTRUM, EPCORMUT, EPCORMTU, EPCORUMT, EPCORUTM, EPCORTMU, EPCORTUM, EPMCOUTR, EPMCOURT, EPMCOTUR, EPMCOTRU, EPMCORUT,
EPMCORTU, EPMUCOTR, EPMUCORT, EPMUTCOR, EPMUTRCO, EPMURCOT, EPMURTCO, EPMTCOUR, EPMTCORU, EPMTUCOR, EPMTURCO, EPMTRCOU, EPMTRUCO, EPMRCOUT, EPMRCOTU, EPMRUCOT, EPMRUTCO, EPMRTCOU, EPMRTUCO, EPUCOMTR, EPUCOMRT, EPUCOTMR, EPUCOTRM, EPUCORMT, EPUCORTM, EPUMCOTR, EPUMCORT, EPUMTCOR, EPUMTRCO, EPUMRCOT, EPUMRTCO, EPUTCOMR, EPUTCORM, EPUTMCOR, EPUTMRCO, EPUTRCOM, EPUTRMCO, EPURCOMT, EPURCOTM, EPURMCOT, EPURMTCO, EPURTCOM, EPURTMCO, EPTCOMUR, EPTCOMRU, EPTCOUMR, EPTCOURM, EPTCORMU, EPTCORUM, EPTMCOUR, EPTMCORU, EPTMUCOR, EPTMURCO,
EPTMRCOU, EPTMRUCO, EPTUCOMR, EPTUCORM, EPTUMCOR, EPTUMRCO, EPTURCOM, EPTURMCO, EPTRCOMU, EPTRCOUM, EPTRMCOU, EPTRMUCO, EPTRUCOM, EPTRUMCO, EPRCOMUT, EPRCOMTU, EPRCOUMT, EPRCOUTM, EPRCOTMU, EPRCOTUM, EPRMCOUT, EPRMCOTU, EPRMUCOT, EPRMUTCO, EPRMTCOU, EPRMTUCO, EPRUCOMT, EPRUCOTM, EPRUMCOT, EPRUMTCO, EPRUTCOM, EPRUTMCO, EPRTCOMU, EPRTCOUM, EPRTMCOU, EPRTMUCO, EPRTUCOM, EPRTUMCO, EUCOMPTR, EUCOMPRT, EUCOMTPR, EUCOMTRP, EUCOMRPT, EUCOMRTP, EUCOPMTR, EUCOPMRT, EUCOPTMR, EUCOPTRM, EUCOPRMT, EUCOPRTM, EUCOTMPR, EUCOTMRP, EUCOTPMR,
EUCOTPRM, EUCOTRMP, EUCOTRPM, EUCORMPT, EUCORMTP, EUCORPMT, EUCORPTM, EUCORTMP, EUCORTPM, EUMCOPTR, EUMCOPRT, EUMCOTPR, EUMCOTRP, EUMCORPT, EUMCORTP, EUMPCOTR, EUMPCORT, EUMPTCOR, EUMPTRCO, EUMPRCOT, EUMPRTCO, EUMTCOPR, EUMTCORP, EUMTPCOR, EUMTPRCO, EUMTRCOP, EUMTRPCO, EUMRCOPT, EUMRCOTP, EUMRPCOT, EUMRPTCO, EUMRTCOP, EUMRTPCO, EUPCOMTR, EUPCOMRT, EUPCOTMR, EUPCOTRM, EUPCORMT, EUPCORTM, EUPMCOTR, EUPMCORT, EUPMTCOR, EUPMTRCO, EUPMRCOT, EUPMRTCO, EUPTCOMR, EUPTCORM, EUPTMCOR, EUPTMRCO, EUPTRCOM, EUPTRMCO, EUPRCOMT, EUPRCOTM,
EUPRMCOT, EUPRMTCO, EUPRTCOM, EUPRTMCO, EUTCOMPR, EUTCOMRP, EUTCOPMR, EUTCOPRM, EUTCORMP, EUTCORPM, EUTMCOPR, EUTMCORP, EUTMPCOR, EUTMPRCO, EUTMRCOP, EUTMRPCO, EUTPCOMR, EUTPCORM, EUTPMCOR, EUTPMRCO, EUTPRCOM, EUTPRMCO, EUTRCOMP, EUTRCOPM, EUTRMCOP, EUTRMPCO, EUTRPCOM, EUTRPMCO, EURCOMPT, EURCOMTP, EURCOPMT, EURCOPTM, EURCOTMP, EURCOTPM, EURMCOPT, EURMCOTP, EURMPCOT, EURMPTCO, EURMTCOP, EURMTPCO, EURPCOMT, EURPCOTM, EURPMCOT, EURPMTCO, EURPTCOM, EURPTMCO, EURTCOMP, EURTCOPM, EURTMCOP, EURTMPCO, EURTPCOM, EURTPMCO, ETCOMPUR,
