Contrasts other than treatment coding for factors with more than two
levels have always confused me. I try to design all my own studies to
never have more than two levels per categorical factor, but students in
my data skills class are always trying to analyse data with three-level
categories (or worse).
I thought it was just me, but some recent Twitter discussion showed
me I’m not alone. There’s a serious jingle-jangle problem with
contrasts. Here are some of the explainers that I found useful (thanks
to everyone who recommended them).
- Contrasts
in R by Marissa Barlaz
- Coding
categorical predictor variables in factorial designs by Dale
Barr
- Contrast Coding
in Multiple Regression Analysis by Matthew Davis
- R
Library Contrast Coding Systems for categorical variables by UCLA
Statistical Consulting
- Rosetta
store: Contrasts by GAMLj
- Coding Schemes
for Categorical Variables by Phillip Alday
- Experimental
personality designs: analyzing categorical by continuous variable
interactions by West, Aiken & Krull
Terminology
Contrasts often have multiple names. The names I’m using try to
maintain the relationship with the base R function, apart from anova
coding, which was suggested by Dale Barr after I got frustrated that
people use so many different labels for that (extremely useful) coding
and each of the terms used is also used to refer to totally different
codings by others.
Treatment |
Treatment (2),
Dummy (1,
4,
6),
Simple (5) |
contr.treatment |
contr_code_treatment |
Anova |
Deviation (2),
Contrast (1),
Simple (4) |
contr.treatment - 1/k |
contr_code_anova |
Sum |
Sum (1,
2,
6),
Effects (3),
Deviation (4,
5),
Unweighted Effects (7) |
contr.sum |
contr_code_sum |
Difference |
Contrast (3),
Forward/Backward (4),
Repeated (5) |
MASS::contr.sdif |
contr_code_difference |
Helmert |
Reverse Helmert (1,
4),
Difference (5),
Contrast (7) |
contr.helmert / (column_i+1) |
contr_code_helmert |
Polynomial |
Polynomial (5),
Orthogonal Polynomial (4),
Trend (3) |
contr.poly |
contr_code_poly |
Faux Contrast Functions
These functions are under development
First, we’ll set up a simple experimental design and analyse it with
lm()
. I set empirical = TRUE
to make
interpreting the estimates easier.
df <- sim_design(between = list(pet = c("cat", "dog", "ferret")),
n = c(50), mu = c(2, 4, 9), empirical = TRUE)
![](data:image/png;base64,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)
Notice that the default contrast is treatment coding, with “cat” as
the baseline condition. The estimate for the intercept is the mean value
for cats (\(2\)), while the term
petdog
is the mean value for dogs minus cats (\(4 - 2\)), and the term
petferret
is the mean value for ferrets minus cats (\(9 - 2\)).
Contrasts
|
lm(y ~ pet, df)
|
|
dog
|
ferret
|
cat
|
0
|
0
|
dog
|
1
|
0
|
ferret
|
0
|
1
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
2
|
0.141
|
14.1
|
0
|
petdog
|
2
|
0.200
|
10.0
|
0
|
petferret
|
7
|
0.200
|
35.0
|
0
|
|
In all the subsequent examples, try putting into words what the
estimates for the intercept and terms mean in relation to the mean
values for each group in the data.
Treatment
Treatment coding (also called dummy coding) sets the mean of the
reference group as the intercept. It is straightforward to interpret,
especially when your factors have an obvious default or baseline value.
This is the same type of coding as the default for factors shown above
(unless you change your default using options()
), but with
clearer term labels.
df$pet <- contr_code_treatment(df$pet)
Contrasts
|
lm(y ~ pet, df)
|
|
.dog-cat
|
.ferret-cat
|
cat
|
0
|
0
|
dog
|
1
|
0
|
ferret
|
0
|
1
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
2
|
0.141
|
14.1
|
0
|
pet.dog-cat
|
2
|
0.200
|
10.0
|
0
|
pet.ferret-cat
|
7
|
0.200
|
35.0
|
0
|
|
Each contrast compares one level with the reference level, which
defaults to the first level, but you can set with the base
argument. Now the intercept estimates the mean value for dogs (\(4\)).
df$pet <- contr_code_treatment(df$pet, base = "dog")
Contrasts
|
lm(y ~ pet, df)
|
|
.cat-dog
|
.ferret-dog
|
cat
|
1
|
0
|
dog
|
0
|
0
|
ferret
|
0
|
1
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
4
|
0.141
|
28.3
|
0
|
pet.cat-dog
|
-2
|
0.200
|
-10.0
|
0
|
pet.ferret-dog
|
5
|
0.200
|
25.0
|
0
|
|
Set the reference level to the third level (“ferret”).
df$pet <- contr_code_treatment(df$pet, base = 3)
Contrasts
|
lm(y ~ pet, df)
|
|
.cat-ferret
|
.dog-ferret
|
cat
|
1
|
0
|
dog
|
0
|
1
|
ferret
|
0
|
0
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
9
|
0.141
|
63.6
|
0
|
pet.cat-ferret
|
-7
|
0.200
|
-35.0
|
0
|
pet.dog-ferret
|
-5
|
0.200
|
-25.0
|
0
|
|
Anova
Anova coding is identical to treatment coding, but sets the grand
mean as the intercept. Each contrast compares one level with a reference
level. This gives us values that are relatively easy to interpret and
map onto ANOVA values.
Below is anova coding with the first level (“cat”) as the default
base. Now the intercept is the grand mean, which is the mean of the
three group means (\((2 + 4 + 9)/3\)).
Notice that this is different from the mean value of y in our dataset
(5, since the number of pets in each group is unbalanced. The term
pet_dog-cat
is the mean value for dogs minus cats (\(4 - 2\)) and the term
pet_ferret-cat
is the mean value for ferrets minus cats
(\(9 - 2\)).
df$pet <- contr_code_anova(df$pet)
Contrasts
|
lm(y ~ pet, df)
|
|
.dog-cat
|
.ferret-cat
|
cat
|
-0.333
|
-0.333
|
dog
|
0.667
|
-0.333
|
ferret
|
-0.333
|
0.667
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.082
|
61.2
|
0
|
pet.dog-cat
|
2
|
0.200
|
10.0
|
0
|
pet.ferret-cat
|
7
|
0.200
|
35.0
|
0
|
|
Anova coding with “dog” as the base. How does the interpretation of
the terms change?
df$pet <- contr_code_anova(df$pet, base = "dog")
Contrasts
|
lm(y ~ pet, df)
|
|
.cat-dog
|
.ferret-dog
|
cat
|
0.667
|
-0.333
|
dog
|
-0.333
|
-0.333
|
ferret
|
-0.333
|
0.667
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.082
|
61.2
|
0
|
pet.cat-dog
|
-2
|
0.200
|
-10.0
|
0
|
pet.ferret-dog
|
5
|
0.200
|
25.0
|
0
|
|
Anova coding with the third level (“ferret”) as the base.
df$pet <- contr_code_anova(df$pet, base = 3)
Contrasts
|
lm(y ~ pet, df)
|
|
.cat-ferret
|
.dog-ferret
|
cat
|
0.667
|
-0.333
|
dog
|
-0.333
|
0.667
|
ferret
|
-0.333
|
-0.333
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.082
|
61.2
|
0
|
pet.cat-ferret
|
-7
|
0.200
|
-35.0
|
0
|
pet.dog-ferret
|
-5
|
0.200
|
-25.0
|
0
|
|
Sum
Sum coding also sets the grand mean as the intercept. Each contrast
compares one level with the grand mean. Therefore, the estimate for
pet_cat-intercept
is the difference between the mean value
for cats and the grand mean (\(2 -
5\)).
df$pet <- contr_code_sum(df$pet)
Contrasts
|
lm(y ~ pet, df)
|
|
.cat-intercept
|
.dog-intercept
|
cat
|
1
|
0
|
dog
|
0
|
1
|
ferret
|
-1
|
-1
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.082
|
61.24
|
0
|
pet.cat-intercept
|
-3
|
0.115
|
-25.98
|
0
|
pet.dog-intercept
|
-1
|
0.115
|
-8.66
|
0
|
|
You can’t compare all levels with the grand mean, and have to omit
one level. This is the last level by default, but you can change it with
the omit
argument.
df$pet <- contr_code_sum(df$pet, omit = "dog")
Contrasts
|
lm(y ~ pet, df)
|
|
.cat-intercept
|
.ferret-intercept
|
cat
|
1
|
0
|
dog
|
-1
|
-1
|
ferret
|
0
|
1
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.082
|
61.2
|
0
|
pet.cat-intercept
|
-3
|
0.115
|
-26.0
|
0
|
pet.ferret-intercept
|
4
|
0.115
|
34.6
|
0
|
|
Omit the first level (“cat”).
df$pet <- contr_code_sum(df$pet, omit = 1)
Contrasts
|
lm(y ~ pet, df)
|
|
.dog-intercept
|
.ferret-intercept
|
cat
|
-1
|
-1
|
dog
|
1
|
0
|
ferret
|
0
|
1
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.082
|
61.24
|
0
|
pet.dog-intercept
|
-1
|
0.115
|
-8.66
|
0
|
pet.ferret-intercept
|
4
|
0.115
|
34.64
|
0
|
|
Difference
A slightly different form of contrast coding is difference coding,
also called forward, backward, or successive differences coding. It
compares each level to the previous one, rather than to a baseline
level.
df$pet <- contr_code_difference(df$pet)
Contrasts
|
lm(y ~ pet, df)
|
|
.dog-cat
|
.ferret-dog
|
cat
|
-0.667
|
-0.333
|
dog
|
0.333
|
-0.333
|
ferret
|
0.333
|
0.667
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.082
|
61.2
|
0
|
pet.dog-cat
|
2
|
0.200
|
10.0
|
0
|
pet.ferret-dog
|
5
|
0.200
|
25.0
|
0
|
|
If you want to change which levels are compared, you can re-order the
factor levels.
df$pet <- contr_code_difference(df$pet, levels = c("ferret", "cat", "dog"))
Contrasts
|
lm(y ~ pet, df)
|
|
.cat-ferret
|
.dog-cat
|
ferret
|
-0.667
|
-0.333
|
cat
|
0.333
|
-0.333
|
dog
|
0.333
|
0.667
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.082
