MAT 156 FINAL PROJECT 2 SolutionsIn this project you will explain the formula NiMsKiIiIkYkKiZGJEYkIiIkISIiRicqJkYkRiQiIiZGJ0YkKiZGJEYkIiIoRidGJw==+...=NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI= . We define a sequence of definite integrals by the formula NiMvLUkiVEc2IjYjSSJuR0YmLUkkSW50R0YmNiQpLUkkdGFuR0YmNiNJInhHRiZGKC9GMDsiIiEqJkkjUGlHSSpwcm90ZWN0ZWRHRjYiIiIiIiUhIiI= .1. Calculate NiMtSSJURzYiNiMiIiE= and NiMtSSJURzYiNiMiIiI=. Use a substitution in NiMtSSJURzYiNiMiIiI= to show that it is equal to NiMqJi1JI2xuRzYiNiMiIiMiIiJGKCEiIg==. This part does not require numerical integration. Explain your answer and your choice of substitution.with(student); with(plots);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T:=n->Int(tan(x)^n, x=0..Pi/4);NiM+SSJURzYiZio2I0kibkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkSW50R0koX3N5c2xpYkdGJTYkKS1JJHRhbkdGJTYjSSJ4R0YlOSQvRjQ7IiIhLCRJI1BpR0kqcHJvdGVjdGVkR0Y7IyIiIiIiJUYlRiVGJQ==value(T(0));NiMsJEkjUGlHSSpwcm90ZWN0ZWRHRiUjIiIiIiIlvalue(T(1));NiMsJC1JI2xuRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2IyIiIyMiIiJGKw==T(1);NiMtSSRJbnRHSShfc3lzbGliRzYiNiQtSSR0YW5HNiRJKnByb3RlY3RlZEdGK0YlNiNJInhHRiYvRi07IiIhLCRJI1BpR0YrIyIiIiIiJQ==R:=changevar(u=cos(x), T(1), u);NiM+SSJSRzYiLUkkSW50R0koX3N5c2xpYkdGJTYkKiRJInVHRiUhIiIvRis7LCQqJCIiIyMiIiJGMUYyRjM=value(R);NiMsJC1JI2xuRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2IyIiIyMiIiJGKw==We get after we integrate ln(u) to be evaluated at 1 and NiMqJi1JJXNxcnRHNiRJKnByb3RlY3RlZEdGJ0koX3N5c2xpYkc2IjYjIiIjIiIiLUkmRmxvYXRHRic2JEYrIiIhISIi At 1 we get 0 and the answer at NiMqJi1JJXNxcnRHNiRJKnByb3RlY3RlZEdGJ0koX3N5c2xpYkc2IjYjIiIjIiIiRishIiI= has to be subtracted to give-lnNiMqJi1JJXNxcnRHNiRJKnByb3RlY3RlZEdGJ0koX3N5c2xpYkc2IjYjIiIjIiIiRishIiI==-lnNiMtSSVzcXJ0RzYkSSpwcm90ZWN0ZWRHRiZJKF9zeXNsaWJHNiI2IyIiIw===ln(NiMqJiIiIkYkLUklc3FydEc2JEkqcHJvdGVjdGVkR0YoSShfc3lzbGliRzYiNiMiIiMhIiI=). The substitution is motivated by the fact that NiMvLUkkdGFuRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2I0kieEdGKSomLUkkc2luR0YmRioiIiItSSRjb3NHRiZGKiEiIg== and the numerator is minus the derivative of the denominator. 2. Calculate numerically NiMtSSJURzYiNiNJIm5HRiU= for NiMvSSJuRzYiIiIi, 2, ...20 and decide whether the sequence is increasing or decreasing. What is its limit? for n from 1 to 20 do evalf(value(T(n))); od;NiMkIisuZnRsTSEjNQ==NiMkIitsJD1nOSMhIzU=NiMkIisoNGtVYCIhIzU=NiMkIitvXEooPSIhIzU=NiMkIiouZnRsKiEjNQ==NiMkIipLXW83KSEjNQ==NiMkIiprMiQ0cSEjNQ==NiMkIiooUicpZWghIzU=NiMkIipPI3AhXCYhIzU=NiMkIio5WkEmXCEjNQ==NiMkIiprMiQ0WCEjNQ==NiMkIiomPm1RVCEjNQ==NiMkIipxRFMjUSEjNQ==NiMkIip1WE9iJCEjNQ==NiMkIipYSik9TCEjNQ==NiMkIiojNC04SiEjNQ==NiMkIipibzYkSCEjNQ==NiMkIiotSyRwRiEjNQ==NiMkIiorKFFDRSEjNQ==NiMkIiopZSNRXCMhIzU=It is a decreasing sequence. It seems that its limit is 0.3. Graph on the same graph the functions NiMpLUkkdGFuRzYiNiNJInhHRiZJIm5HRiY= for NiMvSSJuRzYiIiIi, 2, ..., 5 for in [0, NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI=]. Which one is larger, which one is smaller? Why? What does this imply for the sequence NiMtSSJURzYiNiNJIm5HRiU= ?plot([tan(x), tan(x)^2, tan(x)^3, tan(x)^4, tan(x)^5], x=0..Pi/4, color=[black, blue, green, yellow, red]);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It is clear that the higher the exponent the smaller the function, so that the largest one is NiMtSSR0YW5HNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYjSSJ4R0Yo and the smallest one is NiMqJC1JJHRhbkc2JEkqcHJvdGVjdGVkR0YnSShfc3lzbGliRzYiNiNJInhHRikiIiY=. By integrating over [0, NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI=] we get NiMtSSJURzYiNiMiIiI==NiMtSSRJbnRHSShfc3lzbGliRzYiNiQtSSR0YW5HNiRJKnByb3RlY3RlZEdGK0YlNiNJInhHRiYvRi07IiIhKiZJI1BpR0YrIiIiIiIlISIi <NiMtSSRJbnRHSShfc3lzbGliRzYiNiQqJC1JJHRhbkc2JEkqcHJvdGVjdGVkR0YsRiU2I0kieEdGJiIiIy9GLjsiIiEqJkkjUGlHRiwiIiIiIiUhIiI= =NiMtSSJURzYiNiMiIiM= <NiMtSSJURzYiNiMiIiQ==NiMtSSRJbnRHSShfc3lzbGliRzYiNiQqJC1JJHRhbkc2JEkqcHJvdGVjdGVkR0YsRiU2I0kieEdGJiIiJC9GLjsiIiEqJkkjUGlHRiwiIiIiIiUhIiI= etc. This implies that the sequence NiMtSSJURzYiNiNJIm5HRiU= is indeed decreasing. The