ETCOMPRU, ETCOMUPR, ETCOMURP, ETCOMRPU, ETCOMRUP, ETCOPMUR, ETCOPMRU, ETCOPUMR, ETCOPURM, ETCOPRMU, ETCOPRUM, ETCOUMPR, ETCOUMRP, ETCOUPMR, ETCOUPRM, ETCOURMP, ETCOURPM, ETCORMPU, ETCORMUP, ETCORPMU, ETCORPUM, ETCORUMP, ETCORUPM, ETMCOPUR, ETMCOPRU, ETMCOUPR, ETMCOURP, ETMCORPU, ETMCORUP, ETMPCOUR, ETMPCORU, ETMPUCOR, ETMPURCO, ETMPRCOU, ETMPRUCO, ETMUCOPR, ETMUCORP, ETMUPCOR, ETMUPRCO, ETMURCOP, ETMURPCO, ETMRCOPU, ETMRCOUP, ETMRPCOU, ETMRPUCO, ETMRUCOP, ETMRUPCO, ETPCOMUR, ETPCOMRU, ETPCOUMR, ETPCOURM, ETPCORMU, ETPCORUM,
ETPMCOUR, ETPMCORU, ETPMUCOR, ETPMURCO, ETPMRCOU, ETPMRUCO, ETPUCOMR, ETPUCORM, ETPUMCOR, ETPUMRCO, ETPURCOM, ETPURMCO, ETPRCOMU, ETPRCOUM, ETPRMCOU, ETPRMUCO, ETPRUCOM, ETPRUMCO, ETUCOMPR, ETUCOMRP, ETUCOPMR, ETUCOPRM, ETUCORMP, ETUCORPM, ETUMCOPR, ETUMCORP, ETUMPCOR, ETUMPRCO, ETUMRCOP, ETUMRPCO, ETUPCOMR, ETUPCORM, ETUPMCOR, ETUPMRCO, ETUPRCOM, ETUPRMCO, ETURCOMP, ETURCOPM, ETURMCOP, ETURMPCO, ETURPCOM, ETURPMCO, ETRCOMPU, ETRCOMUP, ETRCOPMU, ETRCOPUM, ETRCOUMP, ETRCOUPM, ETRMCOPU, ETRMCOUP, ETRMPCOU, ETRMPUCO, ETRMUCOP,
ETRMUPCO, ETRPCOMU, ETRPCOUM, ETRPMCOU, ETRPMUCO, ETRPUCOM, ETRPUMCO, ETRUCOMP, ETRUCOPM, ETRUMCOP, ETRUMPCO, ETRUPCOM, ETRUPMCO, ERCOMPUT, ERCOMPTU, ERCOMUPT, ERCOMUTP, ERCOMTPU, ERCOMTUP, ERCOPMUT, ERCOPMTU, ERCOPUMT, ERCOPUTM, ERCOPTMU, ERCOPTUM, ERCOUMPT, ERCOUMTP, ERCOUPMT, ERCOUPTM, ERCOUTMP, ERCOUTPM, ERCOTMPU, ERCOTMUP, ERCOTPMU, ERCOTPUM, ERCOTUMP, ERCOTUPM, ERMCOPUT, ERMCOPTU, ERMCOUPT, ERMCOUTP, ERMCOTPU, ERMCOTUP, ERMPCOUT, ERMPCOTU, ERMPUCOT, ERMPUTCO, ERMPTCOU, ERMPTUCO, ERMUCOPT, ERMUCOTP, ERMUPCOT, ERMUPTCO,
ERMUTCOP, ERMUTPCO, ERMTCOPU, ERMTCOUP, ERMTPCOU, ERMTPUCO, ERMTUCOP, ERMTUPCO, ERPCOMUT, ERPCOMTU, ERPCOUMT, ERPCOUTM, ERPCOTMU, ERPCOTUM, ERPMCOUT, ERPMCOTU, ERPMUCOT, ERPMUTCO, ERPMTCOU, ERPMTUCO, ERPUCOMT, ERPUCOTM, ERPUMCOT, ERPUMTCO, ERPUTCOM, ERPUTMCO, ERPTCOMU, ERPTCOUM, ERPTMCOU, ERPTMUCO, ERPTUCOM, ERPTUMCO, ERUCOMPT, ERUCOMTP, ERUCOPMT, ERUCOPTM, ERUCOTMP, ERUCOTPM, ERUMCOPT, ERUMCOTP, ERUMPCOT, ERUMPTCO, ERUMTCOP, ERUMTPCO, ERUPCOMT, ERUPCOTM, ERUPMCOT, ERUPMTCO, ERUPTCOM, ERUPTMCO, ERUTCOMP, ERUTCOPM, ERUTMCOP,
ERUTMPCO, ERUTPCOM, ERUTPMCO, ERTCOMPU, ERTCOMUP, ERTCOPMU, ERTCOPUM, ERTCOUMP, ERTCOUPM, ERTMCOPU, ERTMCOUP, ERTMPCOU, ERTMPUCO, ERTMUCOP, ERTMUPCO, ERTPCOMU, ERTPCOUM, ERTPMCOU, ERTPMUCO, ERTPUCOM, ERTPUMCO, ERTUCOMP, ERTUCOPM, ERTUMCOP, ERTUMPCO, ERTUPCOM, ERTUPMCO, RCOMPUTE, RCOMPUET, RCOMPTUE, RCOMPTEU, RCOMPEUT, RCOMPETU, RCOMUPTE, RCOMUPET, RCOMUTPE, RCOMUTEP, RCOMUEPT, RCOMUETP, RCOMTPUE, RCOMTPEU, RCOMTUPE, RCOMTUEP, RCOMTEPU, RCOMTEUP, RCOMEPUT, RCOMEPTU, RCOMEUPT, RCOMEUTP, RCOMETPU, RCOMETUP, RCOPMUTE, RCOPMUET,