|
61.2
|
0
|
pet.cat-ferret
|
-7
|
0.200
|
-35.0
|
0
|
pet.dog-cat
|
2
|
0.200
|
10.0
|
0
|
|
Helmert
Helmert coding sets the grand mean as the intercept. Each contrast
compares one level with the mean of previous levels. This coding is
somewhat different than the results from
stats::contr.helmert()
to make it easier to interpret the
estimates. Thus, pet_ferret-cat.dog
is the mean value for
ferrets minus the mean value for cats and dogs averaged together (\(9-(2+4)/2\)).
df$pet <- contr_code_helmert(df$pet)
Contrasts
|
lm(y ~ pet, df)
|
|
.dog-cat
|
.ferret-cat.dog
|
cat
|
-0.5
|
-0.333
|
dog
|
0.5
|
-0.333
|
ferret
|
0.0
|
0.667
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.082
|
61.2
|
0
|
pet.dog-cat
|
2
|
0.200
|
10.0
|
0
|
pet.ferret-cat.dog
|
6
|
0.173
|
34.6
|
0
|
|
You can change the comparisons by reordering the levels.
df$pet <- contr_code_helmert(df$pet, levels = c("ferret", "dog", "cat"))
Contrasts
|
lm(y ~ pet, df)
|
|
.dog-ferret
|
.cat-ferret.dog
|
ferret
|
-0.5
|
-0.333
|
dog
|
0.5
|
-0.333
|
cat
|
0.0
|
0.667
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5.0
|
0.082
|
61.2
|
0
|
pet.dog-ferret
|
-5.0
|
0.200
|
-25.0
|
0
|
pet.cat-ferret.dog
|
-4.5
|
0.173
|
-26.0
|
0
|
|
Polynomial
Polynomial coding is the default for ordered factors in R. We’ll set
up a new data simulation with five ordered times.
df <- sim_design(list(time = 1:5),
mu = 1:5 * 0.25 + (1:5 - 3)^2 * 0.5,
sd = 5, long = TRUE)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABgAAAAMACAYAAADi1qzMAAAEDmlDQ1BrQ0dDb2xvclNwYWNlR2VuZXJpY1JHQgAAOI2NVV1oHFUUPpu5syskzoPUpqaSDv41lLRsUtGE2uj+ZbNt3CyTbLRBkMns3Z1pJjPj/KRpKT4UQRDBqOCT4P9bwSchaqvtiy2itFCiBIMo+ND6R6HSFwnruTOzu5O4a73L3PnmnO9+595z7t4LkLgsW5beJQIsGq4t5dPis8fmxMQ6dMF90A190C0rjpUqlSYBG+PCv9rt7yDG3tf2t/f/Z+uuUEcBiN2F2Kw4yiLiZQD+FcWyXYAEQfvICddi+AnEO2ycIOISw7UAVxieD/Cyz5mRMohfRSwoqoz+xNuIB+cj9loEB3Pw2448NaitKSLLRck2q5pOI9O9g/t/tkXda8Tbg0+PszB9FN8DuPaXKnKW4YcQn1Xk3HSIry5ps8UQ/2W5aQnxIwBdu7yFcgrxPsRjVXu8HOh0qao30cArp9SZZxDfg3h1wTzKxu5E/LUxX5wKdX5SnAzmDx4A4OIqLbB69yMesE1pKojLjVdoNsfyiPi45hZmAn3uLWdpOtfQOaVmikEs7ovj8hFWpz7EV6mel0L9Xy23FMYlPYZenAx0yDB1/PX6dledmQjikjkXCxqMJS9WtfFCyH9XtSekEF+2dH+P4tzITduTygGfv58a5VCTH5PtXD7EFZiNyUDBhHnsFTBgE0SQIA9pfFtgo6cKGuhooeilaKH41eDs38Ip+f4At1Rq/sjr6NEwQqb/I/DQqsLvaFUjvAx+eWirddAJZnAj1DFJL0mSg/gcIpPkMBkhoyCSJ8lTZIxk0TpKDjXHliJzZPO50dR5ASNSnzeLvIvod0HG/mdkmOC0z8VKnzcQ2M/Yz2vKldduXjp9bleLu0ZWn7vWc+l0JGcaai10yNrUnXLP/8Jf59ewX+c3Wgz+B34Df+vbVrc16zTMVgp9um9bxEfzPU5kPqUtVWxhs6OiWTVW+gIfywB9uXi7CGcGW/zk98k/kmvJ95IfJn/j3uQ+4c5zn3Kfcd+AyF3gLnJfcl9xH3OfR2rUee80a+6vo7EK5mmXUdyfQlrYLTwoZIU9wsPCZEtP6BWGhAlhL3p2N6sTjRdduwbHsG9kq32sgBepc+xurLPW4T9URpYGJ3ym4+8zA05u44QjST8ZIoVtu3qE7fWmdn5LPdqvgcZz8Ww8BWJ8X3w0PhQ/wnCDGd+LvlHs8dRy6bLLDuKMaZ20tZrqisPJ5ONiCq8yKhYM5cCgKOu66Lsc0aYOtZdo5QCwezI4wm9J/v0X23mlZXOfBjj8Jzv3WrY5D+CsA9D7aMs2gGfjve8ArD6mePZSeCfEYt8CONWDw8FXTxrPqx/r9Vt4biXeANh8vV7/+/16ffMD1N8AuKD/A/8leAvFY9bLAAAAOGVYSWZNTQAqAAAACAABh2kABAAAAAEAAAAaAAAAAAACoAIABAAAAAEAAAYAoAMABAAAAAEAAAMAAAAAAOjEkxwAAEAASURBVHgB7N0JnBxlnTju7yST+yRAIIEECOEGuW8QIchyLCBBlxVRUNSPCC4ILuL6VxDwRIVdkUU5FAT0xyGiAQQhIHLJKVeADSEHkpCT3Occ/6nW6UyHZLrT0013dT/lp5l6z3rf5207M/XtqmpobdvCRoAAAQIECBAgQIAAAQIECBAgQIAAAQIECNSUQLeamo3JECBAgAABAgQIECBAgAABAgQIECBAgAABAhkBAQBvBAIECBAgQIAAAQIECBAgQIAAAQIECBAgUIMCAgA1uKimRIAAAQIECBAgQIAAAQIECBAgQIAAAQIEBAC8BwgQIECAAAECBAgQIECAAAECBAgQIECAQA0KCADU4KKaEgECBAgQIECAAAECBAgQIECAAAECBAgQEADwHiBAgAABAgQIECBAgAABAgQIECBAgAABAjUoIABQg4tqSgQIECBAgAABAgQIECBAgAABAgQIECBAQADAe4AAAQIECBAgQIAAAQIECBAgQIAAAQIECNSggABADS6qKREgQIAAAQIECBAgQIAAAQIECBAgQIAAAQEA7wECBAgQIECAAAECBAgQIECAAAECBAgQIFCDAgIANbiopkSAAAECBAgQIECAAAECBAgQIECAAAECBAQAvAcIECBAgAABAgQIECBAgAABAgQIECBAgEANCggA1OCimhIBAgQIECBAgAABAgQIECBAgAABAgQIEGhEULjAY489FjNmzCi8gZoEyizQ2toayat969ZNTK/dwk8CBIoT8LlSnJtWBAisW8DnyrptlBAgULxAS0tLtrG/g7IUdggQ6IKAz5Uu4GladoG99torttxyy6KOIwCwHmy//OUv45FHHlmPFqoSIECAAAECBAgQIECAAAECBAgQIECAAIHiBb797W8LABTPt34tDzrooLjqqqvWr5HaBMoksGLFipg3b16m9759+8agQYPKdCTdEiBQLwKrVq2KOXPmZKbbu3fv2GCDDepl6uZJgECZBJqbm2PWrFmZ3nv06BEbbbRRmY6kWwIE6kmg/er87t27x9ChQ+tp6uZKgECZBGbOnBnJVQANDQ2x6aablukouiWwfgLLly+PffbZZ/0arVHbFQBrgORLJpcW9urVK1815QTeN4H292Pys33/fTu4AxEgUHMCHf+d87lSc8trQgQqIpAEANp/R0kCAO37FRmMgxIgUDMC7Z8lSQCgfb9mJmciBAhURCD5LGkPAPhcqcgSOGiZBNwwvEywuiVAgAABAgQIECBAgAABAgQIECBAgAABApUUEACopL5jEyBAgAABAgQIECBAgAABAgQIECBAgACBMgkIAJQJVrcECBAgQIAAAQIECBAgQIAAAQIECBAgQKCSAgIAldR3bAIECBAgQIAAAQIECBAgQIAAAQIECBAgUCYBAYAyweqWAAECBAgQIECAAAECBAgQIECAAAECBAhUUkAAoJL6jk2AAAECBAgQIECAAAECBAgQIECAAAECBMokIABQJljdEiBAgAABAgQIECBAgAABAgQIECBAgACBSgoIAFRS37EJECBAgAABAgQIECBAgAABAgQIECBAgECZBAQAygSrWwIECBAgQIAAAQIECBAgQIAAAQIECBAgUEkBAYBK6js2AQIECBAgQIAAAQIECBAgQIAAAQIECBAok4AAQJlgdUuAAAECBAgQIECAAAECBAgQIECAAAECBCopIABQSX3HJkCAAAECBAgQIECAAAECBAgQIECAAAECZRIQACgTrG4JECBAgAABAgQIECBAgAABAgQIECBAgEAlBQQAKqnv2AQIECBAgAABAgQIECBAgAABAgQIECBAoEwCAgBlgtUtAQIECBAgQIAAAQIECBAgQIAAAQIECBCopIAAQCX1HZsAAQIECBAgQIAAAQIECBAgQIAAAQIECJRJQACgTLC6JUCAAAECBAgQIECAAAECBAgQIECAAAEClRQQAKikvmMTIECAAAECBAgQIECAAAECBAgQIECAAIEyCQgAlAlWtwQIECBAgAABAgQIECBAgAABAgQIECBAoJICAgCV1HdsAgQIECBAgAABAgQIECBAgAABAgQIECBQJgEBgDLB6pYAAQIECBAgQIAAAQIECBAgQIAAAQIECFRSQACgkvqOTYAAAQIECBAgQIAAAQIECBAgQIAAAQIEyiQgAFAmWN0SIECAAAECBAgQIECAAAECBAgQIECAAIFKCggAVFLfsQkQIECAAAECBAgQIECAAAECBAgQIECAQJkEBADKBKtbAgQIECBAgAABAgQIECBAgAABAgQIECBQSQEBgErqOzYBAgQIECBAgAABAgQIECBAgAABAgQIECiTgABAmWB1S4AAAQIECBAgQIAAAQIECBAgQIAAAQIEKinQWMmDOzYBAgQIECBAgAABAgQIECBAgAABAgQqLXDxA8fGguWzo2f3PnH9aRMqPRzHJ1AyAQGAklHqiAABAgQIECBAgAABAgQIECBAgACBNAqsal4Rq5qXR0MaB2/MBDoRcAugTnAUESBAgAABAgQIECBAgAABAgQIECBAgACBtAoIAKR15YybAAECBAgQIECAAAECBAgQIECAAAECBAh0IiAA0AmOIgIECBAgQIAAAQIECBAgQIAAAQIECBAgkFYBAYC0rpxxEyBAgAABAgQIECBAgAABAgQIECBAgACBTgQEADrBUUSAAAECBAgQIECAAAECBAgQIECAAAECBNIqIACQ1pUzbgIECBAgQIAAAQIECBAgQIAAAQIECBAg0ImAAEAnOIoIECBAgAABAgQIECBAgAABAgQIECBAgEBaBQQA0rpyxk2AAAECBAgQIECAAAECBAgQIECAAAECBDoREADoBEcRAQIECBAgQIAAAQIECBAgQIAAAQIECBBIq4AAQFpXzrgJECBAgAABAgQIECBAgAABAgQIECBAgEAnAgIAneAoIkCAAAECBAgQIECAAAECBAgQIECAAAECaRUQAEjryhk3AQIECBAgQIAAAQIECBAgQIAAAQIECBDoREAAoBMcRQQIECBAgAABAgQIECBAgAABAgQIECBAIK0CAgBpXTnjJkCAAAECBAgQIECAAAECBAgQIECAAAECnQgIAHSCo4gAAQIECBAgQIAAAQIECBAgQIAAAQIECKRVQAAgrStn3AQIECBAgAABAgQIECBAgAABAgQIECBAoBMBAYBOcBQRIECAAAECBAgQIECAAAECBAgQIECAAIG0CggApHXljJsAAQIECBAgQIAAAQIECBAgQIAAAQIECHQiIADQCY4iAgQIECBAgAABAgQIECBAgAABAgQIECCQVgEBgLSunHETIECAAAECBAgQIECAAAECBAgQIECAAIFOBAQAOsFRRIAAAQIECBAgQIAAAQIECBAgQIAAAQIE0iogAJDWlTNuAgQIECBAgAABAgQIECBAgAABAgQIECDQiYAAQCc4iggQIECAAAECBAgQIECAAAECBAgQIECAQFoFBADSunLGTYAAAQIECBAgQIAAAQIECBAgQIAAAQIEOhEQAOgERxEBAgQIECBAgAABAgQIECBAgAABAgQIEEirgABAWlfOuAkQIECAAAECBAgQIECAAAECBAgQIECAQCcCAgCd4CgiQIAAAQIECBAgQIAAAQIECBAgQIAAAQJpFRAASOvKGTcBAgQIECBAgAABAgQIECBAgAABAgQIEOhEQACgExxFBAgQIECAAAECBAgQIECAAAECBAgQIEAgrQICAGldOeMmQIAAAQIECBAgQIAAAQIECBAgQIAAAQKdCAgAdIKjiAABAgQIECBAgAABAgQIECBAgAABAgQIpFVAACCtK2fcBAgQIECAAAECBAgQIECAAAECBAgQIECgEwEBgE5wFBEgQIAAAQIECBAgQIAAAQIECBAgQIAAgbQKNKZ14JUad0tLSzQ1NVXq8I5LIEegubk5m25tbfXezGrYIUCgWAGfK8XKaUeAwLoEkt+fO25+l+6oYZ8Aga4K+Duoq4LaEyCwNgG/r6xNRV4lBNrfi8m/d8VuAgDrIZecFFm1alXMnj17PVqpSuD9EVi2bFkkLxsBAgRKJbBixQr/5pUKUz8ECGQE/C7tjUCAQKkFkiCjv9FLrao/AvUqsPoEq8+Ven0PVN+8k7/Lk00A4H1am27dukXPnj1jyJAh79MRHYZA5wLJH9GLFi3KVOrVq1f069ev8wZKCRAgkEcg+XbBwoULM7WSf/P69++fp4ViAgQIdC6QnJybP39+plJjY2MMHDiw8wZKCRAgUIDAvHnzMrWSv9MHDx5cQAtVCBAgULiAc3+FW6lZXoH2AEBDQ0PRB3IFwHrQJdDJKznRaiNQbQLdu3f33qy2RTEeAikUSP6Ibt+Sff/mtWv4SYBAsQIdby3md+liFbUjQGBdAj5X1iUjnwCB9RdYfYLV30Hrr6dFeQWSf++K3Vb/lV9sD9oRIECAAAECBAgQIECAAAECBAgQIECAAAECVScgAFB1S2JABAgQIECAAAECBAgQIECAAAECBAgQIECg6wICAF031AMBAgQIECBAgAABAgQIECBAgAABAgQIEKg6AQGAqlsSAyJAgAABAgQIECBAgAABAgQIECBAgAABAl0XEADouqEeCBAgQIAAAQIECBAgQIAAAQIECBAgQIBA1QkIAFTdkhgQAQIECBAgQIAAAQIECBAgQIAAAQIECBDouoAAQNcN9UCAAAECBAgQIECAAAECBAgQIECAAAECBKpOQACg6pbEgAgQIECAAAECBAgQIECAAAECBAgQIECAQNcFBAC6bqgHAgQIECBAgAABAgQIECBAgAABAgQIECBQdQKNVTciAyJAoGCBd5cvjiffeSNTf6sNN43dBg0quK2KBAgQIECAAAECBAgQIECAAAECBAjUtoAAQG2vr9nVuMDLs9+Ks/98Y2aWn9jhoNht5DY1PmPTI0CAAAECBAgQIECAAAECBAgQIECgUAG3ACpUSj0CBAgQIECAAAECBAgQIECAAAECBAgQIJAiAQGAFC2WoRIgQIAAAQIECBAgQIAAAQIECBAgQIAAgUIFBAAKlVKPAAECBAgQIECAAAECBAgQIECAAAECBAikSEAAIEWLZagECBAgQIAAAQIECBAgQIAAAQIECBAgQKBQAQGAQqXUI0CAAAECBAgQIECAAAECBAgQIECAAAECKRIQAEjRYhkqAQIECBAgQIAAAQIECBAgQIAAAQIECBAoVEAAoFAp9QgQIECAAAECBAgQIECAAAECBAgQIECAQIoEBABStFiGSoAAAQIECBAgQIAAAQIECBAgQIAAAQIEChUQAChUSj0CBAgQIECAAAECBAgQIECAAAECBAgQIJAiAQGAFC2WoRIgQIAAAQIECBAgQIAAAQIECBAgQIAAgUIFBAAKlVKPAAECBAgQIECAAAECBAgQIECAAAECBAikSEAAIEWLZagECBAgQIAAAQIECBAgQIAAAQIECBAgQKBQAQGAQqXUI0CAAAECBAgQIECAAAECBAgQIECAAAECKRIQAEjRYhkqAQIECBAgQIAAAQIECBAgQIAAAQIECBAoVEAAoFAp9QgQIECAAAECBAgQIECAAAECBAgQIECAQIoEBABStFiGSoAAAQIECBAgQIAAAQIECBAgQIAAAQIEChUQAChUSj0CBAgQIECAAAECBAgQIECAAAECBAgQIJAiAQGAFC2WoRIgQIAAAQIECBAgQIAAAQIECBAgQIAAgUIFBAAKlVKPAAECBAgQIECAAAECBAgQIECAAAECBAikSEAAIEWLZagECBAgQIAAAQIECBAgQIAAAQIECBAgQKBQAQGAQqXUI0CAAAECBAgQIECAAAECBAgQIECAAAECKRIQAEjRYhkqAQIECBAgQIAAAQIECBAgQIAAAQIECBAoVEAAoFAp9QgQIECAAAECBAgQIECAAAECBAgQIECAQIoEBABStFiGSoAAAQIECBAgQIAAAQIECBAgQIAAAQIEChUQAChUSj0CBAgQIECAAAECBAgQIECAAAECBAgQIJAiAQGAFC2WoRIgQIAAAQIECBAgQIAAAQIECBAgQIAAgUIFBAAKlVKPAAECBAgQIECAAAECBAgQIECAAAECBAikSEAAIEWLZagECBAgQIAAAQIECBAgQIAAAQIECBAgQKBQAQGAQqXUI0CAAAECBAgQIECAAAECBAgQIECAAAECKRIQAEjRYhkqAQIECBAgQIAAAQIECBAgQIAAAQIECBAoVEAAoFAp9QgQIECAAAECBAgQIECAAAECBAgQIECAQIoEBABStFiGSoAAAQIECBAgQIAAAQIECBAgQIAAAQIEChUQAChUSj0CBAgQIECAAAECBAgQIECAAAECBAgQIJAiAQGAFC2WoRIgQIAAAQIECBAgQIAAAQIECBAgQIAAgUIFBAAKlVKPAAECBAgQIECAAAECBAgQIECAAAECBAikSKAxRWM1VAIECBAgQIAAAQIECBAgQIBArBh7e0RLa3QbPiDizk8TIUCAAAECBNYhIACwDhjZBAgQIECAAAECBAgQIECAQHUKtD41PRMAaNlycHUO0KgIECBAgECVCLgFUJUshGEQIECAAAECBAgQIECAAAECBAgQIECAAIFSCggAlFJTXwQIECBAgAABAgQIECBAgAABAgQIECBAoEoEBACqZCEMgwABAgQIECBAgAABAgQIECBAgAABAgQIlFJAAKCUmvoiQIAAAQIECBAgQIAAAQIECBAgQIAAAQJVIiAAUCULYRgECBAgQIAAAQIECBAgQIAAAQIECBAgQKCUAgIApdTUFwECBAgQIECAAAECBAgQIECAAAECBAgQqBIBAYAqWQjDIECAAAECBAgQIECAAAECBAgQIECAAAECpRQQACilpr4IECBAgAABAgQIECBAgAABAgQIECBAgECVCAgAVMlCGAYBAgQIECBAgAABAgQIECBAgAABAgQIECilgABAKTX1RYAAAQIECBAgQIAAAQIECBAgQIAAAQIEqkRAAKBKFsIwCBAgQIAAAQIECBAgQIAAAQIECBAgQIBAKQUEAEqpqS8CBAgQIECAAAECBAgQIECAAAECBAgQIFAlAgIAVbIQhkGAAAECBAgQIECAAAECBAgQIECAAAECBEopIABQSk19ESBAgAABAgQIECBAgAABAgQIECBAgACBKhEQAKiShTAMAgQIECBAgAABAgQIECBAgAABAgQIECBQSgEBgFJq6osAAQIECBAgQIAAAQIECBAgQIAAAQIECFSJgABAlSyEYRAgQIAAAQIECBAgQIAAAQIECBAgQIAAgVIKCACUUlNfBAgQIECAAAECBAgQIECAAAECBAgQIECgSgQEAKpkIQyDAAECBAgQIECAAAECBAgQIECAAAECBAiUUkAAoJSa+iJAgAABAgQIECBAgAABAgQIECBAgAABAlUiIABQJQthGAQIECBAgAABAgQIECBAgAABAgQIECBAoJQCAgCl1NQXAQIECBAgQIAAAQIECBAgQIAAAQIECBCoEoHGKhmHYRAgQIAAAQJVINC0aF4sGX9jZiStm28TGxwytgpGZQgECBAgQIAAAQIECBAgQIBAMQICAMWoaUOAAAECBGpUoGnujFh0y0WZ2TXv868RAgA1utKmRYAAAQIECBAgQIAAAQL1IOAWQPWwyuZIgAABAgQIECBAgAABAgQIECBAgAABAnUnIABQd0tuwgQIECBAgAABAgQIECBAgAABAgQIECBQDwICAPWwyuZIgAABAgQIECBAgAABAgQIECBAgAABAnUnIABQd0tuwgQIECBAgAABAgQIECBAgAABAgQIECBQDwICAPWwyuZIgAABAgQIECBAgAABAgQIECBAgAABAnUnIABQd0tuwgQIECBAgAABAgQIECBAgAABAgQIECBQDwICAPWwyuZIgAABAgQIECBAgAABAgQIECBAgAABAnUnIABQd0tuwgQIECBAgAABAgQIECBAgAABAgQIECBQDwICAPWwyuZIgAABAgQIECBAgAABAgQIECBAgAABAnUnIABQd0tuwgQIECBAgAABAgQIECBAgAABAgQIECBQDwKN9TBJcyRAgAABAgQIECBAoDICTU0tMXnSu5mD9x/QOzbaaKPKDMRRCRAgQIAAAQIECNShgABAHS66KRMgQIAAAQIECBB4vwSWLV0Z1171fOZwW40aHB/YddT7dWjHIUCAAAECBAgQIFD3Am4BVPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCAgC1uKrmRIAAAQIECBAgQIAAAQIECBAgQIAAAQJ1LyAAUPdvAQAECBAgQIAAAQIECBAgQIAAAQIECBAgUIsCjbU0qaVLl8Y111zT6ZSOOeaYGD16dKd1FBIgQIAAAQIECBAgQIAAAQIECBAgQIAAgbQL1FQA4I033ojbb7+90zXZbbfdBAA6FVJIgAABAgQIECBAgAABAgQIECBAgAABArUgUFMBgIkTJ2bWZM8994zDDjtsreuzzTbbrDVfJgECBAgQIECAAAECBAgQIECAAAECBAgQqCWBmgwAJCf/jzvuuFpaJ3MhQIAAAQIECBAgQIAAAQIECBAgQIAAAQLrJVBTDwFObgGUbNttt916IahMgAABAgQIECBAgAABAgQIECBAgAABAgRqTaBmAgBNTU3x5ptvRmNjY4waNSqzTgsXLowVK1bU2pqZDwECBAgQIECAAAECBAgQIECAAAECBAgQyCtQM7cAmjp1aqxatSpGjhwZt9xyS9x5550xd+7c6NatWybvk5/8ZBxxxBF5QSZNmrTOOs3NzdHQ0BBJsMFGoBoEWlpassNojVbvzayGHQIEihVobmnOaerfvBwOCQIEihBobl79+0rS3OdKEYiaECDQiYC/gzrBUUSAQJECfl8pEk6zkgu0vxdbW1uL7rtmAgDtDwCeNm1aXHvttbHRRhtF8jDgKVOmZF6XXHJJPPfcc3HBBResEysBPfroo9dZvsMOO8SAAQNi9uzZ66yjgMD7KbBkyZLs4Zqamr03sxp2CBAoVmBV29Vz7VsSZPRvXruGnwQIFCuwZPHKbNOWtj9cfK5kOewQIFAiAZ8rJYLUDYG6F1h9gtXnSt2/GaoGoP3uNgIAbUvSfv//5AT9d77zndhtt90yC5XgJFcDXHHFFXH33XfHfvvtFx/60IeqZhENhAABAgQIECBAgAABAgQIECBAgAABAgQIlEOgZq4AOPXUU2PMmDExaNCgGD58eNYquWXP2LFjM1cBJIGAm266aZ0BgOR2QYcffni27Zo7c+bMydxSqFevXmsWSROoiEBj9+7Z43Zre697b2Y57BAgUKRAa9uzdDpuPlc6atgnQKAYgZUdHsnVEH5fKcZQGwIE3iuwvEOW31c6YNglQKAkAj5XSsKokyoRyP0rv0oGVcwwkm/+J7foWdeWnNhPAgCTJ0+O5JYGycn+Nbck76c//ema2dn05z73ucz+kCFDsnl2CFRSoM+8vtnDd28LBnhvZjnsECBQpMCiuQNi5j/bJv8u+lwpElIzAgSyAt0aVt+ysO37Cj5XsjJ2CBDoisCCbOMGnytZCzsECHRNoO0XlX9u/g5ql/Cz0gLttwBa27nsQsf23rPghbZMWb1NNtkkM+KVK1dGx/ump2wahkuAAAECBAgQIECAAAECBAgQIECAAAECBAoSqJkrAG677baYO3duHHnkkbHlllu+Z/IzZ/7j+4wDBw7MPMj3PRVkECBAgAABAgQIECBAgAABAgQIECBAgACBGhKomSsAHnjggbj55pvjhhtuWOvyPProo5n8nXbaaa3lMgkQIECAAAECBAgQIECAAAECBAgQIECAQC0J1EwA4NBDD82sy/jx42PSpEk5a/Tss89GcoVAsp1++uk5ZRIECBAgQIAAAQIECBAgQIAAAQIECBAgQKAWBWrmFkAf+9jH4vHHH4/nn38+TjvttNhzzz0zrzfeeCMeeuihzNp98YtfjO22264W19GcCBAgQIAAAQIECBAgQIAAAQIECBAgQIBAjkDNBAC6d+8eP/jBDzK3Abrlllsi+dZ/8kq2ESNGxH/8x3/EfvvtlzN5CQIECBAgQIAAAQIECBAgQIAAAQIECBAgUKsCNRMASBaod+/emVv8nHrqqTF9+vSYP39+jBo1Kvr371+r62deBAgQIECAAAECBAgQIECAAAECBAgQIEBgrQI1FQBon2FjY2OMHDky82rP85MAAQIECBAgQIAAAQIECBAgQIAAAQIECNSTQM08BLieFs1cCRAgQIAAAQIECBAgQIAAAQIECBAgQIBAPgEBgHxCygkQIECAAAECBAgQIECAAAECBAgQIECAQAoFBABSuGiGTIAAAQIECBAgQIAAAQIECBAgQIAAAQIE8gkIAOQTUk6AAAECBAgQIECAAAECBAgQIECAAAECBFIoIACQwkUzZAIECBAgQIAAAQIECBAgQIAAAQIECBAgkE9AACCfkHICBAgQIECAAAECBAgQIECAAAECBAgQIJBCAQGAFC6aIRMgQIAAAQIECBAgQIAAAQIECBAgQIAAgXwCAgD5hJQTIECAAAECBAgQIECAAAECBAgQIECAAIEUCggApHDRDJkAAQIECBAgQIAAAQIECBAgQIAAAQIECOQTEADIJ6ScAAECBAgQIECAAAECBAgQIECAAAECBAikUEAAIIWLZsgECBAgQIAAAQIECBAgQIAAAQIECBAgQCCfgABAPiHlBAgQIECAAAECBAgQIECAAAECBAgQIEAghQICAClcNEMmQIAAAQIECBAgQIAAAQIECBAgQIAAAQL5BAQA8gkpJ0CAAAECBAgQIECAAAECBAgQIECAAAECKRQQAEjhohkyAQIECBAgQIAAAQIECBAgQIAAAQIECBDIJyAAkE9IOQECBAgQIECAAAECBAgQIECAAAECBAgQSKGAAEAKF82QCRAgQIAAAQIECBAgQIAAAQIECBAgQIBAPgEBgHxCygkQIECAAAECBAgQIECAAAECBAgQIECAQAoFBABSuGiGTIAAAQIECBAgQIAAAQIECBAgQIAAAQIE8gkIAOQTUk6AAAECBAgQIECAAAECBAgQIECAAAECBFIoIACQwkUzZAIECBAgQIAAAQIECBAgQIAAAQIECBAgkE9AACCfkHICBAgQIECAAAECBAgQIECAAAECBAgQIJBCAQGAFC6aIRMgQIAAAQIECBAgQIAAAQIECBAgQIAAgXwCAgD5hJQTIECAAAECBAgQIECAAAECBAgQIECAAIEUCggApHDRDJkAAQIECBAgQIAAAQIECBAgQIAAAQIECOQTEADIJ6ScAAECBAgQIECAAAECBAgQIECAAAECBAikUEAAIIWLZsgECBAgQIAAAQIECBAgQIAAAQIECBAgQCCfgABAPiHlBAgQIECAAAECBAgQIECAAAECBAgQIEAghQICAClcNEMmQIAAAQIECBAgQIAAAQIECBAgQIAAAQL5BAQA8gkpJ0CAAAECBAgQIECAAAECBAgQIECAAAECKRQQAEjhohkyAQIECBAgQIAAAQIECBAgQIAAAQIECBDIJyAAkE9IOQECBAgQIECAAAECBAgQIECAAAECBAgQSKGAAEAKF82QCRAgQIAAAQIECBAgQIAAAQIECBAgQIBAPgEBgHxCygkQIECAAAECBAgQIECAAAECBAgQIECAQAoFBABSuGiGTIAAAQIECBAgQIAAAQIECBAgQIAAAQIE8gkIAOQTUk6AAAECBAgQIECAAAECBAgQIECAAAECBFIoIACQwkUzZAIECBAgQIAAAQIECBAgQIAAAQIECBAgkE9AACCfkHICBAgQIECAAAECBAgQIECAAAECBAgQIJBCAQGAFC6aIRMgQIAAAQIECBAgQIAAAQIECBAgQIAAgXwCAgD5hJQTIECAAAECBAgQIECAAAECBAgQIECAAIEUCggApHDRDJkAAQIECBAgQIAAAQIECBAgQIAAAQIECOQTEADIJ6ScAAECBAgQIECAAAECBAgQIECAAAECBAikUEAAIIWLZsgECBAgQIAAAQIECBAgQIAAAQIECBAgQCCfgABAPiHlBAgQIECAAAECBAgQIECAAAECBAgQIEAghQICAClcNEMmQIAAAQIECBAgQIAAAQIECBAgQIAAAQL5BAQA8gkpJ0CAAAECBAgQIECAAAECBAgQIECAAAECKRQQAEjhohkyAQIECBAgQIAAAQIECBAgQIAAAQIECBDIJyAAkE9IOQECBAgQIECAAAECBAgQIECAAAECBAgQSKGAAEAKF82QCRAgQIAAAQIECBAgQIAAAQIECBAgQIBAPgEBgHxCygkQIECAAAECBAgQIECAAAECBAgQIECAQAoFBABSuGiGTIAAAQIECBAgQIAAAQIECBAgQIAAAQIE8gkIAOQTUk6AAAECBAgQIECAAAECBAgQIECAAAECBFIoIACQwkUzZAIECBAgQIAAAQIECBAgQIAAAQIECBAgkE9AACCfkHICBAgQIECAAAECBAgQIECAAAECBAgQIJBCAQGAFC6aIRMgQIAAAQIECBAgQIAAAQIECBAgQIAAgXwCAgD5hJQTIECAAAECBAgQIECAAAECBAgQIECAAIEUCggApHDRDJkAAQIECBAgQIAAAQIECBAgQIAAAQIECOQTEADIJ6ScAAECBAgQIECAAAECBAgQIECAAAECBAikUEAAIIWLZsgECBAgQIAAAQIECBAgQIAAAQIECBAgQCCfgABAPiHlBAgQIECAAAECBAgQIECAAAECBAgQIEAghQICAClcNEMmQIAAAQIECBAgQIAAAQIECBAgQIAAAQL5BAQA8gkpJ0CAAAECBAgQIECAAAECBAgQIECAAAECKRQQAEjhohkyAQIECBAgQIAAAQIECBAgQIAAAQIECBDIJyAAkE9IOQECBAgQIECAAAECBAgQIECAAAECBAgQSKGAAEAKF82QCRAgQIAAAQIECBAgQIAAAQIECBAgQIBAPoHGfBWUEyBAgAABAgQIECBAgAABAgQIECBAoNYE5i2ZEX+ZeEc8M/X+WLB8VmZ6K5uXx9fvPCb22OLwOHibj8bQASNqbdrmU2cCAgB1tuCmS4AAAQIECBAgQIAAAQIECBAgQKCeBZpaVsVtz1wWd7/081jVvOI9FG/Mfi6S1x3PXR7/suNp8fF9vhY9G/u8p54MAmkQEABIwyoZIwECBAgQIECAAAECBAgQIECAAAECXRZYvPzduOz+T8dr7/w1b1/NbYGCe16+pq3uU/HVI2+MwX2H5m2jAoFqE/AMgGpbEeMhQIAAAQIECBAgQIAAAQIECBAgQKDkAsk3/3/4p9MLOvnf8eBvznkhvv/HT8XKpmUds+0TSIWAAEAqlskgCRAgQIAAAQIECBAgQIAAAQIECBDoisCdz/93vDrjiZwu9tny6LZb/PxXTt7Y3b8cB40+MScvCQL8+qnv5uRJEEiDgABAGlbJGAkQIECAAAECBAgQIECAAAECBAgQKFpgwbI58YcXrspp/7E9vxLnHXFdbNhveE7+4L4bx5cOuzJOO+CSnPz7JvwyZi16KydPgkC1CwgAVPsKGR8BAgQIECBAgAABAgQIECBAgAABAl0SePLNP8SKDrfw2WPk4fHRPc/rtM+jdv5s25UAY7N1kmcCPDrxjmzaDoE0CHgIcBpWyRgJECBAgAABAgQIECBAgAABAgQIECha4LmpD+S0HTZo67j35esyeZNm/y2n7JXpj0dLa0smb+MBI3LKnpv2pxi7xzk5eRIEqllAAKCaV8fYCBAgQIAAAQIECBAgQIAAAQIECBDossDrs57O6ePul36Wk+6Y+OvkcZG81rZNnvPy2rLlEahaAbcAqtqlMTACBAgQIECAAAECBAgQIECAAAECBEohsHzlklJ0E00tK0vSj04IvF8CAgDvl7TjECBAgAABAgQIECBAgAABAgQIECBQEYG+vQaW5Lg9u/cuST86IfB+CbgF0Psl7TgECBAgQIAAAQIECBAgQIAAAQIECFREYPtN94lnp96fPfbY3c+JzTbYJpN+/Z2n4v4JN2TLDtn23+IDmx+SSc9Z9Hb8+unvZMtGbbxbdt8OgTQIuAIgDatkjAQIECBAgAABAgQIECBAgAABAgQIFC2w58gP57R9feZTceDWJ8RBo8fGtpvsnVO2ddtJ/iQ/eU2c9WxO2Z5b5PaTUyhBoAoFBACqcFEMiQABAgQIECBAgAABAgQIECBAgACB0gnsO+pfo2/P1bcBemX643HjExdGa2vrOg9y6zOXxTNT78uW92i7/U8SFLARSJOAAECaVstYCRAgQIAAAQIECBAgQIAAAQIECBBYb4H+vQbH2N3Pzml3z8vXxMXjToy3352Ykz9r4dT47r2fiDue+3FO/rEf+EIM6bdpTp4EgWoX8AyAal8h4yNAgAABAgQIECBAgAABAgQIECBAoMsCx7SdwJ8w44l4btoD2b6SdPLquI176Wcdk5n9HYbtHyfuee578mUQqHYBVwBU+woZHwECBAgQIECAAAECBAgQIECAAAECXRbo1tAtzh5zdewx8vD16mun4QfGV464Phq79VivdioTqAYBAYBqWAVjIECAAAECBAgQIECAAAECBAgQIECg7AK9e/SL//yXG+KU/b4Z/XoO6vR4Sd1/2+v8+PrRv4nkFkI2AmkUcAugNK6aMRMgQIAAAQIECBAgQIAAAQIECBAgUJRAciXAsR84Iw7b7uR4cvK4eG7qn9oe9nt/W1//eCDw7iPGxB5bHB77jTo2BvbesKhjaESgWgQEAKplJYyDAAECBAgQIECAAAECBAgQIECAAIH3TaBfr0ExZvtPZF6fv3HXWLB8VvTs3jsuOOqm920MDkSg3AJuAVRuYf0TIECAAAECBAgQIECAAAECBAgQIECAAIEKCAgAVADdIQkQIECAAAECBAgQIECAAAECBAgQIECAQLkFBADKLax/AgQIECBAgAABAgQIECBAgAABAgQIECBQAQEBgAqgOyQBAgQIECBAgAABAgQIECBAgAABAgQIECi3gABAuYX1T4AAAQIECBAgQIAAAQIECBAgQIAAAQIEKiAgAFABdIckQIAAAQIECBAgQIAAAQIECBAgQIAAAQLlFhAAKLew/gkQIECAAAECBAgQIECAAAECBAgQIECAQAUEBAAqgO6QBAgQIECAAAECBAgQIECAAAECBAgQIECg3AICAOUW1j8BAgQIECBAgAABAgQIECBAgAABAgQIEKiAgABABdAdkgABAgQIECBAgAABAgQIECBAgAABAgQIlFtAAKDcwvonQIAAAQIECBAgQIAAAQIECBAgQIAAAQIVEBAAqAC6QxIgQIAAAQIECBAgQIAAAQIECBAgQIAAgXILCACUW1j/BAgQIECAAAECBAgQIECAAAECBAgQIECgAgICABVAd0gCBAgQIECAAAECBAgQIECAAAECBAgQIFBuAQGAcgvrnwABAgQIECBAgAABAgQIECBAgAABAgQIVEBAAKAC6A5JgAABAgQIECBAgAABAgQIECBAgAABAgTKLfC+BgCWLFkSixcvLvec9E+AAAECBAgQIECAAAECBAgQIECAAAECBOpeoKwBgNmzZ8dXvvKVOOSQQ2L48OHRv3//uPDCCzPokydPjoMPPjhuv/32aGlpqfuFAECAAAECBAgQIECAAAECBAgQIECAAAECBEop0FjKztr7am1tjf/+7/+Ob33rWzF//vz27JyfU6ZMiUcffTTzOvnkk+OXv/xl9OjRI6eOBAECBAgQIECAAAECBAgQIECAAAECBAgQIFCcQFmuALjiiiviy1/+cubkf2NjY+y+++4xevTonBE2NTVlT/jfcsstccYZZ+SUSxAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQLFC5Q8APDSSy/F1772tcyIjjnmmJg0aVI899xzkex33D784Q9nypLbACVbcgXA66+/3rGKfQIECBAgQIAAAQIECBAgQIAAAQIECBAgQKBIgZIHAC6//PJYsWJF5lv/t912W4wcOXKdQxsxYkTcd999MWTIkGhubo7rrrtunXUVECBAgAABAgQIECBAgAABAgQIECBAgAABAoULlDwA8Le//S1z9OQqgD59+uQdSVKn/eqAiRMn5q2vAgECBAgQIECAAAECBAgQIECAAAECBAgQIJBfoKQBgORb/K+88krmqHvuuWf+o/+zxpFHHpnZmzZtWsFtVCRAgAABAgQIECBAgAABAgQIECBAgAABAgTWLVDSAED37t2jf//+maMtWLBg3Uddo2T27NmZnOHDh69RIkmAAAECBAgQIECAAAECBAgQIECAAAECBAgUI9BYTKPO2uy6667x0EMPxYMPPph5DkBnddvLkucAJNvOO+/cnlWVP1taWqKpqSnmzp1bleMzqPoTWLp0aXbSTc3em1kMOwQIFC2wYtGibNvk3z3/5mU57BAgUKTAooUrsi1bW8PnSlbDDgECpRFo9blSGki9ECAQbb+o/HPzd1C7hJ+VFkietZtsyd/nxW4lDwDsu+++mQDAxRdfHB/5yEdi9OjRnY7tF7/4Rdx7772ZOutz26BOOy1zYUNDQ5mPoHsChQl0fCc2RNv/vDcLg1OLAIF1C3T8YGmr5XNl3VRKCBAoTGDNz5E104X1ohYBAgTWLeBzZd02SggQKE7A50pxblqVXqAU78WSBwC++tWvxs033xxvvfVW7LXXXvG9730vTjjhhPfMfurUqXHJJZfE9ddfnyk76KCDYuzYse+pV00Z3bp1i549e8aQIUOqaVjGUscCfeb1zc4+uQWX92aWww4BAkUKLJo7IGb+s23y757PlSIhNSNAICvQrWFJdj/5roLPlSyHHQIEuiCw+qbDDT5XuuCoKQECHQVWfxvK7ysdXexXUqD9CoDk7/Nit+JbruOIgwcPjhtuuCGSQSXPATjjjDNi0003jauvvjrT4te//nVsvPHGseWWW8Z1110XrW3XAfft2zeSKwG6MpF1DEc2gZoVSP6/887i+dn5zVu2KJY3rcqm7RAgQIAAAQIECBAgQIAAAQIECBAgUN8CJQ8AJJyHHnpoPPnkk7HffvtlddujFTNmzIg5c+Zk88eMGRPPPPNM3lsFZRvYIVDnAjOXzI+LHv5N7HPtf8Z/PXxzVuPeKS/EB64+Jz4/7qp4bsakbL4dAgQIECBAgAABAgQIECBAgAABAgTqU6DktwBqZ9x7773j8ccfj9tvvz3zc+LEiZG8km8tb7vttrHNNttkAgXHHXdcexM/CRDII3DjCw/HpX+5re2b/ivXWjPJ/+Mbz2deJ+6wf3x3zCnRu7HnWuvKJECAAAECBAgQIECAAAECBAgQIECgtgXKFgBI2JKHFHzsYx/LvGqb0ewIlF/gkkdujWue+1PBB7rj1Sdi4rwZ8ZsTz4v+PXsX3E5FAgQIECBAgAABAgQIECBAgAABAgRqQ6AstwCqDRqzIFA9Ask3/9c8+d+9oVv07dErZ5AD1jjR/+LMKfGle6/JXHmTU1GCAAECBAgQIECAAAECBAgQIECAAIGaFyj5FQDJbX7mz1/9YNL1Edxss81i+PDh69NEXQI1L5Dc8z+57U/HbbdNt4rLj/hMnHH31fHa3LezRQ+femlc8ddx8asXH87mPTj5xbjr9afiI9vvm82zQ4AAAQIECBAgQIAAAQIECBAgQIBA7QuUPABwzjnnxD333FOU3EUXXRQXXnhhUW01IlCrAv/79B9z7vmfnPy/9aP/2XZv/x7vmfKAXn3i24d9Igb16htXPr36/4c/euIuAYD3aMkgQIAAAQIECBAgQIAAAQIECBAgUNsCbgFU2+trdikXSB6afffEZ7KzSG77k3zzf20n/7OV2nbO2//42GbIsGzW1AWz46VZU7NpOwQIECBAgAABAgQIECBAgAABAgQI1L5Aya8AOPfcc+Okk05ap1xzc3MsXLgwJk+eHL///e8zP48++ui45pprYuDAgetsp4BAPQpMnj8zZi5ZkJ168jDf/xp/UzY9re3EfsftlDuviCRIkGyrWpo7FsWjU1+NXYZukZMnQYAAAQIECBAgQIAAAQIECBAgQIBA7QqUPAAwZsyYgrUuvvjiGDt2bOaWQZdddllcfvnlBbdVkUA9CDwzfVLONBesWBpP/P31nLyOiafentgxmbM/fspLccbeR+bkSRAgQIAAAQIECBAgQIAAAQIECBAgULsCFb0FUPKN/+R5AcmDf6+44ooYP3587UqbGYEiBOYtW1xEq7U3Wbxy+doL5BIgQIAAAQIECBAgQIAAAQIECBAgUJMCFQ0AJKI9e/aMI444IoP75z//uSaRTYpAsQIHj9yh2KbvaXfQiNL19Z7OZRAgQIAAAQIECBAgQIAAAQIECBAgUHUCJb8FUDEz3HnnnTPN/vKXvxTTXBsCNSuwdduDfHs39ozlTSszcxzQ9gyAh0+9NAb06pNJ/+st347/mzc9O/8Xv3B5pn6S8fk//G88PPXlbNkBI7bL7tshQIAAAQIECBAgQIAAAQIECBAgQKD2BSp+BUBC/PDDD2eke/TokfnpPwQI/EOgd2OP+NCWO2U5FrXdxueKv47LnORPAgPdGhqyZclOkpe8Hn/r9ZyT//169IoDRmyfU1eCAAECBAgQIECAAAECBAgQIECAAIHaFqh4ACB5BsADDzyQUd5rr71qW9vsCBQh8IU9/yWn1a9efDh+8Nid0dzSkpPfnhg/+aU4856ftSczP0/f/fDo1RZMsBEgQIAAAQIECBAgQIAAAQIECBAgUD8CJb8F0G9/+9t48803OxVsamqKpUuXxvPPPx/jxo3L1G1o+ybzUUcd1Wk7hQTqUWCPYVvHiTvsH3e8+kR2+lc+fU/cN+n5WLB8aTYv2Vnztj9J3uYDN4wv7HVksmsjQIAAAQIECBAgQIAAAQIECBAgQKCOBEoeALjuuusi+Vb/+m7nn39+HHTQQevbTH0CdSHw3TGnxMR5M+LFmVOy803Sa24d7/mflCW3/rn+uLOif9uzA2wECBAgQIAAAQIECBAgQIAAAQIECNSXQMVvAbT77rvHNddcE5deeml9yZstgfUQSO7r/5sTz4sxW32g4FbJN//vPOmC2H6jzQtuoyIBAgQIECBAgAABAgQIECBAgAABArUjUPIrAH7xi1/EsmXL8golD/wdPHhw9O3bN29dFQgQiMy3+JNv8//+9afih0/cFVMXzF4rS/Jt/8/sNiZz2x/f/F8rkUwCBAgQIECAAAECBAgQIECAAAECdSFQ8gDA0KFD6wLOJAlUQiB5Vsbx2++beb00a2r84vkH4/Z/PhtghyGbxQUHnxgHjNjeA38rsTiOSYAAAQIECBAgQIAAAQIECBAgQKDKBCp+C6Aq8zAcAqkR2GXoFnH01ntkx7vHJlvFoVvt4uR/VsQOAQIECBAgQIAAAQIECBAgQIAAgfoWEACo7/U3ewIECBAgQIAAAQIECBAgQIAAAQIECBCoUYGibwH0xBNPxGOPPVZSlgMOOCCSl40AAQIECBAgQIAAAQIECBAgQIAAAQIECBDomkDRAYD7778/Lrrooq4dfY3WSX8CAGugSBIgQIAAAQIECBAgQIAAAQIECBAgQIAAgSIE3AKoCDRNCBAgQIAAAQIECBAgQIAAAQIECBAgQIBAtQsUfQXAOeecE6eddlpJ5zd48OCS9qczAgQIECBAgAABAgQIECBAgAABAgQIECBQrwJFBwAGDRoUyctGgAABAgQIECBAgAABAgQIECBAgAABAgQIVJ9AVd0CqLW1tfqEjIgAAQIECBAgQIAAAQIECBAgQIAAAQIECKRQoOgrAAqZ65QpU+Kdd96JlStXRktLS7ZJcqK/qakpmpubY8mSJTFz5sy4++67Mw8A/vrXv56tZ4cAAQIECBAgQIAAAQIECBAgQIAAAQIECBAoTqAsAYAnn3wyLrjggvjzn/+8XqPae++916u+ygQIECBAgAABAgQIECBAgAABAgQIECBAgMDaBUoeAHj33XfjhBNOyHzzf+2HXHvu8OHDY/vtt197oVwCBAgQIECAAAECBAgQIECAAAECBAgQIEBgvQRKHgD4zne+kz35P2bMmDjuuOOiT58+8fnPfz569eoV1157bea2P1OnTo1bb701Jk2aFKNGjYrXXnstevTosV6DV5kAAQIECBAgQIAAAQIECBAgQIAAAQIECBBYu0DJAwDPPvts5khHHHFE3Hfffdmjfv/738+c7N92221jn332yeSff/75ceSRR8Zf//rX+NGPfpS5bVC2gR0CBAgQIECAAAECBAgQIECAAAECBAgQIECgaIFuRbdcR8OJEydmSs4+++ycGvvvv38m/dBDD2XzBw8eHA888EBsvfXWcfHFF8fkyZOzZXYIECBAgAABAgQIECBAgAABAgQIECBAgACB4gVKGgBYtWpVvP3225nRbLPNNjmj2m677TLpF198MSe/f//+cdRRR8WyZcvizjvvzCmTIECAAAECBAgQIECAAAECBAgQIECAAAECBIoTKGkAILmH/4YbbpgZSWNj7t2F1hUASCofcsghmTYvvfRS5qf/ECBAgAABAgQIECBAgAABAgQIECBAgAABAl0TKGkAIBnK9ttvnxnRmrfz2WGHHTL5ycN+V65cmdlv/0/fvn0zu6+88kp7lp8ECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAFwTKFgC4+uqrc4aVXAGQXBXQ1NQUjzzySE7ZuHHjMukBAwbk5EsQIECAAAECBAgQIECAAAECBBKB1hVNsXTcqzH7i223D24MmHpyAABAAElEQVRpzaC0vr0w5p47LpaNfyNam1tAESBAgAABAmsIlDwA8MlPfjIaGhritttui49+9KPxzDPPZA6Z3B7owAMPzOx/8YtfjOnTp0dra2v84Q9/iNtvvz2TP3r06DWGJ0mAAAECBAgQIECAAAECBAjUu8Ci65+Ot7b+Qcw89oZY/L9/Xc2xqiUWXv5ovDPm2nh7px/Hkt9PWF1mjwABAgQIEIiSBwA++MEPxpe+9KUM7R133BHHHXdclvncc8/N7E+cODFGjBgRw4YNy5TPnj07k58ED2wECBAgQIAAAQIECBAgQIAAgUSgZdmqmHXSzTHn9Duiue3b/p1tq16fE7OOvzFzRYCrATqTUkaAAAEC9SRQ8gBAgvfd7343zjrrrOjfv39svfXWWc9jjz02zjzzzEy6paUlZs6cmS373Oc+FwcddFA2bYcAAQIECBAgQIAAAQIECBCoX4HWtvMGs066JZbc+tJ6ISRXBMz78j9uNbxeDVUmQIAAAQI1KFCWAEDyUN+f/OQn8fbbb8e3v/3tLFtya6Arr7wyrr/++sw3/5OrAA499NC45ppr4uc//3m2nh0CBAgQIECAAAECBAgQIECgvgUW/OCRWPaHV3MQeu4xPPqdsntO3oAz9o3G0Rvm5C38yeOx+P+9kJMnQYAAAQIE6lGgLAGAdsiBAwdGckugNbdPf/rTcdddd8W0adNi/Pjx8dnPfnbNKtIECBAgQIAAAQIECBAgQIBAnQo0z14c878zPmf2A87YL4Y/dVb03HVYTn6fMaNjsxfOjr7H7ZCT/+5X7808ODgnU4IAAQIECNSZQMkDAG+++Wbm4b515mi6BAgQIECAAAECBAgQIECAQIkEFt3wXLQuWpntrfeHR8eGPz0+Grqv/TRGt749Y+PfnBw9dhyabdM0dX4svfu1bNoOAQIECBCoR4G1/8vZBYnkAcDbbLNNXHrppfHWW291oSdNCRAgQIAAAQIECBAgQIAAgXoUWPr7CTnT7v/x3WLFE9Ni+eNTo2nKuzllK1+bnclf+fz06Hfybjlla/aTUyhBgAABAgTqQKCxHHOcNGlSfOMb34gLL7wwxowZE8ktf0444YTo3bt3OQ6nTwIECBAgQIAAAQIECBAgQKCGBFY8/fec2cz5zO056Y6J+f/f/TG/Y0aH/WUPTeqQskuAAAECBOpPoORXAJx++ulx4IEHZiRbWlriT3/6U5x88skxbNiwOOOMM+Kpp56qP2UzJkCAAAECBAgQIECAAAECBAoSaGlqjljeVFDdfJWapy/KV0U5AQIECBCoaYGSBwDGjh0bjz76aCRXAXzrW9+K0aNHZwDnz58fV199dey7776x0047xWWXXRbvvPNOTeOaHAECBAgQIECAAAECBAgQILB+At0au0d0a1i/Ruuo3dC/5zpKZBMgQIAAgfoQKHkAoJ1t1KhR8c1vfjMmTpwYjz/+eObb/0OGDMkUT5gwIc4///wYMWJEHHvssfHb3/42Vq5c/XCf9j78JECAAAECBAgQIECAAAECBOpPoHGbDXMmPeCMfWPgeQdnXr0+uFVOWZ9jd8iW9ftE7jMAeu0/MqeuBAECBAgQqDeBsgUAOkLuv//+cdVVV8WMGTMyJ/uTqwSS5wE0NTXFuHHj4sQTT4zNNtssbr993ff069iffQIECBAgQIAAAQIECBAgQKB2Bfoes33O5LoN7B0b/vCYzKtv2wn/jtuAU/fIlsXKttsHddj6HZ3bT4ciuwQIECBAoC4E3pcAQLtkz549Mw8DvuOOO2L27Nnxs5/9LDbYYINM8Zw5c+Lll19ur+onAQIECBAgQIAAAQIECBAgUKcC/T+xe87MF/zwkVh6z2s5eWsmFl79ZCy57aVsdkPvxuh74s7ZtB0CBAgQIFCPAo3v96STZwEkAYDktj8PPvhgrFixIjuEPn36ZPftECBAgAABAgQIECBAgAABAvUp0GuPzaLfx3ZZfUK/uTVmHn9jDP7GYRHdc7/L2LJwRcw5665Y9NMncrAGnn1gNA4bmJMnQYAAAQIE6k3gfQkAJCf577777rj55pszPzue9B84cGCcdNJJ8ZnPfCb222+/evM3XwIECBAgQIAAAQIECBAgQGAtAhteeXws/+tb0Txt/j9Km1pi/oUPRDTmBgDmfPaOiJbWnB567rlZDL7w8Jw8CQIECBAgUI8CZQsAtLa2xl/+8pe46aab4rbbbovkm//tW0NDQ3zoQx/KnPRPngfQt2/f9iI/CRAgQIAAAQIECBAgQIAAAQLRfWj/2PTu0