explanation why the functions are arranged in that order is simple: for a fixed NiNJInhHNiI= less than 1, we are computing higher and higher powers of it. These are decreasing numbers, e.g. 0.5, 0.5^2=0.25, 0.5^3=0.125, 0.5^4=0.0625.4. Show that NiMvLCYpLUkkdGFuRzYiNiNJInhHRihJIm5HRigiIiIpRiYsJkYrRiwiIiNGLEYsKiZGJUYsKiQtSSRzZWNHRihGKUYvRiw= by verifying it for various NiNJIm5HNiI= .Which trigonometric identity do you use? Verify it using Maple and without Maple.n:=3;NiM+SSJuRzYiIiIkfactor(tan(x)^n+tan(x)^(n+2));NiMqJi1JJHRhbkc2JEkqcHJvdGVjdGVkR0YnSShfc3lzbGliRzYiNiNJInhHRikiIiQsJiIiIkYuKiRGJCIiI0YuRi4=n:=100;NiM+SSJuRzYiIiQrIg==factor(tan(x)^n+tan(x)^(n+2));NiMqJi1JJHRhbkc2JEkqcHJvdGVjdGVkR0YnSShfc3lzbGliRzYiNiNJInhHRikiJCsiLCYiIiJGLiokRiQiIiNGLkYun=1000;NiMvIiQrIiIlKzU=factor(tan(x)^n+tan(x)^(n+2));NiMqJi1JJHRhbkc2JEkqcHJvdGVjdGVkR0YnSShfc3lzbGliRzYiNiNJInhHRikiJCsiLCYiIiJGLiokRiQiIiNGLkYuSo it seems that we need the identity tan(x)^2+1=sec(x)^2. This is true as follows:simplify(tan(x)^2+1-sec(x)^2);NiMiIiE=We have NiMvLCYqJC1JJHRhbkc2JEkqcHJvdGVjdGVkR0YpSShfc3lzbGliRzYiNiNJInhHRisiIiMiIiJGL0YvLCYqJi1JJHNpbkdGKEYsRi4qJC1JJGNvc0dGKEYsRi4hIiJGL0YvRi8==NiMvKiYsJiokLUkkc2luRzYkSSpwcm90ZWN0ZWRHRipJKF9zeXNsaWJHNiI2I0kieEdGLCIiIyIiIiokLUkkY29zR0YpRi1GL0YwRjBGMSEiIiomRjBGMEYxRjQ== NiMqJC1JJHNlY0c2JEkqcHJvdGVjdGVkR0YnSShfc3lzbGliRzYiNiNJInhHRikiIiM=.5. Use 4. to show that NiMvLCYtSSJURzYiNiNJIm5HRiciIiItRiY2IywmRilGKiIiI0YqRioqJkYqRiosJkYpRipGKkYqISIi . To do this you need to make a substitution in the integral NiMtSSRJbnRHNiI2JComKS1JJHRhbkdGJTYjSSJ4R0YlSSJuR0YlIiIiKiQtSSRzZWNHRiVGKyIiI0YuL0YsOyIiISomSSNQaUdJKnByb3RlY3RlZEdGOEYuIiIlISIi . Warning: Maple may not be able to calculate it for general NiNJIm5HNiI= . Parts 2 and 5 imply that NiMvLUkmbGltaXRHNiI2JC1JIlRHRiY2I0kibkdGJi9GK0kpaW5maW5pdHlHSSpwcm90ZWN0ZWRHRi4iIiE= . We integrate the identity to get NiMvLCYtSSRJbnRHSShfc3lzbGliRzYiNiQpLUkkdGFuRzYkSSpwcm90ZWN0ZWRHRi5GJzYjSSJ4R0YoSSJuR0YoL0YwOyIiISomSSNQaUdGLiIiIiIiJSEiIkY3LUYmNiQpRissJkYxRjciIiNGN0YyRjctRiY2JComRipGNyokLUkkc2VjR0YtRi9GPkY3RjI=. For the last integral we substitute NiMvSSJ1RzYiLUkkdGFuRzYkSSpwcm90ZWN0ZWRHRilJKF9zeXNsaWJHRiU2I0kieEdGJQ== since NiMvLUkiREc2JEkqcHJvdGVjdGVkR0YnSShfc3lzbGliRzYiNiMtSSR0YW5HRiY2I0kieEdGKSktSSRzZWNHRiZGLS1JJkZsb2F0R0YnNiQiIiMiIiE=. We haveS:=changevar(u=tan(x), Int(tan(x)^n*sec(x)^2, x=0..Pi/4), u);NiM+SSJTRzYiLUkkSW50R0koX3N5c2xpYkdGJTYkKiRJInVHRiUiJCsiL0YrOyIiISIiIg==eval(value(S));NiMjIiIiIiQsIg==n:=1000;NiM+SSJuRzYiIiUrNQ==S:=changevar(u=tan(x), Int(tan(x)^n*sec(x)^2, x=0..Pi/4), u);NiM+SSJTRzYiLUkkSW50R0koX3N5c2xpYkdGJTYkKiRJInVHRiUiJSs1L0YrOyIiISIiIg==eval(value(S));NiMjIiIiIiUsNQ==The limit of NiMtSSJURzYiNiNJIm5HRiU= follows from the fact that a decreasing and positive sequence converges to a number, callit NiNJIkxHNiI= But then NiMvLUkmbGltaXRHNiRJKnByb3RlY3RlZEdGJ0koX3N5c2xpYkc2IjYkLUkiVEdGKTYjSSJuR0YpL0YuSSlpbmZpbml0eUdGJ0kiTEdGKQ== NiMvLUkmbGltaXRHNiRJKnByb3RlY3RlZEdGJ0koX3N5c2xpYkc2IjYkLUkiVEdGKTYjLCZJIm5HRikiIiIiIiNGMC9GL0kpaW5maW5pdHlHRidJIkxHRik=, while NiMvLUkmbGltaXRHNiRJKnByb3RlY3RlZEdGJ0koX3N5c2xpYkc2IjYkKiYiIiJGLCwmSSJuR0YpRixGLEYsISIiL0YuSSlpbmZpbml0eUdGJyIiIQ==. So NiMvLCZJIkxHNiIiIiJGJUYnIiIh and NiMvSSJMRzYiIiIh.6. Use NiMvLCYtSSJURzYiNiNJIm5HRiciIiItRiY2IywmRilGKiIiI0YqRioqJkYqRiosJkYpRipGKkYqISIi to show that: NiMtSSJURzYiNiMiIiU= =-(1-1/3-NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI=), NiMtSSJURzYiNiMiIic==(1-1/3+1/5-NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI=) ,etc. NiMtSSJURzYiNiMqJiIiIyIiIkkibkdGJUYp=+-(1-1/3+1/5-1/7+...-NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI=). NiMvLUkiVEc2IjYjIiIlKiYiIiJGKiIiJCEiIg==-NiMtSSJURzYiNiMiIiM==1/3-(1-NiMtSSJURzYiNiMiIiE=)=1/3-1+NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI=. Similarly NiMvLUkiVEc2IjYjIiInKiYiIiJGKiIiJiEiIg==-NiMvLUkiVEc2IjYjIiIlLCYqJiIiIkYrIiImISIiRissJiomRitGKyIiJEYtRistRiU2IyIiI0YtRi0= =1/5-1/3+NiMtSSJURzYiNiMiIiM==1/5-1/3+1-NiMtSSJURzYiNiMiIiE==1/5-1/3+1-NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI=. The general formula follows by repeated application of the given identity. These results together with the limit from 5, show the formula required.7. Use the formula to calculate the first two decimal digits of NiNJI1BpR0kqcHJvdGVjdGVkR0Yk. How are you certain of the answer you provided? Hint: Alternating series.sums[-1]:=0;for n from 0 to 1000 do sums[n]:=evalf(sums[n-1]+4*(-1)^n*1/(2*n+1)) ;od; NiM+Jkklc3Vtc0c2IjYjISIiIiIhNiM+Jkklc3Vtc0c2IjYjIiIhJCIiJUYoNiM+Jkklc3Vtc0c2IjYjIiIiJCIrbm1tbUUhIio=NiM+Jkklc3Vtc0c2IjYjIiIjJCIrbm1tbU0hIio=NiM+Jkklc3Vtc0c2IjYjIiIkJCIrJzRRXypHISIqNiM+Jkklc3Vtc0c2IjYjIiIlJCIrU0RvUkwhIio=NiM+Jkklc3Vtc0c2IjYjIiImJCIrd2gvd0ghIio=NiM+Jkklc3Vtc0c2IjYjIiInJCIrJVtRUEckISIqNiM+Jkklc3Vtc0c2IjYjIiIoJCIrPD0yPEkhIio=NiM+Jkklc3Vtc0c2IjYjIiIpJCIrTmZPX0shIio=NiM+Jkklc3Vtc0c2IjYjIiIqJCIrPidSPS8kISIqNiM+Jkklc3Vtc0c2IjYjIiM1JCIrNWVKS0shIio=NiM+Jkklc3Vtc0c2IjYjIiM2JCIrbUZTZUkhIio=NiM+Jkklc3Vtc0c2IjYjIiM3JCIrbUZTPUshIio=NiM+Jkklc3Vtc0c2IjYjIiM4JCIrPVlEcUkhIio=NiM+Jkklc3Vtc0c2IjYjIiM5JCIrX2M9M0shIio=NiM+Jkklc3Vtc0c2IjYjIiM6JCIrJVJgInpJISIqNiM+Jkklc3Vtc0c2IjYjIiM7JCIrOmJPK0shIio=NiM+Jkklc3Vtc0c2IjYjIiM8JCIrLCl6ZzMkISIqNiM+Jkklc3Vtc0c2IjYjIiM9JCIrNHo9JT4kISIqNiM+Jkklc3Vtc0c2IjYjIiM+JCIrMVFpIjQkISIqNiM+Jkklc3Vtc0c2IjYjIiM/JCIrI3klPSo9JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiNAJCIrRTo7JzQkISIqNiM+Jkklc3Vtc0c2IjYjIiNBJCIrOi8wJj0kISIqNiM+Jkklc3Vtc0c2IjYjIiNCJCIrS1MlKio0JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiNDJCIrJm93Oj0kISIqNiM+Jkklc3Vtc0c2IjYjIiNEJCIrN2A5LkohIio=NiM+Jkklc3Vtc0c2IjYjIiNFJCIrNXFoeUohIio=NiM+Jkklc3Vtc0c2IjYjIiNGJCIrUCgqKWU1JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiNHJCIrd14xd0ohIio=NiM+Jkklc3Vtc0c2IjYjIiNIJCIrbSZvIzNKISIqNiM+Jkklc3Vtc0c2IjYjIiNJJCIrT0IlUTwkISIqNiM+Jkklc3Vtc0c2IjYjIiNKJCIrdC1ONUohIio=NiM+Jkklc3Vtc0c2IjYjIiNLJCIrTigpKT08JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiNMJCIrVXM9N0ohIio=NiM+Jkklc3Vtc0c2IjYjIiNNJCIrYyNlLDwkISIqNiM+Jkklc3Vtc0c2IjYjIiNOJCIrRy0jUTYkISIqNiM+Jkklc3Vtc0c2IjYjIiNPJCIrXFpob0ohIio=NiM+Jkklc3Vtc0c2IjYjIiNQJCIrOzlHOkohIio=NiM+Jkklc3Vtc0c2IjYjIiNRJCIrbyVIczskISIqNiM+Jkklc3Vtc0c2IjYjIiNSJCIrZGxmO0ohIio=NiM+Jkklc3Vtc0c2IjYjIiNTJCIrdCN6ZjskISIqNiM+Jkklc3Vtc0c2IjYjIiNUJCIrLWx5PEohIio=NiM+Jkklc3Vtc0c2IjYjIiNVJCIrRWAlWzskISIqNiM+Jkklc3Vtc0c2IjYjIiNWJCIrOiRvKT1KISIqNiM+Jkklc3Vtc0c2IjYjIiNXJCIrTkAiUTskISIqNiM+Jkklc3Vtc0c2IjYjIiNYJCIrIjRjKT5KISIqNiM+Jkklc3Vtc0c2IjYjIiNZJCIrV28nRzskISIqNiM+Jkklc3Vtc0c2IjYjIiNaJCIrImVoMjckISIqNiM+Jkklc3Vtc0c2IjYjIiNbJCIrJXApKj47JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiNcJCIrYVlmQEohIio=NiM+Jkklc3Vtc0c2IjYjIiNdJCIrOScpPmhKISIqNiM+Jkklc3Vtc0c2IjYjIiNeJCIrak9PQUohIio=NiM+Jkklc3Vtc0c2IjYjIiNfJCIrLCplLzskISIqNiM+Jkklc3Vtc0c2IjYjIiNgJCIrQmQyQkohIio=NiM+Jkklc3Vtc0c2IjYjIiNhJCIrckh4ZkohIio=NiM+Jkklc3Vtc0c2IjYjIiNiJCIrTnB0QkohIio=NiM+Jkklc3Vtc0c2IjYjIiNjJCIrbF44ZkohIio=NiM+Jkklc3Vtc0c2IjYjIiNkJCIrY0ROQ0ohIio=NiM+Jkklc3Vtc0c2IjYjIiNlJCIrIWZTJmVKISIqNiM+Jkklc3Vtc0c2IjYjIiNmJCIrWHIjXDckISIqNiM+Jkklc3Vtc0c2IjYjIiNnJCIrJypcKXo6JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiNoJCIrcllZREohIio=NiM+Jkklc3Vtc0c2IjYjIiNpJCIrcllZZEohIio=NiM+Jkklc3Vtc0c2IjYjIiNqJCIrMydvZjckISIqNiM+Jkklc3Vtc0c2IjYjIiNrJCIrZ2oocDokISIqNiM+Jkklc3Vtc0c2IjYjIiNsJCIrND9XRUohIio=NiM+Jkklc3Vtc0c2IjYjIiNtJCIrKD48bDokISIqNiM+Jkklc3Vtc0c2IjYjIiNuJCIrbnYpbzckISIqNiM+Jkklc3Vtc0c2IjYjIiNvJCIrWlkzY0ohIio=NiM+Jkklc3Vtc0c2IjYjIiNwJCIrcHdJRkohIio=NiM+Jkklc3Vtc0c2IjYjIiNxJCIramtuYkohIio=NiM+Jkklc3Vtc0c2IjYjIiNyJCIrTldxRkohIio=NiM+Jkklc3Vtc0c2IjYjIiNzJCIrVTFIYkohIio=NiM+Jkklc3Vtc0c2IjYjIiN0JCIrZSh6IUdKISIqNiM+Jkklc3Vtc0c2IjYjIiN1JCIrJ1JEXDokISIqNiM+Jkklc3Vtc0c2IjYjIiN2JCIrSWBWR0ohIio=NiM+Jkklc3Vtc0c2IjYjIiN3JCIrQCJ6WDokISIqNiM+Jkklc3Vtc0c2IjYjIiN4JCIrcEV4R0ohIio=NiM+Jkklc3Vtc0c2IjYjIiN5JCIrdy5EYUohIio=NiM+Jkklc3Vtc0c2IjYjIiN6JCIrVko0SEohIio=NiM+Jkklc3Vtc0c2IjYjIiMhKSQiK2t5JFI6JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiMiKSQiKygpelJISiEiKg==NiM+Jkklc3Vtc0c2IjYjIiMjKSQiKzYva2BKISIqNiM+Jkklc3Vtc0c2IjYjIiMkKSQiKzokKW9ISiEiKg==NiM+Jkklc3Vtc0c2IjYjIiMlKSQiK2FwTmBKISIqNiM+Jkklc3Vtc0c2IjYjIiMmKSQiK1ReJypISiEiKg==NiM+Jkklc3Vtc0c2IjYjIiMnKSQiK0dsM2BKISIqNiM+Jkklc3Vtc0c2IjYjIiMoKSQiKyZRSC04JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiMpKSQiK2IjR0c6JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiMqKSQiKycpPVtJSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiMhKiQiK004ZV9KISIqNiM+Jkklc3Vtc0c2IjYjIiMiKiQiKzVNc0lKISIqNiM+Jkklc3Vtc0c2IjYjIiMjKiQiK0tdTV9KISIqNiM+Jkklc3Vtc0c2IjYjIiMkKiQiK2VZJjQ4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiMlKiQiK3onPUA6JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiMmKiQiK3JpPEpKISIqNiM+Jkklc3Vtc0c2IjYjIiMnKiQiK2c7IT46JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiMoKiQiK1IpKVFKSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiMpKiQiKzNNcF5KISIqNiM+Jkklc3Vtc0c2IjYjIiMqKiQiKzBIZkpKISIqNiM+Jkklc3Vtc0c2IjYjIiQrIiQiKy5NXF5KISIqNiM+Jkklc3Vtc0c2IjYjIiQsIiQiK3EqKXlKSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQtIiQiK2w2SV5KISIqNiM+Jkklc3Vtc0c2IjYjIiQuIiQiKyVceD44JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQvIiQiK11pNl5KISIqNiM+Jkklc3Vtc0c2IjYjIiQwIiQiKy8qZUA4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQxIiQiK1ojUTQ6JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQyIiQiKydmTEI4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQzIiQiK3dud11KISIqNiM+Jkklc3Vtc0c2IjYjIiQ0IiQiK08+XUtKISIqNiM+Jkklc3Vtc0c2IjYjIiQ1IiQiKyVbLDE6JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ2IiQiK2tVbUtKISIqNiM+Jkklc3Vtc0c2IjYjIiQ3IiQiK1U/V11KISIqNiM+Jkklc3Vtc0c2IjYjIiQ4IiQiKygqMyNHOCQhIio=NiM+Jkklc3Vtc0c2IjYjIiQ5IiQiK1kiKUddSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ6IiQiK0hAKEg4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ7IiQiKzYmUiw6JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ8IiQiK00jPUo4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ9IiQiK3JlKipcSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ+IiQiK3AlZks4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ/IiQiK3pwJilcSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRAIiQiK3VnUkxKISIqNiM+Jkklc3Vtc0c2IjYjIiRBIiQiKzBFc1xKISIqNiM+Jkklc3Vtc0c2IjYjIiRCIiQiK3QjR044JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRDIiQiK0lEZlxKISIqNiM+Jkklc3Vtc0c2IjYjIiREIiQiK3ZpbExKISIqNiM+Jkklc3Vtc0c2IjYjIiRFIiQiK19sWVxKISIqNiM+Jkklc3Vtc0c2IjYjIiRGIiQiK3gteUxKISIqNiM+Jkklc3Vtc0c2IjYjIiRHIiQiK3pXTVxKISIqNiM+Jkklc3Vtc0c2IjYjIiRIIiQiK2svIVI4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRJIiQiK01oQVxKISIqNiM+Jkklc3Vtc0c2IjYjIiRKIiQiKzRxLE1KISIqNiM+Jkklc3Vtc0c2IjYjIiRLIiQiK1w4NlxKISIqNiM+Jkklc3Vtc0c2IjYjIiRMIiQiK3crOE1KISIqNiM+Jkklc3Vtc0c2IjYjIiRNIiQiK2sqKioqW0ohIio=NiM+Jkklc3Vtc0c2IjYjIiROIiQiKzspUlU4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRPIiQiK0o9KilbSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRQIiQiK3dqTU1KISIqNiM+Jkklc3Vtc0c2IjYjIiRRIiQiKzRveVtKISIqNiM+Jkklc3Vtc0c2IjYjIiRSIiQiKyIqKVxXOCQhIio=NiM+Jkklc3Vtc0c2IjYjIiRTIiQiK21ab1tKISIqNiM+Jkklc3Vtc0c2IjYjIiRUIiQiKyFcXVg4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRVIiQiK3liZVtKISIqNiM+Jkklc3Vtc0c2IjYjIiRWIiQiKydIW1k4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRXIiQiK0UiKltbSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRYIiQiK0FNdU1KISIqNiM+Jkklc3Vtc0c2IjYjIiRZIiQiKypIJlJbSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRaIiQiK3hmJFs4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRbIiQiKyEqUklbSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRcIiQiK2tnI1w4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRdIiQiKyxeQFtKISIqNiM+Jkklc3Vtc0c2IjYjIiReIiQiKyJ5OF04JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRfIiQiK04mRyJbSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRgIiQiKz4jKjROSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRhIiQiKy5VL1tKISIqNiM+Jkklc3Vtc0c2IjYjIiRiIiQiK25DPU5KISIqNiM+Jkklc3Vtc0c2IjYjIiRjIiQiKz8/J3o5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRkIiQiKzJPRU5KISIqNiM+Jkklc3Vtc0c2IjYjIiRlIiQiKy8+KXk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRmIiQiKz5GTU5KISIqNiM+Jkklc3Vtc0c2IjYjIiRnIiQiK3lQIXk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRoIiQiK3gpPmE4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRpIiQiK3B2c1pKISIqNiM+Jkklc3Vtc0c2IjYjIiRqIiQiK2BeXE5KISIqNiM+Jkklc3Vtc0c2