RCOPMTUE, RCOPMTEU, RCOPMEUT, RCOPMETU, RCOPUMTE, RCOPUMET, RCOPUTME, RCOPUTEM, RCOPUEMT, RCOPUETM, RCOPTMUE, RCOPTMEU, RCOPTUME, RCOPTUEM, RCOPTEMU, RCOPTEUM, RCOPEMUT, RCOPEMTU, RCOPEUMT, RCOPEUTM, RCOPETMU, RCOPETUM, RCOUMPTE, RCOUMPET, RCOUMTPE, RCOUMTEP, RCOUMEPT, RCOUMETP, RCOUPMTE, RCOUPMET, RCOUPTME, RCOUPTEM, RCOUPEMT, RCOUPETM, RCOUTMPE, RCOUTMEP, RCOUTPME, RCOUTPEM, RCOUTEMP, RCOUTEPM, RCOUEMPT, RCOUEMTP, RCOUEPMT, RCOUEPTM, RCOUETMP, RCOUETPM, RCOTMPUE, RCOTMPEU, RCOTMUPE, RCOTMUEP, RCOTMEPU, RCOTMEUP, RCOTPMUE,
RCOTPMEU, RCOTPUME, RCOTPUEM, RCOTPEMU, RCOTPEUM, RCOTUMPE, RCOTUMEP, RCOTUPME, RCOTUPEM, RCOTUEMP, RCOTUEPM, RCOTEMPU, RCOTEMUP, RCOTEPMU, RCOTEPUM, RCOTEUMP, RCOTEUPM, RCOEMPUT, RCOEMPTU, RCOEMUPT, RCOEMUTP, RCOEMTPU, RCOEMTUP, RCOEPMUT, RCOEPMTU, RCOEPUMT, RCOEPUTM, RCOEPTMU, RCOEPTUM, RCOEUMPT, RCOEUMTP, RCOEUPMT, RCOEUPTM, RCOEUTMP, RCOEUTPM, RCOETMPU, RCOETMUP, RCOETPMU, RCOETPUM, RCOETUMP, RCOETUPM, RMCOPUTE, RMCOPUET, RMCOPTUE, RMCOPTEU, RMCOPEUT, RMCOPETU, RMCOUPTE, RMCOUPET, RMCOUTPE, RMCOUTEP, RMCOUEPT, RMCOUETP,
RMCOTPUE, RMCOTPEU, RMCOTUPE, RMCOTUEP, RMCOTEPU, RMCOTEUP, RMCOEPUT, RMCOEPTU, RMCOEUPT, RMCOEUTP, RMCOETPU, RMCOETUP, RMPCOUTE, RMPCOUET, RMPCOTUE, RMPCOTEU, RMPCOEUT, RMPCOETU, RMPUCOTE, RMPUCOET, RMPUTCOE, RMPUTECO, RMPUECOT, RMPUETCO, RMPTCOUE, RMPTCOEU, RMPTUCOE, RMPTUECO, RMPTECOU, RMPTEUCO, RMPECOUT, RMPECOTU, RMPEUCOT, RMPEUTCO, RMPETCOU, RMPETUCO, RMUCOPTE, RMUCOPET, RMUCOTPE, RMUCOTEP, RMUCOEPT, RMUCOETP, RMUPCOTE, RMUPCOET, RMUPTCOE, RMUPTECO, RMUPECOT, RMUPETCO, RMUTCOPE, RMUTCOEP, RMUTPCOE, RMUTPECO, RMUTECOP,
RMUTEPCO, RMUECOPT, RMUECOTP, RMUEPCOT, RMUEPTCO, RMUETCOP, RMUETPCO, RMTCOPUE, RMTCOPEU, RMTCOUPE, RMTCOUEP, RMTCOEPU, RMTCOEUP, RMTPCOUE, RMTPCOEU, RMTPUCOE, RMTPUECO, RMTPECOU, RMTPEUCO, RMTUCOPE, RMTUCOEP, RMTUPCOE, RMTUPECO, RMTUECOP, RMTUEPCO, RMTECOPU, RMTECOUP, RMTEPCOU, RMTEPUCO, RMTEUCOP, RMTEUPCO, RMECOPUT, RMECOPTU, RMECOUPT, RMECOUTP, RMECOTPU, RMECOTUP, RMEPCOUT, RMEPCOTU, RMEPUCOT, RMEPUTCO, RMEPTCOU, RMEPTUCO, RMEUCOPT, RMEUCOTP, RMEUPCOT, RMEUPTCO, RMEUTCOP, RMEUTPCO, RMETCOPU, RMETCOUP, RMETPCOU, RMETPUCO,