+Kdo66P5r8vXC3SFgjI2dY4+d9j501ik7s+Fd369MipJkGAAAECBOpRoOQBgNdeey1uuOGGuOWWW2LatGk5pltssUWceuqpcdppp8VWW22VUyZBgAABAgQIECBAgAABAgQIEOgo0HPnTWP401+K5Fv+y+7u/BkA0RDR/1NtDwT+yfHRbUCvjt3YJ0CAAAECdStQ8gDAeeedF/fcc08WNLmv/wknnJD5tv9hhx0Wybf/bQQIECBAgAABAgQIECBAgACBQgQaNx0Qm447LZY98mYs/uWzsWTca9E6e0m2afeRg6LvsTvGgM/tHb12HZ7Nt0OAAAECBAi03TmvXAj77LNP5qT/v//7v8egQYPKdRj9EiBAgAABAgQIECBAgAABAnUg0OeDoyJ5bdw218ndLohIbvu/xaAYOeVrdTB7UyRAgAABAsUJlDwAcMopp8Rll10WO+64Y3Ej0ooAAQIECBAgQIAAAQIECBAg0JlAcneBtmcPustAZ0jKCBAgQIBAGa4A+PjHP86VAAECBAgQIECAAAECBAgQIECAAAECBAgQqLBAtwof3+EJECBAgAABAgQIECBAgAABAgQIECBAgACBMggIAJQBVZcECBAgQIAAAQIECBAgQIAAAQIECBAgQKDSAgIAlV4BxydAgAABAlUi0LxscSx59cnsaFbNmhbLpr2aTdshQIAAAQIECBAgQIAAAQIE0iVQ8ocAp2v6RkuAAAECBAgsn/ZazLjp4ljw1D3RumpFFmTVlBfjtTP2iJ7DRsXQE86OjY78TDR096tDFsgOAQIECBAgQIAAAQIECBCocgFXAFT5AhkeAQIECBAop8A7/+/78eqZe8b8x+7MOfnf8ZgrZ7wZf7/q7HjtS/vFihmTOxbZJ0CAAAECBAgQIECAAAECBKpYQACgihfH0AgQIECAQDkFpl15Vsy48aKIlpaCDrN86ivx+pcPiuVvvV5QfZUIECBAgAABAgQIECBAgACBygoIAFTW39EJECBAgEBFBGb//qqYe+91Ocfu1qtvNG64WU5er5E75KSbF82LSd8aG81LF+bkSxAgQIAAAQIECBAgQIAAAQLVJyAAUH1rYkQECBAgQKCsAqvmz4rpN3wz5xgDdjs0drxuQvTeYqec/K2/eUeM/PLPo6FHr2x+ckugmbf+MJu2Q4AAAQIECBAgQIAAAQIECFSngABAda6LUREgQIAAgbIJzP7dT6Jl+ZJs//122D9GXfS76LHBJtm8jjsbHv7J2PKrv+qYFbPu+knbVQCLcvIkCBAgQIAAAQIECBAgQIAAgeoSEACorvUwGgIECBAgUHaB+Y/9LucYI750ZXTr0TMnb83E4P2PjUEHfCSb3bpyeSx85r5s2g4BAgQIECBAgAABAgQIECBQfQKN1TckIyJAgAABAgTKJdC0cG6smP5GtvuGxh4x6RvHZdNNC+dk95Od//vKodHQ/R+/LrS0nfTvuC382/jY4IMf7ZhlnwABAgQIECBAgAABAgQIEKgiAQGAKloMQyFAgAABAuUWWDrp+ZxDtDatilVz387J65homj+zYzJnf/ELD+ekJQgQIECAAAECBAgQIECAAIHqEnALoOpaD6MhQIAAAQLlFWgtb/d6J0CAAAECBAgQIECAAAECBKpHwBUA1bMWRkKAAAECBMou0Hf07jnHSG4B1Dho42xecoug1lUrsunGwUNzbgHUvGhetqz/rh/K7tshQIAAAQIECBAgQIAAAQIEqk/AFQDVtyZGRIAAAQIEyibQOHDD6DV8dLb/5BZAW186Lna+cVLm1W+XQ7Jlyc62P3w4W9Z/lw/mlA3c7bCctAQBAgTWJrBo4ernh6xY0RQrljetrZo8AgQIECBAgAABAgTKICAAUAZUXRIgQIAAgWoWGHzgR3KG99b/nBktq1bm5K2ZWPDkuFjw+O+y2Q09e8fAvf4lm7ZDgACBjgIrVzbFH8dNiAsvuDsu/Nofs0XT314cZ3721vjx98bHC8+v+/kj2QZ2CBAgQIAAAQIECBDokoBbAHWJT2MCBAgQIJA+gY2PPytm/+F/o2X5kszgl7z6RLx50QmxxVeuX+tk5j14c0y78qycsqFtfXTvOyAnT4IAAQKJwGsTZsY1Vz0W785btlaQlpbWePnFGZnXjjtvGp8/88AYOKj3WuvKJECAAAECBAgQIECgawKuAOian9YECBAgQCB1Aj022CSGfepbOeNe9LfxMeGzO8Xyqa/k5E+65KMx9cefjdaVq2/h0XPYqNjk3/4zp54EAQIEEoEnH5scP/rug+s8+b+m0oSX34lLvvHHmD1r8ZpF0gQIECBAgAABAgQIlEBAAKAEiLogQIAAAQJpExh6/Jmx4ZGfyRl2ckVA09zcW3KsmDohp073AUNi62/e0fbt/4E5+RIECBB44/9mx3VXPxnNza05GP3698xJ9+2bm547Z0n8T9vzRpYvX5VTT4IAAQIECBAgQIAAga4LCAB03VAPBAgQIEAglQIjv/TTGHbKNyO6FfbrQO8tdoztLn80eo/cPpXzNWgCBMon0NLSEr/4eXLyvyV7kMGD+8R5Xzss9t53ZDYv2Tnr3IPjxJN2jYaGhmz+239fEON+93I2bYcAAQIECBAgQIAAgdIIFPYXf2mOpRcCBAgQIECgygQ2/fjXYvufPhODDvhINDTmfiu3fag9N90qNj/j8tj+f56MXsO2as/2kwABAlmBJx+bEjOmL8ymBw7sHf/1rSNip12GZfPadxobu8cxx+8cn/vi/u1ZmZ9/uvf1WLxoRU6eBAECBAgQIECAAAECXRMQAOian9YECBAgQCD1An1G7hCjvv7r2OU3b8ewz/84O58eW+4S21/1bOx03YTY+F+/0BYg6JEts0OAAIGOAk8/Oa1jMj7+qT1jo4375+StmdjvwK1irw5XB6xa1RzPP/v3NatJEyBAgAABAgQIECDQBYHGLrTVlAABAgQIEKghge59+ke/HVd/I7fH0C2iT9ttf2wECBDIJ/DKyzOyVbp3b4jHHnkz80oyp/99frYs2fn1r56Nfv3+ccXRkiUrc8peemF6HPyhrXPyJAgQIECAAAECBAgQKF5AAKB4Oy0JECBAgAABAgQI1L3AogXLo2nV6nv/Jw8BfvnF1QGBNYEmT5q7ZlY2/X+vzcru2yFAgAABAgQIECBAoOsCbgHUdUM9ECBAgAABAgQIEKhbgSVLc7/F3xWIVSubu9JcWwIECBAgQIAAAQIE1hAQAFgDRJIAAQIECBAgQIAAgcIFhm4yoPDKeWqO2HKDPDUUEyBAgAABAgQIECCwPgJuAbQ+WuoSIECAAAECBAgQIJAj0K1bQ4zcYoOYNvXdbP7XLjoiNttsUCb961890/Y8gMnZsnO/emiMGr1RJn3P7yfEPX94JVu2086bZvftECBAgAABAgQIECDQdQFXAHTdUA8ECBAgQIAAAQIE6lpg9702z5n/nbe+EL37NEbftof99ujRPaesd58emfzFi1fE+Adezynbfa8ROWkJAgQIECBAgAABAgS6JiAA0DU/rQkQIECAAAECBAjUvcChh28bvXqtvrj4tQkz4+c/fTxWrmxaq82MtxfEj783PpYvW12+8weGxeYjBq+1vkwCBAgQIECAAAECBIoTWP1benHttSJAgAABAgQIECBAoM4FBg7qHceN3SVu+/XzWYmnnpgaE1+fFYM36JPNS3b+OG5CvPi36dHU1JLNT64SOOmUPbJpOwQIECBAgAABAgQIlEbAFQClcdQLAQIECBAgQIAAgboWOOrYHWOf/bfIMXh33rKYPGleTt5zz/w95+R/Unj6F/aLzTb37f8cKAkCBAgQIECAAAECJRAQACgBoi4IECBAgAABAgQIEIj43BcPiMOO2LZgip69useZX/5gW+Bgy4LbqEiAAAECBAgQIECAQOECbgFUuJWaBAgQIECAAAECBAh0ItC9e7c45bS9Y7c9No/bf/N8TJvy7lprNzQ0xL4HbBFj/23X2Gjj/mutI5MAAQIECBAgQIAAga4LCAB03VAPBAgQIECAAAECBAh0EEge6Ju8prc97PfpJ6fEXXe8nCnt179HfPyTe8UHdtss+g/o1aGFXQIECBAgQIAAAQIEyiHgFkDlUNUnAQIECBAgQIAAAQIxfLNBcchho7MSQ4f2iwMOHuXkf1bEDgECBAgQIECAAIHyCggAlNdX7wQIECBAgAABAgQIECBAgAABAgQIECBAoCICAgAVYXdQAgQIECBAgAABAgQIECBAgAABAgQIECBQXgEBgPL66p0AAQIECBAgQIAAAQIECBAgQIAAAQIECFREQACgIuwOSoAAAQIECBAgQIAAAQIECBAgQIAAAQIEyisgAFBeX70TIECAAAECBAgQIECAAAECBAgQIECAAIGKCAgAVITdQQkQIECAAAECBAgQIECAAAECBAgQIECAQHkFBADK66t3AgQIECBAgAABAgQIECBAgAABAgQIECBQEQEBgIqwOygBAgQIECBAgAABAgQIECBAgAABAgQIECivgABAeX31ToAAAQIECBAgQIAAAQIECBAgQIAAAQIEKiIgAFARdgclQIAAAQIECBAgQIAAAQIECBAgQIAAAQLlFRAAKK+v3gkQIECAAAECBAgQIECAAAECBAgQIECAQEUEBAAqwu6gBAgQIECAAAECBAgQIECAAAECBAgQIECgvAICAOX11TsBAgQIECBAgAABAgQIECBAgAABAgQIEKiIgABARdgdlAABAgQIECBAgAABAgQIECBAgAABAgQIlFdAAKC8vnonQIAAAQIECBAgQIAAgf+/vfsA0qI8HwD+XuFEqqAQIoKIQUEHQ8RgiYNdLDFmHPNPmRRrJjGWSWLUGRWNhRh1MIkTS0zMjBXF0bEnagSUaOyKoiKWKESHjASkKHdwd3/eTb7PgyvCfR9f2f2tc95+W9/n9+ws3+2z+y4BAgQIECBAgACBsggoAJSF3U4JECBAgAABAgQIECBAgAABAgQIECBAgMCmFVAA2LS+tk6AAAECBAgQIECAAAECBAgQIECAAAECBMoioABQFnY7JUCAAAECBAgQIECAAAECBAgQIECAAAECm1agftNuvvRbb2xsDHfccUd49tlnw5IlS8KoUaPCuHHjwiGHHBLq6upK3yB7JECAAAECBAgQIECAAAECBAgQIECAAAECZRBIVQFg6dKl4aSTTgoLFixIKAcOHBj+8pe/JD9PPPFEOO+880JDQ0MZmO2SAAECBAgQIECAAAECBAgQIECAAAECBAiUViBVXQBdeOGFycX/3XffPdx3333h7rvvDtOmTQvbb799eOyxx8Lvfve70uraGwECBAgQIECAAAECBAgQIECAAAECBAgQKJNAagoAr776anj66afD5ptvHi666KLQv3//hHTo0KFh6tSpSfc/Dz74YFi+fHmZqO2WAAECBAgQIECAAAECBAgQIECAAAECBAiUTiA1BYCZM2cmavvss0/o2bPnOoKxK6AJEyaEpqamEIsABgIECBAgQIAAAQIECBAgQIAAAQIECBAgkHaB1BQA5s6dm+Qqdv/T0RALAHGYM2dOR7NNI0CAAAECBAgQIECAAAECBAgQIECAAAECqRJIzUuA//WvfyWJ2WKLLTpMUG567gXBHS3U0tISjjvuuI5mJdM+/vjjpIuhxYsXd7qMGQRKKRCPydywpnlNcGzmNPwmQKC7Ao1tusqL/y46r3RX0noECOQEli9rzI2G1tbgvJLXMEKAQHEEWp1XigNpKwQIhLVfVP43+DsoJ+F3uQUaG//7XTr+fd7dITUFgJUrVyYGuQv964P069cvmZRbbv358XOEfPLJJzualUwbM2ZM2GyzzZKuhDpdyAwCJRRobm7O7y3+QR27uTIQIECgEIFYTGw7OK+01TBOgEB3BNasWZ1frXXtH9bOK3kOIwQIFEnAeaVIkDZDgEBewHklT2GkzALFOBZT0QVQvHC/atWqJB19+/btMC19+vRJpueqJh0uZCIBAgQIECBAgAABAgQIECBAgAABAgQIEEiJQCqeAKitrU265vnkk09CZxf4c9MbGho6TV19fX2YNWtWp/PPPvvsUFNTEwYPHtzpMmYQKKVA7+Uf5HdXX1/n2MxrGCFAoLsCK9aeV3Id3cV/X/2b111J6xEgkBP4qOHTLgtrfZfOsfhNgECBAu/l1/c3ep7CCAECBQrU5Nf3d1CewkiZBXLXtOM16e4OqSgAxOC32mqrEPv3X96m7+K2KLnpvXv3bju53fiQIUPaTctNiBdC4lBXV5eb5DeBsgrkjsnYiJq1/zk2y5oOOyeQCoHamnUfDnReSUVaBUGgrAJtv6/EhjivlDUddk4glQLOK6lMq6AIlFXAeaWs/HbeRiB3LBZSAFj3r/w2G6+20VgAiEPuQv/67V+2bFkyacCAAevP8pkAAQIECBAgQIAAAQIECBAgQIAAAQIECKROIDUFgNyjOW+//XaHScpNjy/yNRAgQIAAAQIECBAgQIAAAQIECBAgQIAAgbQLpKYAcMABByS5euSRR9rlLL4k+NFHH02mjxs3rt18EwgQIECAAAECBAgQIECAAAECBAgQIECAQNoEUlMA2GOPPcKIESPC/Pnzw4MPPrhOnm6++eawePHisO2224bdd999nXk+ECBAgAABAgQIECBAgAABAgQIECBAgACBNAqk5iXA8UUIJ554Ypg8eXKYMmVKePLJJ8OoUaPCyy+/nIz36NEjnHHGGaGQFyak8QAQEwECBAgQIECAAAECBAgQIECAAAECBAikUyA1TwDE9EycODFcccUVYciQIWHGjBnhD3/4Q3LxPz4ZcPnll4dddtklnVkUFQECBAgQIECAAAECBAgQIECAAAECBAgQWE8gNU8A5OL60pe+FKZPn550+bNgwYIQXw4cCwK1tamqdeTC9ZsAAQIECBAgQIAAAQIECBAgQIAAAQIECHQokLoCQC7KLbfcMsQfAwECBAgQIECAAAECBAgQIECAAAECBAgQyKKA2+KzmHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBRQAUp9iARIgQIAAAQIECBAgQIAAAQIECBAgQIBAFgUUALKYdTETIECAAAECBAgQIECAAAECBAgQIECAQOoFFABSn2IBEiBAgAABAgQIECBAgAABAgQIECBAgEAWBRQAsph1MRMgQIAAAQIECBAgQIAAAQIECBAgQIBA6gUUAFKfYgESIECAAAECBAgQIECAAAECBAgQIECAQBYFFACymHUxEyBAgAABAgQIECBAgAABAgQIECBAgEDqBepTH6EACRAgQIAAAQIECBAgQIAAAQIECBAg0IVA/56DQs3a/xrqenaxlFkEqk9AAaD6cqbFBAgQIECAAAECBAgQIECAAAECBAgUUeD0fW4OLS0toaampohbtSkC5RfQBVD5c6AFBAgQIECAAAECBAgQIECAAAECBAgQIECg6AIKAEUntUECBAgQIECAAAECBAgQIECAAAECBAgQIFB+AQWA8udACwgQIECAAAECBAgQIECAAAECBAgQIECAQNEFFACKTmqDBAgQIECAAAECBAgQIECAAAECBAgQIECg/AIKAOXPgRYQIECAAAECBAgQIECAAAECBAgQIECAAIGiCygAFJ3UBgkQIECAAAECBAgQIECAAAECBAgQIECAQPkFFADKnwMtIECAAAECBAgQIECAAAECBAgQIECAAAECRRdQACg6qQ0SIECAAAECBAgQIECAAAECBAgQIECAAIHyCygAlD8HWkCAAAECBAgQIECAAAECBAgQIECAAAECBIouoABQdFIbJECAAAECBAgQIECAAAECBAgQIECAAAEC5RdQACh/DrSAAAECBAgQIECAAAECBAgQIECAAAECBAgUXUABoOikNkiAAAECBAgQIECAAAECBAgQIECAAAECBMovoABQ/hxoAQECBAgQIECAAAECBAgQIECAAAECBAgQKLqAAkDRSW2QAAECBAgQIECAAAECBAgQIECAAAECBAiUX0ABoPw50AICBAgQIECAAAECBAgQIECAAAECBAgQIFB0AQWAopPaIAECBAgQIECAAAECBAgQIECAAAECBAgQKL+AAkD5c6AFBAgQIECAAAECBAgQIECAAAECBAgQIECg6AIKAEUntUECBAgQIECAAAECBAgQIECAAAECBAgQIFB+AQWA8udACwgQIECAAAECBAgQIECAAAECBAgQIECAQNEFFACKTmqDBAgQIECAAAECBAgQIECAAAECBAgQIECg/AIKAOXPgRYQIECAAAECBAgQIECAAAECBAgQIECAAIGiCygAFJ3UBgkQIECAAAECBAgQIECAAAECBAgQIECAQPkFFADKnwMtIECAAAECBAgQIECAAAECBAgQIECAAAECRRdQACg6qQ0SIECAAAECBAgQIECAAAECBAgQIECAAIHyCygAlD8HWkCAAAECBAgQIECAAAECBAgQIECAAAECBIouoABQdFIbJECAAAECBAgQIECAAAECBAgQIECAAAEC5RdQACh/DrSAAAECBAgQIECAAAECBAgQIECAAAECBAgUXUABoOikNkiAAAECBAgQIECAAAECBAgQIECAAAECBMovoABQ/hxoAQECBAgQIECAAAECBAgQIECAAAECBAgQKLqAAkDRSW2QAAECBAgQIECAAAECBAgQIECAAAECBAiUX0