RMETUCOP, RMETUPCO, RPCOMUTE, RPCOMUET, RPCOMTUE, RPCOMTEU, RPCOMEUT, RPCOMETU, RPCOUMTE, RPCOUMET, RPCOUTME, RPCOUTEM, RPCOUEMT, RPCOUETM, RPCOTMUE, RPCOTMEU, RPCOTUME, RPCOTUEM, RPCOTEMU, RPCOTEUM, RPCOEMUT, RPCOEMTU, RPCOEUMT, RPCOEUTM, RPCOETMU, RPCOETUM, RPMCOUTE, RPMCOUET, RPMCOTUE, RPMCOTEU, RPMCOEUT, RPMCOETU, RPMUCOTE, RPMUCOET, RPMUTCOE, RPMUTECO, RPMUECOT, RPMUETCO, RPMTCOUE, RPMTCOEU, RPMTUCOE, RPMTUECO, RPMTECOU, RPMTEUCO, RPMECOUT, RPMECOTU, RPMEUCOT, RPMEUTCO, RPMETCOU, RPMETUCO, RPUCOMTE, RPUCOMET, RPUCOTME,
RPUCOTEM, RPUCOEMT, RPUCOETM, RPUMCOTE, RPUMCOET, RPUMTCOE, RPUMTECO, RPUMECOT, RPUMETCO, RPUTCOME, RPUTCOEM, RPUTMCOE, RPUTMECO, RPUTECOM, RPUTEMCO, RPUECOMT, RPUECOTM, RPUEMCOT, RPUEMTCO, RPUETCOM, RPUETMCO, RPTCOMUE, RPTCOMEU, RPTCOUME, RPTCOUEM, RPTCOEMU, RPTCOEUM, RPTMCOUE, RPTMCOEU, RPTMUCOE, RPTMUECO, RPTMECOU, RPTMEUCO, RPTUCOME, RPTUCOEM, RPTUMCOE, RPTUMECO, RPTUECOM, RPTUEMCO, RPTECOMU, RPTECOUM, RPTEMCOU, RPTEMUCO, RPTEUCOM, RPTEUMCO, RPECOMUT, RPECOMTU, RPECOUMT, RPECOUTM, RPECOTMU, RPECOTUM, RPEMCOUT, RPEMCOTU,
RPEMUCOT, RPEMUTCO, RPEMTCOU, RPEMTUCO, RPEUCOMT, RPEUCOTM, RPEUMCOT, RPEUMTCO, RPEUTCOM, RPEUTMCO, RPETCOMU, RPETCOUM, RPETMCOU, RPETMUCO, RPETUCOM, RPETUMCO, RUCOMPTE, RUCOMPET, RUCOMTPE, RUCOMTEP, RUCOMEPT, RUCOMETP, RUCOPMTE, RUCOPMET, RUCOPTME, RUCOPTEM, RUCOPEMT, RUCOPETM, RUCOTMPE, RUCOTMEP, RUCOTPME, RUCOTPEM, RUCOTEMP, RUCOTEPM, RUCOEMPT, RUCOEMTP, RUCOEPMT, RUCOEPTM, RUCOETMP, RUCOETPM, RUMCOPTE, RUMCOPET, RUMCOTPE, RUMCOTEP, RUMCOEPT, RUMCOETP, RUMPCOTE, RUMPCOET, RUMPTCOE, RUMPTECO, RUMPECOT, RUMPETCO, RUMTCOPE,
RUMTCOEP, RUMTPCOE, RUMTPECO, RUMTECOP, RUMTEPCO, RUMECOPT, RUMECOTP, RUMEPCOT, RUMEPTCO, RUMETCOP, RUMETPCO, RUPCOMTE, RUPCOMET, RUPCOTME, RUPCOTEM, RUPCOEMT, RUPCOETM, RUPMCOTE, RUPMCOET, RUPMTCOE, RUPMTECO, RUPMECOT, RUPMETCO, RUPTCOME, RUPTCOEM, RUPTMCOE, RUPTMECO, RUPTECOM, RUPTEMCO, RUPECOMT, RUPECOTM, RUPEMCOT, RUPEMTCO, RUPETCOM, RUPETMCO, RUTCOMPE, RUTCOMEP, RUTCOPME, RUTCOPEM, RUTCOEMP, RUTCOEPM, RUTMCOPE, RUTMCOEP, RUTMPCOE, RUTMPECO, RUTMECOP, RUTMEPCO, RUTPCOME, RUTPCOEM, RUTPMCOE, RUTPMECO, RUTPECOM, RUTPEMCO,
RUTECOMP, RUTECOPM, RUTEMCOP, RUTEMPCO, RUTEPCOM, RUTEPMCO, RUECOMPT, RUECOMTP, RUECOPMT, RUECOPTM, RUECOTMP, RUECOTPM, RUEMCOPT, RUEMCOTP, RUEMPCOT, RUEMPTCO, RUEMTCOP, RUEMTPCO, RUEPCOMT, RUEPCOTM, RUEPMCOT, RUEPMTCO, RUEPTCOM, RUEPTMCO, RUETCOMP, RUETCOPM, RUETMCOP, RUETMPCO, RUETPCOM, RUETPMCO, RTCOMPUE, RTCOMPEU, RTCOMUPE, RTCOMUEP, RTCOMEPU, RTCOMEUP, RTCOPMUE, RTCOPMEU, RTCOPUME, RTCOPUEM, RTCOPEMU, RTCOPEUM, RTCOUMPE, RTCOUMEP, RTCOUPME, RTCOUPEM, RTCOUEMP, RTCOUEPM, RTCOEMPU, RTCOEMUP, RTCOEPMU, RTCOEPUM, RTCOEUMP,
RTCOEUPM, RTMCOPUE, RTMCOPEU, RTMCOUPE, RTMCOUEP, RTMCOEPU, RTMCOEUP, RTMPCOUE, RTMPCOEU, RTMPUCOE, RTMPUECO, RTMPECOU, RTMPEUCO, RTMUCOPE, RTMUCOEP, RTMUPCOE, RTMUPECO, RTMUECOP, RTMUEPCO, RTMECOPU, RTMECOUP, RTMEPCOU, RTMEPUCO, RTMEUCOP, RTMEUPCO, RTPCOMUE, RTPCOMEU, RTPCOUME, RTPCOUEM, RTPCOEMU, RTPCOEUM, RTPMCOUE, RTPMCOEU, RTPMUCOE, RTPMUECO, RTPMECOU, RTPMEUCO, RTPUCOME, RTPUCOEM, RTPUMCOE, RTPUMECO, RTPUECOM, RTPUEMCO, RTPECOMU, RTPECOUM, RTPEMCOU, RTPEMUCO, RTPEUCOM, RTPEUMCO, RTUCOMPE, RTUCOMEP, RTUCOPME, RTUCOPEM,
RTUCOEMP, RTUCOEPM, RTUMCOPE, RTUMCOEP, RTUMPCOE, RTUMPECO, RTUMECOP, RTUMEPCO, RTUPCOME, RTUPCOEM, RTUPMCOE, RTUPMECO, RTUPECOM, RTUPEMCO, RTUECOMP, RTUECOPM, RTUEMCOP, RTUEMPCO, RTUEPCOM, RTUEPMCO, RTECOMPU, RTECOMUP, RTECOPMU, RTECOPUM, RTECOUMP, RTECOUPM, RTEMCOPU, RTEMCOUP, RTEMPCOU, RTEMPUCO, RTEMUCOP, RTEMUPCO, RTEPCOMU, RTEPCOUM, RTEPMCOU, RTEPMUCO, RTEPUCOM, RTEPUMCO, RTEUCOMP, RTEUCOPM, RTEUMCOP, RTEUMPCO, RTEUPCOM, RTEUPMCO, RECOMPUT, RECOMPTU, RECOMUPT, RECOMUTP, RECOMTPU, RECOMTUP, RECOPMUT, RECOPMTU, RECOPUMT,
RECOPUTM, RECOPTMU, RECOPTUM, RECOUMPT, RECOUMTP, RECOUPMT, RECOUPTM, RECOUTMP, RECOUTPM, RECOTMPU, RECOTMUP, RECOTPMU, RECOTPUM, RECOTUMP, RECOTUPM, REMCOPUT, REMCOPTU, REMCOUPT, REMCOUTP, REMCOTPU, REMCOTUP, REMPCOUT, REMPCOTU, REMPUCOT, REMPUTCO, REMPTCOU, REMPTUCO, REMUCOPT, REMUCOTP, REMUPCOT, REMUPTCO, REMUTCOP, REMUTPCO, REMTCOPU, REMTCOUP, REMTPCOU, REMTPUCO, REMTUCOP, REMTUPCO, REPCOMUT, REPCOMTU, REPCOUMT, REPCOUTM, REPCOTMU, REPCOTUM, REPMCOUT, REPMCOTU, REPMUCOT, REPMUTCO, REPMTCOU, REPMTUCO, REPUCOMT, REPUCOTM,
REPUMCOT, REPUMTCO, REPUTCOM, REPUTMCO, REPTCOMU, REPTCOUM, REPTMCOU, REPTMUCO, REPTUCOM, REPTUMCO, REUCOMPT, REUCOMTP, REUCOPMT, REUCOPTM, REUCOTMP, REUCOTPM, REUMCOPT, REUMCOTP, REUMPCOT, REUMPTCO, REUMTCOP, REUMTPCO, REUPCOMT, REUPCOTM, REUPMCOT, REUPMTCO, REUPTCOM, R
27 June 2016
Counting
30
Factorial