ABoPw50AICBAgQIECAAAECBAgQIECAAAECBAgQIFB0AQWAopPaIAECBAgQIECAAAECBAgQIECAAAECBAgQKL+AAkD5c6AFBAgQIECAAAECBAgQIECAAAECBAgQIECg6AIKAEUntUECBAgQIECAAAECBAgQIECAAAECBAgQIFB+gfryN6F6WtDa2hpaWlrCqlWrqqfRWppqgTWr1+Tja1l7fDo28xxGCBDopsDqNavza8Z/95xX8hxGCBDopkBjU1N+zda1Y84reQ4jBAgURcD3laIw2ggBAiH+/RMHfwc5GCpJoLGxMWlO7vjsTtsUADZCLV78X716dViyZMlGrGVRAptO4JNVn+Q33tzc7NjMaxghQKC7AqtXrMivGr9g+Dcvz2GEAIFuCqxc0aYA4LzSTUWrESDQlYDvK13pmEeAQHcEnFe6o2adTSGgALApVLvYZl1dXaitrQ2DBw/uYimzCJROoPfyD/I7q6+vc2zmNYwQINBdgRVrzyuL/7eyf/O6q2g9AgTaCnzU8HH+Y21Nje8reQ0jBAgUIvBefmXnlTyFEQIEChL48MMPk54/4kZc+yuI0spFFMgVAGrWfo/u7uAJgI2Ui9ixEGAgUAkC8eJcbqgJjs2chd8ECHRfoLbm0/NK3Ip/87pvaU0CBP4r0Pb7SpzivOLIIECg2ALOK8UWtT0C2RZw7S/b+a+06HP/xhVSAFj3r/xKi1B7CBAgQIAAAQIECBAgQIAAAQIECBAgQIAAgW4JKAB0i81KBAgQIECAAAECBAgQIECAAAECBAgQIECgsgUUACo7P1pHgAABAgQIECBAgAABAgQIECBAgAABAgS6JaAA0C02KxEgQIAAAQIECBAgQIAAAQIECBAgQIAAgcoWUACo7PxoHQECBAgQIECAAAECBAgQIECAAAECBAgQ6JaAAkC32KxEgAABAgQIECBAgAABAgQIECBAgAABAgQqW0ABoLLzo3UECBAgQIAAAQIECBAgQIAAAQIECBAgQKBbAgoA3WKzEgECBAgQIECAAAECBAgQIECAAAECBAgQqGwBBYDKzo/WESBAgAABAgQIECBAgAABAgQIECBAgACBbgnUd2stKxEgUBECQ/sMDP83ao+kLbsNGVkRbdIIAgQIECBAgAABAgQIECBAgAABAgQqQ0ABoDLyoBUEuiUwcsDnws93PSxZt1evXt3ahpUIECBAgAABAgQIECBAgAABAgQIEEingC6A0plXUREgQIAAAQIECBAgQIAAAQIECBAgQIBAxgUUADJ+AAifAAECBAgQIECAAAECBAgQIECAAAECBNIpoACQzryKigABAgQIECBAgAABAgQIECBAgAABAgQyLqAAkPEDQPgECBAgQIAAAQIECBAgQIAAAQIECBAgkE4BBYB05lVUBAgQIECAAAECBAgQIECAAAECBAgQIJBxAQWAjB8AwidAgAABAgQIECBAgAABAgQIECBAgACBdAooAKQzr6IiQIAAAQIECBAgQIAAAQIECBAgQIAAgYwLKABk/AAQPgECBAgQIECAAAECBAgQIECAAAECBAikU0ABIJ15FRUBAgQIECBAgAABAgQIECBAgAABAgQIZFxAASDjB4DwCRAgQIAAAQIECBAgQIAAAQIECBAgQCCdAgoA6cyrqAgQIECAAAECBAgQIECAAAECBAgQIEAg4wIKABk/AIRPgAABAgQIECBAgAABAgQIECBAgAABAukUUABIZ15FRYAAAQIECBAgQIAAAQIECBAgQIAAAQIZF1AAyPgBIHwCBAgQIECAAAECBAgQIECAAAECBAgQSKeAAkA68yoqAgQIECBAgAABAgQIECBAgAABAgQIEMi4gAJAxg8A4RMgQIAAAQIECBAgQIAAAQIECBAgQIBAOgUUANKZV1ERIECAAAECBAgQIECAAAECBAgQIECAQMYFFAAyfgAInwABAgQIECBAgAABAgQIECBAgAABAgTSKaAAkM68iooAAQIECBAgQIAAAQIECBAgQIAAAQIEMi6gAJDxA0D4BAgQIECAAAECBAgQIECAAAECBAgQIJBOAQWAdOZVVAQIECBAgAABAgQIECBAgAABAgQIECCQcQEFgIwfAMInQIAAAQIECBAgQIAAAQIECBAgQIAAgXQKKACkM6+iIkCAAAECBAgQIECAAAECBAgQIECAAIGMCygAZPwAED4BAgQIECBAgAABAgQIECBAgAABAgQIpFNAASCdeRUVAQIECBAgQIAAAQIECBAgQIAAAQIECGRcQAEg4weA8AkQIECAAAECBAgQIECAAAECBAgQIEAgnQIKAOnMq6gIECBAgAABAgQIECBAgAABAgQIECBAIOMCCgAZPwCET4AAAQIECBAgQIAAAQIECBAgQIAAAQLpFFAASGdeRUWAAAECBAgQIECAAAECBAgQIECAAAECGRdQAMj4ASB8AgQIECBAgAABAgQIECBAgAABAgQIEEingAJAOvMqKgIECBAgQIAAAQIECBAgQIAAAQIECBDIuIACQMYPAOETIECAAAECBAgQIECAAAECBAgQIECAQDoFFADSmVdRESBAgAABAgQIECBAgAABAgQIECBAgEDGBRQAMn4ACJ8AAQIECBAgQIAAAQIECBAgQIAAAQIE0imgAJDOvIqKAAECBAgQIECAAAECBAgQIECAAAECBDIuUJ/x+IVPgAABAgQIECBAgAABAgQIVJnAZi+duLbFraGuh8saVZY6zSVAgACBEgv4l7LE4HZHgAABAgQIECBAgAABAgQIFCZQs+XmyQZq6uoK25C1CRAgQIBAygV0AZTyBAuPAAECBAgQIECAAAECBAgQIECAAAECBLIpoACQzbyLmgABAgQIECBAgAABAgQIECBAgAABAgRSLqAAkPIEC48AAQIECBAgQIAAAQIECBAgQIAAAQIEsimgAJDNvIuaAAECBAgQIECAAAECBAgQIECAAAECBFIuoACQ8gQLjwABAgQIECBAgAABAgQIECBAgAABAgSyKaAAkM28i5oAAQIECBAgQIAAAQIECBAgQIAAAQIEUi6gAJDyBAuPAAECBAgQIECAAAECBAgQIECAAAECBLIpoACQzbyLmgABAgQIECBAgAABAgQIECBAgAABAgRSLqAAkPIEC48AAQIECBAgQIAAAQIECBAgQIAAAQIEsimgAJDNvIuaAAECBAgQIECAAAECBAgQIECAAAECBFIuoACQ8gQLjwABAgQIECBAgAABAgQIECBAgAABAgSyKaAAkM28i5oAAQIECBAgQIAAAQIECBAgQIAAAQIEUi6gAJDyBAuPAAECBAgQIECAAAECBAgQIECAAAECBLIpoACQzbyLmgABAgQIECBAgAABAgQIECBAgAABAgRSLqAAkPIEC48AAQIECBAgQIAAAQIECBAgQIAAAQIEsimgAJDNvIuaAAECBAgQIECAAAECBAgQIECAAAECBFIuoACQ8gQLjwABAgQIECBAgAABAgQIECBAgAABAgSyKaAAkM28i5oAAQIECBAgQIAAAQIECBAgQIAAAQIEUi6gAJDyBAuPAAECBAgQIECAAAECBAgQIECAAAECBLIpoACQzbyLmgABAgQIECBAgAABAgQIECBAgAABAgRSLqAAkPIEC48AAQIECBAgQIAAAQIECBAgQIAAAQIEsimgAJDNvIuaAAECBAgQIECAAAECBAgQIECAAAECBFIuUJ/y+IRHgAABAgQIbIRA/cAhoe+3z0vW2HybHTZiTYsSIECAAAECBAgQIECAAAEClSagAFBpGdEeAgQIECBQRoH6fluG3gf8IGlBz549y9gSuyZAgAABAgQIECBAgAABAgQKFdAFUKGC1idAgAABAgQIECBAgAABAgQIECBAgAABAhUooABQgUnRJAIECBAgQIAAAQIECBAgQIAAAQIECBAgUKiAAkChgtYnQIAAAQIECBAgQIAAAQIECBAgQIAAAQIVKKAAUIFJ0SQCBAgQIECAAAECBAgQIECAAAECBAgQIFCogAJAoYLWJ0CAAAECBAgQIECAAAECBAgQIECAAAECFSigAFCBSdEkAgQIECBAgAABAgQIECBAgAABAgQIECBQqIACQKGC1idAgAABAgQIECBAgAABAgQIECBAgAABAhUooABQgUnRJAIECBAgQIAAAQIECBAgQIAAAQIECBAgUKiAAkChgtYnQIAAAQIECBAgQIAAAQIECBAgQIAAAQIVKKAAUIFJ0SQCBAgQIECAAAECBAgQIECAAAECBAgQIFCoQH2hG7A+AQIECBAgQIAAAQIEOhPo0VAXvrzH1snswUP6dLaY6QQIECBAgAABAgQIbAIBBYBNgGqTBAgQIECAAAECBAj8V6Bnzx7h698YnXzo0aMHFgIECBAgQIAAAQIESiigC6ASYtsVAQIECBAgQIAAAQIECBAgQIAAAQIECBAolYACQKmk7YcAAQIECBAgQIAAAQIECBAgQIAAAQIECJRQQAGghNh2RYAAAQIECBAgQIAAAQIECBAgQIAAAQIESiWgAFAqafshQIAAAQIECBAgQIAAAQIECBAgQIAAAQIlFFAAKCG2XREgQIAAAQIECBAgQIAAAQIECBAgQIAAgVIJKACUStp+CBAgQIAAAQIECBAgQIAAAQIECBAgQIBACQUUAEqIbVcECBAgQIAAAQIECBAgQIAAAQIECBAgQKBUAgoApZK2HwIECBAgQIAAAQIECBAgQIAAAQIECBAgUEIBBYASYtsVAQIECBAgQIAAAQIECBAgQIAAAQIECBAolYACQKmk7YcAAQIECBAgQIAAAQIECBAgQIAAAQIECJRQQAGghNh2RYAAAQIECBAgQIAAAQIECBAgQIAAAQIESiWgAFAqafshQIAAAQIECBAgQIAAAQIECBAgQIAAAQIlFFAAKCG2XREgQIAAAQIECBAgQIAAAQIECBAgQIAAgVIJKACUStp+CBAgQIAAAQIECBAgQIAAAQIECBAgQIBACQUUAEqIbVcECBAgQIAAAQIECBAgQIAAAQIECBAgQKBUAgoApZK2HwIECBAgQIAAAQIECBAgQIAAAQIECBAgUEIBBYASYtsVAQIECBAgQIAAAQIECBAgQIAAAQIECBAolYACQKmk7YcAAQIECBAgQIAAAQIECBAgQIAAAQIECJRQQAGghNh2RYAAAQIECBAgQIAAAQIECBAgQIAAAQIESiWgAFAqafshQIAAAQIECBAgQIAAAQIECBAgQIAAAQIlFFAAKCG2XREgQIAAAQIECBAgQIAAAQIECBAgQIAAgVIJKACUStp+CBAgQIAAAQIECBAgQIAAAQIECBAgQIBACQUUAEqIbVcECBAgQIAAAQIECBAgQIAAAQIECBAgQKBUAgoApZK2HwIECBAgQIAAAQIECBAgQIAAAQIECBAgUEIBBYASYtsVAQIECBAgQIAAAQIECBAgQIAAAQIECBAolYACQKmk7YcAAQIECBAgQIAAAQIECBAgQIAAAQIECJRQQAGghNh2RYAAAQIECBAgQIAAAQIECBAgQIAAAQIESiVQX6odpWU/H3zwQbj99tvTEo44qlxg9erVYeXKlUkUDQ0NoVevXlUekeYTIFBugebm5rB8+fKkGT169Ai9e/cud5PsnwCBKhdoaWkJy5YtS6Koq6sLffv2rfKINJ8AgUoQWLp0adKM2tra0K9fv0pokjYQIFDlAvH7SvzeUlNTE/r371/l0Wh+WgSampoKDkUBYCMJ58+fH84999yNXMviBAgQIECAAAECBAgQIECAAAECBAgQIECgtAI1rWuH0u6yevcW74qMlUADgUoRePLJJ8OPf/zjpDnf+c53whlnnFEpTdMOAgSqVODNN98MRx99dNL6gw46KFx22WVVGolmEyBQKQJLliwJ++23X9KcXXfdNVx//fWV0jTtIECgigXGjx8f4t/ow4cPD/fcc08VR6LpBAhUisCkSZPCokWLkt4VnnjiiUpplnYQSATq6+uTp1O6w+EJgI1Qi48sxx8DgUoRiI+7rlmzJmlOrOXF7joMBAgQKETAeaUQPesSINCRQPxjJfd9JV6s832lIyXTCBDYWIHYHWq8QS+eX5xXNlbP8gQIdCQQzyvxnBJ/O690JGRatQp4CXC1Zk67CRAgQIAAAQIECBAgQIAAAQIECBAgQIBAFwIKAF3gmEWAAAECBAgQIECAAAECBAgQIECAAAECBKpVQAGgWjOn3QQIECBAgAABAgQIECBAgAABAgQIECBAoAsBBYAucMwiQIAAAQIECBAgQIAAAQIECBAgQIAAAQLVKqAAUK2Z024CBAgQIECAAAECBAgQIECAAAECBAgQINCFQE3r2qGL+WYRIFDBAh9++GF49tlnkxaOGDEijB49uoJbq2kECFSDwIoVK8Ls2bOTpg4ZMiSMGzeuGpqtjQQIVLBAU1NTePTRR5MWDhw4MEyYMKGCW6tpBAhUi8Bf//rXEC9n9OrVK0ycOLFamq2dBAhUsMDMmTPDqlWrQl1dXTjooIMquKWaRmDjBBQANs7L0gQIECBAgAABAgQIECBAgAABAgQIECBAoCoEdAFUFWnSSAIECBAgQIAAAQIECBAgQIAAAQIECBAgsHECCgAb52VpAgQIECBAgAABAgQIECBAgAABAgQIECBQFQIKAFWRJo0kQIAAAQIECBAgQIAAAQIECBAgQIAAAQIbJ6AAsHFeliZAgAABAgQIECBAgAABAgQIECBAgAABAlUhUF8VrdRIAgS6FLj//vvDDTfcEM4///wwZsyYLpc1kwABAp0JzJgxIzz++ONh4cKFoaWlJQwfPjzsueee4aCDDupsFdMJECDQpcAjjzwSZs6cmZxXPv/5z4exY8eG/fbbL8RxAwECBAoVaG1tDRdccEFYsGBBuPjii8PnPve5QjdpfQIEMibw8ccfh+uuu67LqA8//PDwhS98octlzCRQyQIKAJWcHW0jsAECL7/8crj88svDmjVrQmNj4wasYRECBAisKxDPHb/4xS/CCy+8kMzo169f8nvevHnh4YcfDvfcc0+49NJLw+abb77uij4RIECgE4H4veSss84KTz31VLJE3759w9tvvx1mz54dbrnlluScstNOO3WytskECBDYMIHbbrstxEJjHJqamjZsJUsRIECgjcCbb74Z7rjjjjZT2o+OGzdOAaA9iylVJKAAUEXJ0lQC6wvEi3XnnXdecvF//Xk+EyBAYEMFfv/73ycX/0eMGBHOOeecsOOOOyarvv7668lddS+++GK48sorwxlnnLGhm7QcAQIZF7j22muTi/9bb711+MlPfhL22muvsGTJknDXXXeFG2+8MZx22mlh2rRpYcstt8y4lPAJEOiuQLxoF881BgIECBQiMH/+/GT18ePHh/3337/DTY0aNarD6SYSqBYBBYBqyZR2EmgjEB9Ru+qqq8Ldd9+dTK2trU2662iziFECBAhskEA8n8Q7/ON5JD5Cv9122+XXGz16dPI4/fe///1w3333hZNPPjn06tUrP98IAQIEOhKId+HmvqMce+yxYeLEicligwYNCj/84Q+TLoFidx3x6YDDDjuso02YRoAAgS4F4tOL8XtLfX198h3G3f9dcplJgEAXArkCQLz4/7Wvfa2LJc0iUL0CXgJcvbnT8gwLnHDCCckf1vFC3OTJk9e5YJdhFqETINANgdiNWHNzcxg2bFiH55JYEIgX7WIfu7H7DgMBAgQ+SyDe6R8v+sc76Q488MB2i+cKAq+99lq7eSYQIEBgQwSuueaa8M4774RTTjnFzQkbAmYZAgQ6FYhPE8Uh9xR0pwuaQaCKBTwBUMXJ0/TsCixdujRMmjQpHH/88clL9G6++ebsYoicAIGCBCZMmJA8AbBq1aoOtxP78f7oo4+SeVtssUWHy5hIgACBtgLxJZyxO7HOhtwf2jvvvHNni5hOgACBTgWeeeaZpL/uPffcM7lb97Ne3tnphswgQCDzAvFvnXiTU3yaaOTIkYnHsmXLwmabbZb8ZB4IQGoEFABSk0qBZEngz3/+c4h/XBsIECBQqEBNTU0YMGBAp5t56KGHkpfq9e/fPwwdOrTT5cwgQIDAZwksXLgw3HvvzzHeJgAAEZNJREFUvUnXP0OGDEneC/BZ65hPgACBtgLxpoSLL744xO8l8UXjBgIECBQi8O6774bVq1eH4cOHh1tuuSV5V9HixYuTrsXitO9973vh4IMPLmQX1iVQEQIKABWRBo0gsHECLv5vnJelCRDonsD7778frr766mTl2G93LBYYCBAgsLEC8+bNC+eff36IBYA4jB07NkyZMiX069dvYzdleQIEMi5w2WWXhXhxLhYBBg4cmHEN4RMgUKhArv//9957L/zxj38MW221VdKF4T//+c8Qfy688MLw/PPPKzgWCm39sgt4B0DZU6ABBAgQIECg8gTiH9c/+9nPQuxyLHYT5IVYlZcjLSJQLQJvvfVW+OSTT/IX6+Lddn//+9+Td4tUSwzaSYBA+QXuv//+MGvWrHDooYfmXy5e/lZpAQEC1SyQ65awb9++4corr0yeAPjNb36T/P7pT3+a3AAVzz0zZ86s5jC1nUDwBICDgAABAgQIEFhHIN4Bc/rpp4cPPvgg7LTTTuGCCy5YZ74PBAgQ2BiBeLHusMMOS1Z54403knPKJZdckhQB4pMABgIECHyWQHwq8be//W2I3Yeddtppn7W4+QQIENgggR/84AfhgAMOSLoV23rrrfPrxCefjzrqqOQpgLvuuivcdNNNYd99983PN0Kg2gQ8AVBtGdNeAgQIECCwCQXmzJkTfvSjHyUX/3fbbbcwderU0Lt37024R5smQCDtAm27D9thhx2Srjvq6urC448/HubOnZv28MVHgECBAs3NzUnhcNWqVeHss8/2vaRAT6sTIPCpQLzzf8yYMaHtxf9P54Zw4IEHJh/feeed0NLS0naWcQJVJeAJgKpKl8YSIECAAIFNJ/Doo4+Giy66KHkR1qRJk5K+LuvrfVXYdOK2TCCbAttuu20YOXJkiP3uxicCdt5552xCiJoAgQ0SiF10xGJhbW1tOPfcc9utE7srjEO8gSEuE38ffvjh7ZYzgQABAhsrkHv/YlNTU1i5cmWIBQMDgWoU8Fd9NWZNmwkQIECAQJEF7r333nDppZcmWz322GPDcccdV+Q92BwBAlkRiBfqHnnkkRD/aP7Wt77VYdg9evRIpisydshjIgEC6wnEp4bisHz58vXmfPoxXpyLw+rVqz+daIwAAQJdCEyfPj15sfghhxwSRowY0W7JRYsWJdP69evn4n87HROqSUABoJqypa0ECBAgQGATCPzjH/8Il112WfKSqzPPPNNdc5vA2CYJZEkgdtNxxx13JP3pHn300WH9i/wfffRRiC8GjkPsEshAgACBrgR23HHHLl/AecQRR4T4FMCNN94Yhg0b1tWmzCNAgMA6AvGGhVdffTXEC/3nnXfeOvPih9mzZyfTPK3YjsaEKhPwDoAqS5jmEiBAgACBYgo0NjaGK664IrS2toYTTjjBxf9i4toWgYwKjB07NgwaNCjEC/3XXHPNOn3mxnPOr3/96xB/x+VGjRqVUSVhEyBAgAABAuUW2G+//ZImxK5Qczcn5Nr03HPPhfiEQByOP/743GS/CVSlgCcAqjJtGk2AAAECBIojEO/Sff/995ONXX/99SH+dDbE9wPsvffenc02nQABAolAQ0ND+OUvfxlOOeWUcNtttyXdAR188MFJ39yzZs0KCxcuTJ4OiH15x/66DQQIECBAgACBcgh84xvfCE888UR44YUXwjHHHBPGjx+f/MR3j8yYMSNp0kknnRTik0gGAtUsoABQzdnTdgIECBAgUKDASy+9lN9Cc3NzfryjkZaWlo4mm0aAAIF2AvHu/muvvTZMnTo1ebT+1ltvTZaJ/XjHYsDJJ58cBgwY0G49EwgQIECAAAECpRKI30vie9BuvvnmcMstt4R413/8iUPsUuzUU08Ne+yxR6maYz8ENplAzdpH/ls32dZtmAABAgQIECBAgACBTAssWbIkvPfee6F3795h+PDhIT4hYCBAgAABAgQIVJLAmjVrkiej4ztFRo4cGfr06VNJzdMWAgUJKAAUxGdlAgQIECBAgAABAgQIECBAgAABAgQIECBQmQI63azMvGgVAQIECBAgQIAAAQIECBAgQIAAAQIECBAoSEABoCA+KxMgQIAAAQIECBAgQIAAAQIECBAgQIAAgcoUUACozLxoFQECBAgQIECAAAECBAgQIECAAAECBAgQKEhAAaAgPisTIECAAAECBAgQIECAAAECBAgQIECAAIHKFFAAqMy8aBUBAgQIECBAgAABAgQIECBAgAABAgQIEChIQAGgID4rEyBAgAABAgQIECBAgAABAgQIECBAgACByhRQAKjMvGgVAQIECBAgQIAAAQIECBAgQIAAAQIECBAoSEABoCA+KxMgQIAAAQIECBAgQIAAAQIECBAgQIAAgcoUUACozLxoFQECBAgQIECAAAECBAgQIECAAAECBAgQKEhAAaAgPisTIECAAAECBAgQIECAAAECBAgQIECAAIHKFFAAqMy8aBUBAgQIECBAgAABAgQIECBAgAABAgQIEChIQAGgID4rEyBAgAABAgQIEEiHwIoVK8KcOXPaBXP66aeHmpqa5KepqandfBMIECBAgAABAgQIEKhcAQWAys2NlhEgQIAAAQIECBAoicDtt98eRo8eHR544IF2+2ttbW03zQQCBAgQIECAAAECBKpDoL46mqmVBAgQIECAAAECBAhsCoFFixaFb37zm51uukePHqFnz56dzjeDAAECBAgQIECAAIHKFfAEQOXmRssIECBAgAABAgQIlF3gkksuCZ988kny09DQUPb2aAABAgQIECBAgAABAhsuoACw4VaWJECAAAECBAgQIECAAAECBAgQIECAAAECVSOgC6CqSZWGEiBAgAABAgQIECiuwDPPPBMWL16c3+jChQvD008/nXweP358qKurCwsWLAgffPBBMu3LX/5y8jLg+KG5uTk899xzyfSddtop9OnTJ6xZsyY8//zzYdasWWHgwIFh3333Ddtvv32yTO5/ufVmzpyZbH/MmDHh4IMPDvX1Xf9pEt9FMH/+/PDSSy+FuXPnhq233jqMGzcujB07Nmy++ea5zftNgAABAgQIECBAgEAbgZq1X6S91asNiFECBAgQIECAAAECWRGI/fvHi/YdDUuXLg39+/cPP//5z8PUqVOTRRobG0OuG6A4f8CAAcn0xx57LKxYsSJ8+9vfDh999NE6m4sX6eP8vn37htmzZ4cjjzwy/Oc//2m3zK233pq8iHidGf/78Oabb4bvfve74amnnmo3e/DgweFPf/pT+OpXv9pungkECBAgQIAAAQIEsi6gC6CsHwHiJ0CAAAECBAgQyKxAvMv/i1/8Yj7+oUOHht122y35iXf/b+gwffr05MJ+vPgf78w/4IADwqBBg5LVX3zxxXDssceGv/3tb+GQQw4Jy5YtS+7anzhxYthss83yyxxzzDGho3uT7rzzzuRO/3jxv6amJkyYMCHZ3oEHHhj69esX/v3vf4cjjjginHnmmRvaXMsRIECAAAECBAgQyIyAJwAyk2qBEiBAgAABAgQIEGgvsGjRojBkyJBkxq9+9atw1llnrbPQhjwBEFeITwM88MADYY899kjWj08ExLvyY3dAcaitrQ2xu594p3/sticOy5cvT7oJit0GxSF2C7TPPvsk4/F/S5YsCaNGjUq6KRo2bFi48cYb15kfuy+KTx08/PDDyTrxCYOvfOUr+fWNECBAgAABAgQIEMi6gCcAsn4EiJ8AAQIECBAgQIBAgQLx4n68sJ+7+B83F98JMHny5HW2fNNNN+Uv/scZsVugq666Kr/MvHnz8uNxJK4fL/LH7U+bNm2di/9x/pZbbpkUHXbcccf4MZx66qmhpaUlGfc/AgQIECBAgAABAgTW3ogDgQABAgQIECBAgAABAoUI7LrrrmHSpEntNrHzzjvnp8XiQHwfwPpD7uJ9nP7uu+/mZ8eXBV933XXJ50MPPTTstdde+XltR+LLg+OF/zjEJwleeeWVtrONEyBAgAABAgQIEMi0QH2moxc8AQIECBAgQIAAAQIFC3R0YT9udIsttshve/vtt8+Ptx3p3bt3/mNTU1N+/L333gvxpcNxiO8piN0BdTbssMMO+Vnz588Pu+yyS/6zEQIECBAgQIAAAQJZFlAAyHL2xU6AAAECBAgQIECgCAJtL/R3trnBgwd3OCu+2Lej4Y033shPnjJlSog/GzLEAoCBAAECBAgQIECAAIH/CugCyJFAgAABAgQIECBAgEBBAj179ixo/Y5WXrhwYUeTP3PaggULPnMZCxAgQIAAAQIECBDIioAnALKSaXESIECAAAECBAgQ2EQCnd3FX8juttlmm/zqN9xwQ/j617+e/9zVSENDQ1ezzSNAgAABAgQIECCQKQEFgEylW7AECBAgQIAAAQIEqkNg1KhR+YbOmzcv9O3bN//ZCAECBAgQIECAAAECGyagC6ANc7IUAQIECBAgQIAAgVQKtL17v7W1tWJiHDFiRMh1LXT//feHlpaWTts2ffr05EXBRx55ZJg9e3any5lBgAABAgQIECBAIGsCCgBZy7h4CRAgQIAAAQIECLQRyF1kj5MWL17cZk55R2tra8Npp52WNOLFF18MV199dYcNWrFiRZg8eXKYM2dOeOihh8Lo0aM7XM5EAgQIECBAgAABAlkUUADIYtbFTIAAAQIECBAgQOB/Ar179w49evRIPt15553hvvvuCzNmzAhNTU1lNzrnnHPC0KFDk3bEYsDZZ58dVq5cmXxubGwMDz74YDjssMPC66+/nkw76aSTwlZbbVX2dmsAAQIECBAgQIAAgUoRUAColExoBwECBAgQIECAAIEyCNTV1YWJEycme37nnXfCEUccEfbff/8wd+7cMrRm3V326dMnTJs2LQwbNiw0NzeHKVOmhH79+iV3+ccL/fHi/+OPP56sdNRRR4VLL7103Q34RIAAAQIECBAgQCDjAgoAGT8AhE+AAAECBAgQIEDg1ltvDfvss09oaGjIY7z22mv58XKO7L333uGVV14JJ554YnLxP74LIL4UOHb9E4ftttsuXHfddeG2224LsZhhIECAAAECBAgQIEDgU4GatS/6qpw3fX3aLmMECBAgQIAAAQIECJRYIHb789Zbb4VBgwZVbFc6CxYsSJ5OiO8uGDlyZNhmm21CfF+AgQABAgQIECBAgACB9gIKAO1NTCFAgAABAgQIECBAgAABAgQIECBAgAABAlUv4FaZqk+hAAgQIECAAAECBAgQIECAAAECBAgQIECAQHsBBYD2JqYQIECAAAECBAgQIECAAAECBAgQIECAAIGqF1AAqPoUCoAAAQIECBAgQIAAAQIECBAgQIAAAQIECLQXUABob2IKAQIECBAgQIAAAQIECBAgQIAAAQIECBCoegEFgKpPoQAIECBAgAABAgQIECBAgAABAgQIECBAgEB7AQWA9iamECBAgAABAgQIECBAgAABAgQIECBAgACBqhdQAKj6FAqAAAECBAgQIECAAAECBAgQIECAAAECBAi0F1AAaG9iCgECBAgQIECAAAECBAgQIECAAAECBAgQqHoBBYCqT6EACBAgQIAAAQIECBAgQIAAAQIECBAgQIBAewEFgPYmphAgQIAAAQIECBAgQIAAAQIECBAgQIAAgaoXUACo+hQKgAABAgQIECBAgAABAgQIECBAgAABAgQItBdQAGhvYgoBAgQIECBAgAABAgQIECBAgAABAgQIEKh6AQWAqk+hAAgQIECAAAECBAgQIECAAAECBAgQIECAQHsBBYD2JqYQIECAAAECBAgQIECAAAECBAgQIECAAIGqF1AAqPoUCoAAAQIECBAgQIAAAQIECBAgQIAAAQIECLQXUABob2IKAQIECBAgQIAAAQIECBAgQIAAAQIECBCoegEFgKpPoQAIECBAgAABAgQIECBAgAABAgQIECBAgEB7AQWA9iamECBAgAABAgQIECBAgAABAgQIECBAgACBqhf4f9iIa1KFdvboAAAAAElFTkSuQmCC)
The function contr_code_poly()
uses
contr.poly()
to set up the polynomial contrasts for the
linear (^1
), quadratic (^2
), cubic
(^3
), and quartic (^4
) components.
df$time <- contr_code_poly(df$time)
Contrasts
|
lm(y ~ pet, df)
|
^1
|
^2
|
^3
|
^4
|
-0.632
|
0.535
|
-0.316
|
0.120
|
-0.316
|
-0.267
|
0.632
|
-0.478
|
0.000
|
-0.535
|
0.000
|
0.717
|
0.316
|
-0.267
|
-0.632
|
-0.478
|
0.632
|
0.535
|
0.316
|
0.120
|
|
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
2.031
|
0.223
|
9.110
|
0.000
|
time^1
|
0.239
|
0.498
|
0.480
|
0.631
|
time^2
|
1.946
|
0.498
|
3.905
|
0.000
|
time^3
|
-0.198
|
0.498
|
-0.397
|
0.692
|
time^4
|
-0.004
|
0.498
|
-0.009
|
0.993
|
|
Add Contrasts
The function add_contrasts()
lets you add contrasts to a
column in a data frame and also adds new columns for each contrast
(unless add_cols = FALSE
). This is especially helpful if
you want to test only a subset of the contrasts.
df <- sim_design(list(time = 1:5),
mu = 1:5 * 0.25 + (1:5 - 3)^2 * 0.5,
sd = 5, long = TRUE, plot = FALSE) %>%
add_contrast("time", "poly")
# test only the linear and quadratic contrasts
lm(y ~ `time^1` + `time^2`, df) %>% broom::tidy()
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
1.69
|
0.239
|
7.09
|
0.000
|
time^1
|
0.78
|
0.534
|
1.46
|
0.145
|
time^2
|
2.06
|
0.534
|
3.85
|
0.000
|
You can set colnames
to change the default column names
for the contrasts. This can be useful if you want to add different
codings for the same factor or if the default names are too long.
btwn <- list(condition = c("control", "experimental"))
df <- sim_design(between = btwn, n = 1, plot = FALSE) %>%
add_contrast("condition", "treatment", colnames = "cond.tr") %>%
add_contrast("condition", "anova", colnames = "cond.aov") %>%
add_contrast("condition", "difference", colnames = "cond.dif") %>%
add_contrast("condition", "sum", colnames = "cond.sum") %>%
add_contrast("condition", "helmert", colnames = "cond.hmt") %>%
add_contrast("condition", "poly", colnames = "cond.poly")
id
|
condition
|
y
|
cond.tr
|
cond.aov
|
cond.dif
|
cond.sum
|
cond.hmt
|
cond.poly
|
S1
|
control
|
0.697
|
0
|
-0.5
|
-0.5
|
1
|
-0.5
|
-0.707
|
S2
|
experimental
|
0.512
|
1
|
0.5
|
0.5
|
-1
|
0.5
|
0.707
|
However, if a new column has a duplicate name to an existing column,
add_contrast()
will automatically add a contrast suffix to
the new column.
btwn <- list(pet = c("cat", "dog", "ferret"))
df <- sim_design(between = btwn, n = 1, plot = FALSE) %>%
add_contrast("pet", "treatment") %>%
add_contrast("pet", "anova") %>%
add_contrast("pet", "sum") %>%
add_contrast("pet", "difference") %>%
add_contrast("pet", "helmert") %>%
add_contrast("pet", "poly")
id
|
pet
|
y
|
pet.dog-cat
|
pet.ferret-cat
|
pet.dog-cat.aov
|
pet.ferret-cat.aov
|
pet.cat-intercept
|
pet.dog-intercept
|
pet.dog-cat.dif
|
pet.ferret-dog
|
pet.dog-cat.hmt
|
pet.ferret-cat.dog
|
pet^1
|
pet^2
|
S1
|
cat
|
-0.72
|
0
|
0
|
-0.33
|
-0.33
|
1
|
0
|
-0.67
|
-0.33
|
-0.5
|
-0.33
|
-0.71
|
0.41
|
S2
|
dog
|
-0.36
|
1
|
0
|
0.67
|
-0.33
|
0
|
1
|
0.33
|
-0.33
|
0.5
|
-0.33
|
0.00
|
-0.82
|
S3
|
ferret
|
-1.43
|
0
|
1
|
-0.33
|
0.67
|
-1
|
-1
|
0.33
|
0.67
|
0.0
|
0.67
|
0.71
|
0.41
|
Examples
2x2 Design
Let’s use simulated data with empirical = TRUE
to
explore how to interpret interactions between two 2-level factors coded
in different ways.