How to write a factorial method?
long factorial(int number)
{
if (number <= 1)
return 1;
else return (number * factorial(--number));
}
27 June 2016
Counting
31
Computing Combinations
List combinations(String str)
{ List combinations = new List();
if (str.length() == 1) combinations.add(str);
else
{
char[] strChars = str.toCharArray();
for (int i = 0; i < strChars.length; i++)
{
// get the sub part of the string to get more combinations
// sub part is original string minus the current ith character
char[] subStrChars = new char[strChars.length - 1];
// get subcombos
List subCombos = combinations(new String(subStrChars));
// add current char to beginning of other strings
for (int j = 0; j < subCombos.size(); j++)
combinations.add(new String(strChars[i] + subCombos.get(j).toString()));
}
}
return combinations;
}
27 June 2016
Counting
32
Permutations

Different ways of arranging objects
– In a line or circle
– Without duplication/ all items distinguishable
– Note: order is taken into account

Number of linear permutations of N objects = N!
– N possible for 1st position * (N-1) for 2nd * …* (1) for last

Number of circular permutations of N objects =
(N-1)!
– Fix one person,
– Then (N-1) possible for next position * (N-2) for 2nd * …*
(1) for last
27 June 2016
Counting
33
Theater Seating

6 people sit in a row with exactly 6 seats.
How many ways can they be seated together in the row?
6! = 720


One is a doctor who must sit on the aisle.
How many ways can they be seated together in the row?


– Two aisles = 2  5! = 240
– One aisle = 5! = 120



6 people are 3 married couples. Each wants to sit
together with the husband on the left.
How many ways can they be seated together in the row?
3! = 6
27 June 2016
Counting
34
Permutations

What if just want 5-letter words from
COMPUTER?
=87654
8!

8  5!
27 June 2016
Counting
35
r-Permutations

If there are n things in the set, and you want to
line-up only r of them.
n!
P ( n, r )  r P n 
(n  r )!

Example:
– Class = {Alice, Bob, Carol, Dan}
– Select a president and a vice president to represent
the class
27 June 2016
Counting
36
Combinations

Different ways of selecting objects
– Counting subsets
– Without duplication / all items distinguishable
– Note: order is not taken into account
0
n, r  Z where n  r ,
 n  P(n, r )
n!
C (n, r )    

r!
(n  r )! r!
r

Examples:
– Class = {Alice, Bob, Carol, Dan}
 Select two class representatives
 Select three class representatives
27 June 2016
Counting
37
Combinations Example
Braille code is represented by
rectangular arrangement of six dots,
each of which is raised or flat.
 Given that at least one of six dots
must be raised, how many symbols
can be represented?

 6  6  6  6  6  6
=  1    2    3    4    5    6   6  15  20  15  6  1  63
           
= 26 – 1 = 64 – 1 = 63
27 June 2016
Counting
38
Harder Examples
selecting “class representatives”

Class = {Alice, Bob, Carol, Dan, Erin, Fred}





Select 2 –
Select 2 –
Select 3 –
Select 3 –
Select 3 –
together
27 June 2016
no restrictions
assuming Alice and Bob must stay together
no restrictions
assuming Alice and Bob must stay together
assuming Alice and Bob refuse to serve
Counting
39
Different Types of Members

{Alice, Bob, Carol, Dan, Erin, Fred, George, Harry}
– pink names are girls and blue names are boys

8 people in the set: 3 girls & 5 boys
–
–
–
–
Make
Make
Make
Make
27 June 2016
a
a
a
a
5
5
5
5
member
member
member
member
team
team
team
team
of 2 girls and 3 boys
that has only one girl
that has no girls
that has at least one girl
Counting
40
Student Council
(Counting Subsets of a Set)

A student council consists of:
–3
–4
–4
–5

Freshmen
Sophomores
Juniors
Seniors
How many committees of eight members
of the council contain at least one member
from each class?
27 June 2016
Counting
41
Student Council
(Counting Subsets of a Set)
16  16!
 12,870
 Total number of committees is:   
 8  8!  8!




Answer is total – number of committees with no
members from at least one class
Let A1, A2, A3, A4 be sets without freshmen, sophomores,
juniors, seniors
A1  A2  A3  A4 is the set with no members from at
least one class
N(A1  A2  A3  A4) =
N(A1) + N(A2) + N(A3) + N(A4) –
N(A1  A2) – N(A1  A3) – N(A1  A4) –
N(A2  A3) – N(A2  A4) – N(A3  A4) +
N(Ai  Aj  Ak) –
N(A1  A2  A3  A4)
27 June 2016
Counting
42
Combinations with Repetition


{a,b,c,d}
How many 3-combinations can I make without
repetition?
– [a,b,c] [a,b,d] [a,c,d] [b,c,d]

How many 3-combinations can I make with
unlimited repetition allowed?
–
–
–
–
–
–
[a,a,a]
[a,b,b]
[a,c,c]
[b,b,b]
[b,c,c]
[c,c,c]
27 June 2016
[a,a,b]
[a,b,c]
[a,c,d]
[b,b,c]
[b,c,d]
[c,c,d]
[a,a,c] [a,a,d]
[a,b,d]
[a,d,d]
[b,b,d]
[b,d,d]
[c,d,d] [d,d,d]
Counting
43
Combinations with Repetition


Is there an easy way to count these?
Reform problem to putting 3 marks in 4 categories
–
–
–
–

a
x
xx
x
b
c
x
x
d
x
xx
We can also represent this as:
– X||X|X
– XX||X|
– X|||XX

[a,c,d]
[a,a,c]
[a,d,d]
[a,c,d]
[a,a,c]
[a,d,d]
Easy to solve in this form …
6
6!
  