mu <- c(0, 4, 6, 10)
df <- sim_design(between = list(time = c("am", "pm"),
pet = c("cat", "dog")),
n = c(50, 60, 70, 80), mu = mu, empirical = TRUE)
![](data:image/png;base64,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)
The table below shows the cell and marginal means. The notation \(Y_{..}\) is used to denote a mean for a
specific grouping. The .
is used to indicate the mean over
all groups of that factor; Y..
is the grand mean. While
you’ll usually see the subscripts written as numbers to indicate the
factor levels, we’re using letters here so you don’t have to keep
referring to the order of factors and levels.
am |
\(Y_{ca} = 0\) |
\(Y_{da} = 4\) |
\(Y_{.a} = 2\) |
pm |
\(Y_{cp} = 6\) |
\(Y_{dp} = 10\) |
\(Y_{.p} = 8\) |
mean |
\(Y_{c.} = 3\) |
\(Y_{d.} = 7\) |
\(Y_{..} = 5\) |
Treatment
intercept |
cat when am |
\(Y_{ca}\) |
\(0\) |
pet.dog-cat |
dog minus cat, when am |
\(Y_{da} -
Y_{ca}\) |
\(4 - 0 = 4\) |
time.pm-am |
pm minus am, for cats |
\(Y_{cp} -
Y_{ca}\) |
\(6 - 0 = 6\) |
pet.dog-cat:time.pm-am |
dog minus cat when pm, minus dog minus cat when am |
\((Y_{dp} - Y_{cp}) - (Y_{da}
- Y_{ca})\) |
\((10 - 6) - (4 - 0) =
0\) |
df %>%
add_contrast("pet", "treatment") %>%
add_contrast("time", "treatment") %>%
lm(y ~ pet * time, .) %>%
broom::tidy() %>% kable() %>% kable_styling()
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
0
|
0.141
|
0.0
|
1
|
pet.dog-cat
|
4
|
0.191
|
20.9
|
0
|
time.pm-am
|
6
|
0.185
|
32.4
|
0
|
pet.dog-cat:time.pm-am
|
0
|
0.252
|
0.0
|
1
|
Anova
intercept |
grand mean |
\(Y_{..}\) |
\(5\) |
pet.dog-cat |
mean dog minus mean cat |
\(Y_{d.} -
Y_{c.}\) |
\(7 - 3 = 4\) |
time.pm-am |
mean pm minus mean am |
\(Y_{.p} -
Y_{.a}\) |
\(8 - 2 = 6\) |
pet.dog-cat:time.pm-am |
dog minus cat when pm, minus dog minus cat when am |
\((Y_{dp} - Y_{cp}) - (Y_{da}
- Y_{ca})\) |
\((10 - 6) - (4 - 0) =
0\) |
df %>%
add_contrast("pet", "anova") %>%
add_contrast("time", "anova") %>%
lm(y ~ pet * time, .) %>%
broom::tidy() %>% kable() %>% kable_styling()
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.063
|
79.4
|
0
|
pet.dog-cat
|
4
|
0.126
|
31.8
|
0
|
time.pm-am
|
6
|
0.126
|
47.6
|
0
|
pet.dog-cat:time.pm-am
|
0
|
0.252
|
0.0
|
1
|
Sum
intercept |
grand mean |
\(Y_{..}\) |
\(3\) |
pet.cat-intercept |
mean cat minus grand mean |
\(Y_{c.} -
Y_{..}\) |
\(3 - 5 = -2\) |
time.am-intercept |
mean am minus grand mean |
\(Y_{.a} -
Y_{..}\) |
\(2 - 5 = -3\) |
pet.cat-intercept:time.am-intercept |
cat minus mean when am, minus cat minus mean when pm,
divided by 2 |
\(\frac{(Y_{ca} - Y_{.a}) -
(Y_{cp} - Y_{.p})}{2}\) |
\(\frac{(0 - 2) - (6 - 8)}{2}
= 0\) |
df %>%
add_contrast("pet", "sum") %>%
add_contrast("time", "sum") %>%
lm(y ~ pet * time, .) %>%
broom::tidy() %>% kable() %>% kable_styling()
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.063
|
79.4
|
0
|
pet.cat-intercept
|
-2
|
0.063
|
-31.8
|
0
|
time.am-intercept
|
-3
|
0.063
|
-47.6
|
0
|
pet.cat-intercept:time.am-intercept
|
0
|
0.063
|
0.0
|
1
|
Difference
intercept |
grand mean |
\(Y_{..}\) |
\(5\) |
pet.dog-cat |
mean dog minus mean cat |
\(Y_{d.} -
Y_{c.}\) |
\(7 - 3 = 4\) |
time.pm-am |
mean pm minus mean am |
\(Y_{.p} -
Y_{.a}\) |
\(8 - 2 = 6\) |
pet.dog-cat:time.pm-am |
dog minus cat when pm, minus dog minus cat when am |
\((Y_{dp} - Y_{cp}) - (Y_{da}
- Y_{ca})\) |
\((10 - 6) - (4 - 0) =
0\) |
df %>%
add_contrast("pet", "difference") %>%
add_contrast("time", "difference") %>%
lm(y ~ pet * time, .) %>%
broom::tidy() %>% kable() %>% kable_styling()
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.063
|
79.4
|
0
|
pet.dog-cat
|
4
|
0.126
|
31.8
|
0
|
time.pm-am
|
6
|
0.126
|
47.6
|
0
|
pet.dog-cat:time.pm-am
|
0
|
0.252
|
0.0
|
1
|
Helmert
intercept |
grand mean |
\(Y_{..}\) |
\(5\) |
pet.dog-cat |
mean dog minus mean cat |
\(Y_{d.} -
Y_{c.}\) |
\(7 - 3 = 4\) |
time.pm-am |
mean pm minus mean am |
\(Y_{.p} -
Y_{.a}\) |
\(8 - 2 = 6\) |
pet.dog-cat:time.pm-am |
dog minus cat when pm, minus dog minus cat when am |
\((Y_{dp} - Y_{cp}) - (Y_{da}
- Y_{ca})\) |
\((10 - 6) - (4 - 0) =
0\) |
df %>%
add_contrast("pet", "helmert") %>%
add_contrast("time", "helmert") %>%
lm(y ~ pet * time, .) %>%
broom::tidy() %>% kable() %>% kable_styling()
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
5
|
0.063
|
79.4
|
0
|
pet.dog-cat
|
4
|
0.126
|
31.8
|
0
|
time.pm-am
|
6
|
0.126
|
47.6
|
0
|
pet.dog-cat:time.pm-am
|
0
|
0.252
|
0.0
|
1
|
N.B. In the case of 2-level factors, anova, difference, and
Helmert coding are identical. Treatment coding differs only in the
intercept.
Remember that interactions can always be described in two ways, since
(A1 - A2) - (B1 - B2) == (A1 - B1) - (A2 - B2)
. Therefore,
“dog minus cat when pm, minus dog minus cat when am” is the same as “pm
minus am for dogs, minus pm minus am for cats”. The way you describe it
in a paper depends on which version maps onto your hypothesis more
straightforwardly. The examples above might be written as “the
difference between dogs and cats was bigger in the evening than the
morning” or “the difference between evening and morning was bigger for
dogs than for cats”. Make sure you check the plots to make sure you are
describing the relationships in the right direction.
2x3 Design
Let’s use simulated data with empirical = TRUE
to
explore how to interpret interactions between a 2-level factor and a
3-level factor coded in different ways.
mu <- c(0, 5, 7, 6, 2, 1)
df <- sim_design(between = list(time = c("am", "pm"),
pet = c("cat", "dog", "ferret")),
n = c(50, 60, 70, 80, 90, 100), mu = mu, empirical = TRUE)
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)
am |
\(Y_{ca} = 0\) |
\(Y_{da} = 5\) |
\(Y_{fa} = 7\) |
\(Y_{.a} = 4\) |
pm |
\(Y_{cp} = 6\) |
\(Y_{dp} = 2\) |
\(Y_{fp} = 1\) |
\(Y_{.p} = 3\) |
mean |
\(Y_{c.} = 3\) |
\(Y_{d.} = 3.5\) |
\(Y_{f.} = 4\) |
\(Y_{..} = 3.5\) |
Treatment
intercept |
cat when am |
\(Y_{ca}\) |
\(0\) |
pet.dog-cat |
dog minus cat, when am |
\(Y_{da} -
Y_{ca}\) |
\(5 - 0 = 5\) |
pet.ferret-cat |
ferret minus cat, when am |
\(Y_{fa} -
Y_{ca}\) |
\(7 - 0 = 7\) |
time.pm-am |
pm minus am, for cats |
\(Y_{cp} -
Y_{ca}\) |
\(6 - 0 = 6\) |
pet.dog-cat:time.pm-am |
dog minus cat when pm, minus dog minus cat when am |
\((Y_{dp} - Y_{cp}) - (Y_{da}
- Y_{ca})\) |
\((2 - 6) - (5 - 0) =
-9\) |
pet.ferret-cat:time.pm-am |
ferret minus cat when pm, minus ferret minus cat when
am |
\((Y_{fp} - Y_{cp}) - (Y_{fa}
- Y_{ca})\) |
\((1 - 6) - (7 - 0) =
-12\) |
df %>%
add_contrast("pet", "treatment") %>%
add_contrast("time", "treatment") %>%
lm(y ~ pet * time, .) %>%
broom::tidy() %>% kable() %>% kable_styling()
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
0
|
0.141
|
0.0
|
1
|
pet.dog-cat
|
5
|
0.191
|
26.1
|
0
|
pet.ferret-cat
|
7
|
0.185
|
37.8
|
0
|
time.pm-am
|
6
|
0.180
|
33.3
|
0
|
pet.dog-cat:time.pm-am
|
-9
|
0.246
|
-36.7
|
0
|
pet.ferret-cat:time.pm-am
|
-12
|
0.238
|
-50.4
|
0
|
Anova
intercept |
grand mean |
\(Y_{..}\) |
\(3.5\) |
pet.dog-cat |
mean dog minus mean cat |
\(Y_{d.} -
Y_{c.}\) |
\(3.5 - 3 = 0.5\) |
pet.ferret-cat |
mean ferret minus mean cat |
\(Y_{f.} -
Y_{c.}\) |
\(4 - 3 = 1\) |
time.pm-am |
mean pm minus mean am |
\(Y_{.p} -
Y_{.a}\) |
\(3 - 4 = -1\) |
pet.dog-cat:time.pm-am |
dog minus cat when pm, minus dog minus cat when am |
\((Y_{dp} - Y_{cp}) - (Y_{da}
- Y_{ca})\) |
\((2 - 6) - (5 - 0) =
-9\) |
pet.ferret-cat:time.pm-am |
ferret minus cat when pm, minus ferret minus cat when
am |
\((Y_{fp} - Y_{cp}) - (Y_{fa}
- Y_{ca})\) |
\((1 - 6) - (7 - 0) =
-12\) |
df %>%
add_contrast("pet", "anova") %>%
add_contrast("time", "anova") %>%
lm(y ~ pet * time, .) %>%
broom::tidy() %>% kable() %>% kable_styling()
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
3.5
|
0.048
|
72.22
|
0
|
pet.dog-cat
|
0.5
|
0.123
|
4.07
|
0
|
pet.ferret-cat
|
1.0
|
0.119
|
8.39
|
0
|
time.pm-am
|
-1.0
|
0.097
|
-10.32
|
0
|
pet.dog-cat:time.pm-am
|
-9.0
|
0.246
|
-36.66
|
0
|
pet.ferret-cat:time.pm-am
|
-12.0
|
0.238
|
-50.36
|
0
|
Sum
intercept |
grand mean |
\(Y_{..}\) |
\(3\) |
pet.cat-intercept |
mean cat minus grand mean |
\(Y_{c.} -
Y_{..}\) |
\(3 - 3.5 =
-0.5\) |
pet.dog-intercept |
mean dog minus grand mean |
\(Y_{d.} -
Y_{..}\) |
\(3.5 - 3.5 = 0\) |
time.am-intercept |
mean am minus grand mean |
\(Y_{.a} -
Y_{..}\) |
\(4 - 3.5 = 0.5\) |
pet.cat-intercept:time.am-intercept |
cat minus mean when am, minus cat minus mean when pm,
divided by 2 |
\(\frac{(Y_{ca} - Y_{.a}) -
(Y_{cp} - Y_{.p})}{2}\) |
\(\frac{(0 - 4) - (6 - 3)}{2}
= -3.5\) |
pet.dog-intercept:time.am-intercept |
dog minus mean when am, minus dog minus mean when pm,
divided by 2 |
\(\frac{(Y_{da} - Y_{.a}) -
(Y_{dp} - Y_{.p})}{2}\) |
\(\frac{(5 - 4) - (2 - 3)}{2}
= 1\) |
df %>%
add_contrast("pet", "sum") %>%
add_contrast("time", "sum") %>%
lm(y ~ pet * time, .) %>%
broom::tidy() %>% kable() %>% kable_styling()
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
3.5
|
0.048
|
72.22
|
0
|
pet.cat-intercept
|
-0.5
|
0.071
|
-7.03
|
0
|
pet.dog-intercept
|
0.0
|
0.068
|
0.00
|
1
|
time.am-intercept
|
0.5
|
0.048
|
10.32
|
0
|
pet.cat-intercept:time.am-intercept
|
-3.5
|
0.071
|
-49.22
|
0
|
pet.dog-intercept:time.am-intercept
|
1.0
|
0.068
|
14.64
|
0
|
Difference
intercept |
grand mean |
\(Y_{..}\) |
\(3.5\) |
pet.dog-cat |
mean dog minus mean cat |
\(Y_{d.} -
Y_{c.}\) |
\(3.5 - 3 = 0.5\) |
pet.ferret-dog |
mean ferret minus mean dog |
\(Y_{f.} -
Y_{d.}\) |
\(4 - 3.5 = 0.5\) |
time.pm-am |
mean pm minus mean am |
\(Y_{.p} -
Y_{.a}\) |
\(3 - 4 = -1\) |
pet.dog-cat:time.pm-am |
dog minus cat when pm, minus dog minus cat when am |
\((Y_{dp} - Y_{cp}) - (Y_{da}
- Y_{ca})\) |
\((2 - 6) - (5 - 0) =
-9\) |
pet.ferret-dog:time.pm-am |
ferret minus dog when pm, minus ferret minus dog when
am |
\((Y_{fp} - Y_{dp}) - (Y_{fa}
- Y_{da})\) |
\((1 - 2) - (7 - 5) =
-3\) |
df %>%
add_contrast("pet", "difference") %>%
add_contrast("time", "difference") %>%
lm(y ~ pet * time, .) %>%
broom::tidy() %>% kable() %>% kable_styling()
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
3.5
|
0.048
|
72.22
|
0
|
pet.dog-cat
|
0.5
|
0.123
|
4.07
|
0
|
pet.ferret-dog
|
0.5
|
0.114
|
4.38
|
0
|
time.pm-am
|
-1.0
|
0.097
|
-10.32
|
0
|
pet.dog-cat:time.pm-am
|
-9.0
|
0.246
|
-36.66
|
0
|
pet.ferret-dog:time.pm-am
|
-3.0
|
0.228
|
-13.15
|
0
|
Helmert
intercept |
grand mean |
\(Y_{..}\) |
\(3.5\) |
pet.dog-cat |
mean dog minus mean cat |
\(Y_{d.} -
Y_{c.}\) |
\(3.5 - 3 = 0.5\) |
pet.ferret-cat.dog |
mean ferret minus mean of cat and dog |
\(Y_{f.} - \frac{Y_{c.} +
Y_{d.}}{2}\) |
\(4 - \frac{3 + 3.5}{2} =
0.75\) |
time.pm-am |
mean pm minus mean am |
\(Y_{.p} -
Y_{.a}\) |
\(3 - 4 = -1\) |
pet.dog-cat:time.pm-am |
dog minus cat when pm, minus dog minus cat when am |
\((Y_{dp} - Y_{cp}) - (Y_{da}
- Y_{ca})\) |
\((2 - 6) - (5 - 0) =
-9\) |
pet.ferret-cat.dog:time.pm-am |
ferret minus mean of cat and dog when pm, minus ferret
minus mean of cat and dog when am |
\((Y_{fp} - \frac{Y_{cp} +
Y_{dp}}{2}) - (Y_{fa} - \frac{Y_{ca} + Y_{da}}{2})\) |
\((1 - \frac{6 + 2}{2}) - (7
- \frac{0 + 5}{2}) = -7.5\) |
df %>%
add_contrast("pet", "helmert") %>%
add_contrast("time", "helmert") %>%
lm(y ~ pet * time, .) %>%
broom::tidy() %>% kable() %>% kable_styling()
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
3.50
|
0.048
|
72.22
|
0
|
pet.dog-cat
|
0.50
|
0.123
|
4.07
|
0
|
pet.ferret-cat.dog
|
0.75
|
0.099
|
7.56
|
0
|
time.pm-am
|
-1.00
|
0.097
|
-10.32
|
0
|
pet.dog-cat:time.pm-am
|
-9.00
|
0.246
|
-36.66
|
0
|
pet.ferret-cat.dog:time.pm-am
|
-7.50
|
0.198
|
-37.81
|
0
|
N.B. In this case, difference coding is identical to anova
coding except that the second pet contrast is ferret versus dog instead
of ferret versus cat.
3x3 Design
Please just don’t. You’re going to break my head.