 20
 3  3!  3!
– How many words can you make from XXX|||
27 June 2016
Counting
44
r-Combinations w/ Repetitions

A large pile of coins consists of pennies, nickels,
dimes and quarters (at least 30 each)

How many different collections of 30 coins can
be chosen?  30  4  1  33  33!
 


30
    
 5456
  30  3!  30!
If the different kinds of collections of 30 coins
are equally likely, what is the probability that a
combination contains at least four coins of each
type?  30  4  4  4  1 17   17! 


27 June 2016
30  4  4
5456


  

14    3!  14!   680  12.5%
5456
5456
5456
Counting
45
Permutation w/ Repeated Elements
What about NEEDLES
 NE1E2DLE3S  7!

– NE1E2DLE3S, NE1E3DLE2S,
– NE2E1DLE3S, NE2E3DLE1S
– NE3E1DLE2S, NE3E2DLE1S
7! 7!
 
6 3!
27 June 2016
Counting
46
Permutations w/ Repeated Elements
What about MISSISSIPPI?
 MI1S1S2I2S3S4I3P1P2I4
 11!


M (1), I (4), S (4), P(2)
11!

1!  4!  4!  2!
27 June 2016
Counting
47
Permutations but of
indistinguishable items

Assume you have a set of 15 beads
–3
–2
–4
–6

Red
Black
Orange
Green
Select positions of R’s, then B’s, then O’s
then G’s
15  12  10   6 
15!
           
 3   2   4   6  3!  2!  4!  6!
27 June 2016
Counting
48
Combinations with Repitition

In general
– n – categories
– r – items to choose from
– Repetition allowed and order doesn’t count
xxx |||
r
n-1
 r  n  1


 r 
27 June 2016
Counting
49
Combinations w/ Repetition Example
A person giving a party wants to set out 15
assorted cans of soft drinks,
 The store he shops at sells five different types of
soft drinks

– How many different selections of cans of 15 soft 15  5  1


drinks can he make?
 15 
– If root beer is one of the types, how many selections
 9  5  1
include at least six cans of root beer?


 9 
– If each selection is equally likely, what is the
probability a selection contains at least six cans of
root beer?
27 June 2016
Counting
50
Combinations w/ Repetition Example


There are 6 kinds of computers
How many ways to choose 25?
–xxxxxxxxxxxxxxxxxxxxxxxxx|||||
– r – choose 25
– n – 6 categories

Assume one type is an iPAQ, how many ways
can you choose if exactly 10 must be iPAQs?
– Restate as 15 computers, 5 types

What if at least 10 must be iPAQs?
– Restate as 15 computers, 6 types

What are the chances that if we select 25 at
random, that exactly 10 will be iPAQs?
27 June 2016
Counting
51
Probability with Combinations
Assume there are 32 people in the class
 And that 7 will be chosen to get extra homework
 What is the probability that you get extra
homework

Number of ways to select the “lucky 7”
 Number of ways to select if “I get HW”


P(I get HW)
27 June 2016
Counting
52
Properties of r-Permutations
and proofs of those properties
P(n,1) = n
 P(n,2) = n2 – n
 P(n,2) + P(n,1) = n2

P(n,n) = n!
 P(n,n–1) = n!

27 June 2016
Counting
53
Properties of Combinations
(Can you prove this?)
n
   1
0
n
   n
1
 n  n(n  1)
  
2
 2
27 June 2016
n
   1
n
 n 

  n
 n 1
 n  n(n  1)

 
2
 n  2
 n  n 
   

r  n  r
Counting
54
Pascal’s Triangle
27 June 2016
Counting
55
Binomial Theorem
(x+y)2
 (x+y)3

…
 (x+y)n

 Given
any real numbers a and b
and any nonnegative integer n,
n
 n  nk k
n
a  b     a b
k 0  k 
27 June 2016
Counting
56
Conditional Probability

Probability of B given that A is known to have
happened
P( A  B)
P ( B | A) 
P ( A)

If P(B) = P(B|A),
then event B is Independent of event A
27 June 2016
Counting
57