IjYjIiRrIiQiKzNLbFpKISIqNiM+Jkklc3Vtc0c2IjYjIiRsIiQiKzsnb2I4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRtIiQiK0cxZVpKISIqNiM+Jkklc3Vtc0c2IjYjIiRuIiQiK0gua05KISIqNiM+Jkklc3Vtc0c2IjYjIiRvIiQiK2woNHY5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRwIiQiK2Iuck5KISIqNiM+Jkklc3Vtc0c2IjYjIiRxIiQiK2cwV1pKISIqNiM+Jkklc3Vtc0c2IjYjIiRyIiQiK18oeWQ4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRzIiQiK2JIUFpKISIqNiM+Jkklc3Vtc0c2IjYjIiR0IiQiK3hiJWU4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR1IiQiKyYqb0laSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiR2IiQiKyUpMyJmOCQhIio=NiM+Jkklc3Vtc0c2IjYjIiR3IiQiK0hCQ1pKISIqNiM+Jkklc3Vtc0c2IjYjIiR4IiQiK0JaKGY4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR5IiQiKzAjenI5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR6IiQiK1dyLk9KISIqNiM+Jkklc3Vtc0c2IjYjIiQhPSQiK3d1NlpKISIqNiM+Jkklc3Vtc0c2IjYjIiQiPSQiKyM+KTRPSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQjPSQiKyc0ZHE5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQkPSQiKzh6Ok9KISIqNiM+Jkklc3Vtc0c2IjYjIiQlPSQiK0AhKSpwOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQmPSQiK11qQE9KISIqNiM+Jkklc3Vtc0c2IjYjIiQnPSQiKzYtJXA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQoPSQiK1dORk9KISIqNiM+Jkklc3Vtc0c2IjYjIiQpPSQiK0NPKW85JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQqPSQiK00mSGo4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQhPiQiK0EjR285JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQiPiQiK2VWUU9KISIqNiM+Jkklc3Vtc0c2IjYjIiQjPiQiK29SeFlKISIqNiM+Jkklc3Vtc0c2IjYjIiQkPiQiK14hUWs4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQlPiQiK0Yzc1lKISIqNiM+Jkklc3Vtc0c2IjYjIiQmPiQiK1sxXE9KISIqNiM+Jkklc3Vtc0c2IjYjIiQnPiQiK2wob205JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQoPiQiKyQ9VWw4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQpPiQiK114aFlKISIqNiM+Jkklc3Vtc0c2IjYjIiQqPiQiKyhvI2ZPSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQrIyQiK1x4Y1lKISIqNiM+Jkklc3Vtc0c2IjYjIiQsIyQiKyI+VW04JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQtIyQiK00oPWw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQuIyQiK0MycE9KISIqNiM+Jkklc3Vtc0c2IjYjIiQvIyQiK3YxWllKISIqNiM+Jkklc3Vtc0c2IjYjIiQwIyQiKzokUW44JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQxIyQiK1hOVVlKISIqNiM+Jkklc3Vtc0c2IjYjIiQyIyQiKyIqXHlPSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQzIyQiKzx0UFlKISIqNiM+Jkklc3Vtc0c2IjYjIiQ0IyQiK3kyJG84JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ1IyQiK20+TFlKISIqNiM+Jkklc3Vtc0c2IjYjIiQ2IyQiKyxkKG84JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ3IyQiK211R1lKISIqNiM+Jkklc3Vtc0c2IjYjIiQ4IyQiKyZ5PnA4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ5IyQiKyV6Vmk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ6IyQiK19JJ3A4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ7IyQiK0Y0P1lKISIqNiM+Jkklc3Vtc0c2IjYjIiQ8IyQiK0RiK1BKISIqNiM+Jkklc3Vtc0c2IjYjIiQ9IyQiK1YpZWg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ+IyQiK0VzL1BKISIqNiM+Jkklc3Vtc0c2IjYjIiQ/IyQiK0B2NllKISIqNiM+Jkklc3Vtc0c2IjYjIiRAIyQiK3ciKTNQSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRBIyQiK1NwMllKISIqNiM+Jkklc3Vtc0c2IjYjIiRCIyQiKyVSR3I4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRDIyQiKyEzUGc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiREIyQiKyt6O1BKISIqNiM+Jkklc3Vtc0c2IjYjIiRFIyQiK0F6KmY5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRGIyQiKzhuP1BKISIqNiM+Jkklc3Vtc0c2IjYjIiRHIyQiK1slZmY5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRIIyQiK15bQ1BKISIqNiM+Jkklc3Vtc0c2IjYjIiRJIyQiK1Q7I2Y5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRKIyQiK0tCR1BKISIqNiM+Jkklc3Vtc0c2IjYjIiRLIyQiKyRbJSllOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiRMIyQiK3QiPnQ4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRNIyQiK2V6JWU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiROIyQiKypRYnQ4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRPIyQiK1w/ImU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRQIyQiKycqNFJQSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRRIyQiK1NueFhKISIqNiM+Jkklc3Vtc0c2IjYjIiRSIyQiKzRnVVBKISIqNiM+Jkklc3Vtc0c2IjYjIiRTIyQiKzw/dVhKISIqNiM+Jkklc3Vtc0c2IjYjIiRUIyQiK1cvWVBKISIqNiM+Jkklc3Vtc0c2IjYjIiRVIyQiK255cVhKISIqNiM+Jkklc3Vtc0c2IjYjIiRWIyQiKzpWXFBKISIqNiM+Jkklc3Vtc0c2IjYjIiRXIyQiK3VVblhKISIqNiM+Jkklc3Vtc0c2IjYjIiRYIyQiK013X1BKISIqNiM+Jkklc3Vtc0c2IjYjIiRZIyQiK0M3a1hKISIqNiM+Jkklc3Vtc0c2IjYjIiRaIyQiKzsvY1BKISIqNiM+Jkklc3Vtc0c2IjYjIiRbIyQiKzEoM2M5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRcIyQiK3VFZlBKISIqNiM+Jkklc3Vtc0c2IjYjIiRdIyQiKzFuZFhKISIqNiM+Jkklc3Vtc0c2IjYjIiReIyQiKz9XaVBKISIqNiM+Jkklc3Vtc0c2IjYjIiRfIyQiKzdfYVhKISIqNiM+Jkklc3Vtc0c2IjYjIiRgIyQiK21jbFBKISIqNiM+Jkklc3Vtc0c2IjYjIiRhIyQiKzdVXlhKISIqNiM+Jkklc3Vtc0c2IjYjIiRiIyQiK0Jrb1BKISIqNiM+Jkklc3Vtc0c2IjYjIiRjIyQiKyVwJFtYSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRkIyQiKy9uclBKISIqNiM+Jkklc3Vtc0c2IjYjIiRlIyQiK1tPWFhKISIqNiM+Jkklc3Vtc0c2IjYjIiRmIyQiKz5sdVBKISIqNiM+Jkklc3Vtc0c2IjYjIiRnIyQiK2lTVVhKISIqNiM+Jkklc3Vtc0c2IjYjIiRoIyQiK3lleFBKISIqNiM+Jkklc3Vtc0c2IjYjIiRpIyQiK0VcUlhKISIqNiM+Jkklc3Vtc0c2IjYjIiRqIyQiKyR6L3k4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRrIyQiK0lpT1hKISIqNiM+Jkklc3Vtc0c2IjYjIiRsIyQiK3RLJHk4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRtIyQiK2p6TFhKISIqNiM+Jkklc3Vtc0c2IjYjIiRuIyQiK0Y4J3k4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRvIyQiKzwsSlhKISIqNiM+Jkklc3Vtc0c2IjYjIiRwIyQiK24qKSl5OCQhIio=NiM+Jkklc3Vtc0c2IjYjIiRxIyQiKyNvI0dYSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRyIyQiKyo+O3o4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRzIyQiK1xjRFhKISIqNiM+Jkklc3Vtc0c2IjYjIiR0IyQiK05JJXo4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR1IyQiKzQhSF85JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR2IyQiKyJbcHo4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR3IyQiK2FGP1hKISIqNiM+Jkklc3Vtc0c2IjYjIiR4IyQiK1piKno4JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR5IyQiK3dvPFhKISIqNiM+Jkklc3Vtc0c2IjYjIiR6IyQiK1Q3LVFKISIqNiM+Jkklc3Vtc0c2IjYjIiQhRyQiK204OlhKISIqNiM+Jkklc3Vtc0c2IjYjIiQiRyQiK3FsL1FKISIqNiM+Jkklc3Vtc0c2IjYjIiQjRyQiKztpN1hKISIqNiM+Jkklc3Vtc0c2IjYjIiQkRyQiK1U6MlFKISIqNiM+Jkklc3Vtc0c2IjYjIiQlRyQiKz45NVhKISIqNiM+Jkklc3Vtc0c2IjYjIiQmRyQiK2xoNFFKISIqNiM+Jkklc3Vtc0c2IjYjIiQnRyQiK29wMlhKISIqNiM+Jkklc3Vtc0c2IjYjIiQoRyQiK1kvN1FKISIqNiM+Jkklc3Vtc0c2IjYjIiQpRyQiK2JHMFhKISIqNiM+Jkklc3Vtc0c2IjYjIiQqRyQiKyNSVyJRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQhSCQiK3UhSF05JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQiSCQiKzYhbyJRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQjSCQiKz1jK1hKISIqNiM+Jkklc3Vtc0c2IjYjIiQkSCQiKzM4PlFKISIqNiM+Jkklc3Vtc0c2IjYjIiQlSCQiK3pDKVw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQmSCQiKypHOSNRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQnSCQiK18nZlw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQoSCQiK2pwQlFKISIqNiM+Jkklc3Vtc0c2IjYjIiQpSCQiK0pyJFw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQqSCQiK04kZiNRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQrJCQiKzRcIlw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQsJCQiKzU5R1FKISIqNiM+Jkklc3Vtc0c2IjYjIiQtJCQiKyEpSCpbOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQuJCQiKyU+LiRRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQvJCQiK1E4KFs5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQwJCQiKyRwQyRRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQxJCQiK3kqXFs5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQyJCQiKzhmTVFKISIqNiM+Jkklc3Vtc0c2IjYjIiQzJCQiKyYqKUdbOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQ0JCQiK2ZvT1FKISIqNiM+Jkklc3Vtc0c2IjYjIiQ1JCQiKyQzM1s5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ2JCQiK1B2UVFKISIqNiM+Jkklc3Vtc0c2IjYjIiQ3JCQiK1B2eVdKISIqNiM+Jkklc3Vtc0c2IjYjIiQ4JCQiK196U1FKISIqNiM+Jkklc3Vtc0c2IjYjIiQ5JCQiK19zd1dKISIqNiM+Jkklc3Vtc0c2IjYjIiQ6JCQiKzMiRyVRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ7JCQiK0JzdVdKISIqNiM+Jkklc3Vtc0c2IjYjIiQ8JCQiKzUhWyVRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ9JCQiK1h1c1dKISIqNiM+Jkklc3Vtc0c2IjYjIiQ+JCQiK2t3WVFKISIqNiM+Jkklc3Vtc0c2IjYjIiQ/JCQiKzl6cVdKISIqNiM+Jkklc3Vtc0c2IjYjIiRAJCQiK3VxW1FKISIqNiM+Jkklc3Vtc0c2IjYjIiRBJCQiK0MnKW9XSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRCJCQiK1dpXVFKISIqNiM+Jkklc3Vtc0c2IjYjIiRDJCQiK3MmcFk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiREJCQiK3peX1FKISIqNiM+Jkklc3Vtc0c2IjYjIiRFJCQiK2AybFdKISIqNiM+Jkklc3Vtc0c2IjYjIiRGJCQiKyQpUWFRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRHJCQiK2pAaldKISIqNiM+Jkklc3Vtc0c2IjYjIiRIJCQiK2dCY1FKISIqNiM+Jkklc3Vtc0c2IjYjIiRJJCQiKyh6OFk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRKJCQiKzkxZVFKISIqNiM+Jkklc3Vtc0c2IjYjIiRLJCQiK19jZldKISIqNiM+Jkklc3Vtc0c2IjYjIiRMJCQiK14nKWZRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRNJCQiK0N4ZFdKISIqNiM+Jkklc3Vtc0c2IjYjIiROJCQiK3NraFFKISIqNiM+Jkklc3Vtc0c2IjYjIiRPJCQiKzMrY1dKISIqNiM+Jkklc3Vtc0c2IjYjIiRQJCQiKyMzTSdRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRRJCQiKyxEYVdKISIqNiM+Jkklc3Vtc0c2IjYjIiRSJCQiKyZbXidRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRTJCQiKytfX1dKISIqNiM+Jkklc3Vtc0c2IjYjIiRUJCQiKyZvbydRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRVJCQiKywiM1g5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRWJCQiKyZvJm9RSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRXJCQiKys3XFdKISIqNiM+Jkklc3Vtc0c2IjYjIiRYJCQiKylbLShRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRZJCQiKyVcdVc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRaJCQiKyk0PihRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRbJCQiK3p6WFdKISIqNiM+Jkklc3Vtc0c2IjYjIiRcJCQiKz1idFFKISIqNiM+Jkklc3Vtc0c2IjYjIiRdJCQiK187V1dKISIqNiM+Jkklc3Vtc0c2IjYjIiReJCQiK188dlFKISIqNiM+Jkklc3Vtc0c2IjYjIiRfJCQiKzZiVVdKISIqNiM+Jkklc3Vtc0c2IjYjIiRgJCQiKy15d1FKISIqNiM+Jkklc3Vtc0c2IjYjIiRhJCQiK14mNFc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRiJCQiK3NPeVFKISIqNiM+Jkklc3Vtc0c2IjYjIiRjJCQiK3FQUldKISIqNiM+Jkklc3Vtc0c2IjYjIiRkJCQiK2skKnpRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRlJCQiK2wieVY5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRmJCQiKyQpWyIpUUohIio=NiM+Jkklc3Vtc0c2IjYjIiRnJCQiK0xGT1dKISIqNiM+Jkklc3Vtc0c2IjYjIiRoJCQiK0ktJClRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRpJCQiK3J1TVdKISIqNiM+Jkklc3Vtc0c2IjYjIiRqJCQiKzNhJSlRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRrJCQiK3dCTFdKISIqNiM+Jkklc3Vtc0c2IjYjIiRsJCQiKz8vJylRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRtJCQiK1l1SldKISIqNiM+Jkklc3Vtc0c2IjYjIiRuJCQiK3BfKClRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRvJCQiK3hFSVdKISIqNiM+Jkklc3Vtc0c2IjYjIiRwJCQiK2QqKikpUUohIio=NiM+Jkklc3Vtc0c2IjYjIiRxJCQiK28hKUdXSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRyJCQiKylbLypRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRzJCQiKztPRldKISIqNiM+Jkklc3Vtc0c2IjYjIiR0JCQiK2spPSpRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiR1JCQiKz0kZlU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR2JCQiKyczTCpRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiR3JCQiK3JeQ1dKISIqNiM+Jkklc3Vtc0c2IjYjIiR4JCQiK2VyJSpRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiR5JCQiK3U2QldKISIqNiM+Jkklc3Vtc0c2IjYjIiR6JCQiKyMzaCpRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQhUSQiK0N0QFdKISIqNiM+Jkklc3Vtc0c2IjYjIiQiUSQiK2dbKCpRSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQjUSQiKz1PP1dKISIqNiM+Jkklc3Vtc0c2IjYjIiQkUSQiKyVcKSkqUUohIio=NiM+Jkklc3Vtc0c2IjYjIiQlUSQiK2ErPldKISIqNiM+Jkklc3Vtc0c2IjYjIiQmUSQiKygpPitSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQnUSQiK0ptPFdKISIqNiM+Jkklc3Vtc0c2IjYjIiQoUSQiK1RgLFJKISIqNiM+Jkklc3Vtc0c2IjYjIiQpUSQiK1lMO1dKISIqNiM+Jkklc3Vtc0c2IjYjIiQqUSQiK2UmRyFSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQhUiQiKyg+XVQ5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQiUiQiK1M7L1JKISIqNiM+Jkklc3Vtc0c2IjYjIiQjUiQiKyI9UFQ5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQkUiQiKyplYSFSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQlUiQiKyhIQ1Q5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQmUiQiKzJ1MVJKISIqNiM+Jkklc3Vtc0c2IjYjIiQnUiQiK1Y6NldKISIqNiM+Jkklc3Vtc0c2IjYjIiQoUiQiKyc0ITNSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQpUiQiKzwqKTRXSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQqUiQiK2ZFNFJKISIqNiM+Jkklc3Vtc0c2IjYjIiQrJSQiKzxrM1dKISIqNiM+Jkklc3Vtc0c2IjYjIiQsJSQiKyg0MCJSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQtJSQiK1RTMldKISIqNiM+Jkklc3Vtc0c2IjYjIiQuJSQiKzd1NlJKISIqNiM+Jkklc3Vtc0c2IjYjIiQvJSQiKyl5aFM5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQwJSQiKzEnSCJSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQxJSQiK2InXFM5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQyJSQiKyFvVCJSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQzJSQiK1R3LldKISIqNiM+Jkklc3Vtc0c2IjYjIiQ0JSQiK09POlJKISIqNiM+Jkklc3Vtc0c2IjYjIiQ1JSQiK1ZkLVdKISIqNiM+Jkklc3Vtc0c2IjYjIiQ2JSQiK3dhO1JKISIqNiM+Jkklc3Vtc0c2IjYjIiQ3JSQiK2hSLFdKISIqNiM+Jkklc3Vtc0c2IjYjIiQ4JSQiKy1zPFJKISIqNiM+Jkklc3Vtc0c2IjYjIiQ5JSQiKyNILVM5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ6JSQiKzkpKT1SSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ7JSQiK04yKlI5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ8JSQiKzsuP1JKISIqNiM+Jkklc3Vtc0c2IjYjIiQ9JSQiKypHelI5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ+JSQiKzQ8QFJKISIqNiM+Jkklc3Vtc0c2IjYjIiQ/JSQiK196J1I5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRAJSQiKyUqSEFSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRBJSQiK0FuJlI5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRCJSQiK3NUQlJKISIqNiM+Jkklc3Vtc0c2IjYjIiRDJSQiKyhmWFI5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiREJSQiK1dfQ1JKISIqNiM+Jkklc3Vtc0c2IjYjIiRFJSQiK3dYJFI5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRGJSQiKzhpRFJKISIqNiM+Jkklc3Vtc0c2IjYjIiRHJSQiK2VPI1I5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRIJSQiKyIzbiNSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRJJSQiK1VHIlI5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRKJSQiK1t5RlJKISIqNiM+Jkklc3Vtc0c2IjYjIiRLJSQiK0RAIVI5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRMJSQiKzomKUdSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRNJSQiKzI6KlE5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiROJSQiKyUzKkhSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRPJSQiKyYpNClROSQhIio=NiM+Jkklc3Vtc0c2IjYjIiRQJSQiK2MmNCRSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRRJSQiK2YwKFE5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRSJSQiK0wqPiRSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRTJSQiK0ctJ1E5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRUJSQiKzwtTFJKISIqNiM+Jkklc3Vtc0c2IjYjIiRVJSQiKyIqKlxROSQhIio=NiM+Jkklc3Vtc0c2IjYjIiRWJSQiKzMvTVJKISIqNiM+Jkklc3Vtc0c2IjYjIiRXJSQiK1kpUlE5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRYJSQiKzMwTlJKISIqNiM+Jkklc3Vtc0c2IjYjIiRZJSQiKyJ6SFE5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRaJSQiKzwwT1JKISIqNiM+Jkklc3Vtc0c2IjYjIiRbJSQiK0UpPlE5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRcJSQiK1EvUFJKISIqNiM+Jkklc3Vtc0c2IjYjIiRdJSQiK10qNFE5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiReJSQiK3ItUVJKISIqNiM+Jkklc3Vtc0c2IjYjIiRfJSQiK2gsIVE5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRgJSQiKz0rUlJKISIqNiM+Jkklc3Vtc0c2IjYjIiRhJSQiK2UvelZKISIqNiM+Jkklc3Vtc0c2IjYjIiRiJSQiK3onKlJSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRjJSQiK1MzeVZKISIqNiM+Jkklc3Vtc0c2IjYjIiRkJSQiK2IjNCVSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRlJSQiKzA4eFZKISIqNiM+Jkklc3Vtc0c2IjYjIiRmJSQiK1soPSVSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRnJSQiK2A9d1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiRoJSQiK2YiRyVSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRpJSQiKyRbX1A5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRqJSQiKylbUCVSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRrJSQiKyQ+VlA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRsJSQiK1FuV1JKISIqNiM+Jkklc3Vtc0c2IjYjIiRtJSQiKyQpUnRWSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRuJSQiKzNmWFJKISIqNiM+Jkklc3Vtc0c2IjYjIiRvJSQiK15bc1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiRwJSQiKytdWVJKISIqNiM+Jkklc3Vtc0c2IjYjIiRxJSQiKyh6OlA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRyJSQiKzpTWlJKISIqNiM+Jkklc3Vtc0c2IjYjIiRzJSQiKz5vcVZKISIqNiM+Jkklc3Vtc0c2IjYjIiR0JSQiK2FIW1JKISIqNiM+Jkklc3Vtc0c2IjYjIiR1JSQiKzx6cFZKISIqNiM+Jkklc3Vtc0c2IjYjIiR2JSQiKz09XFJKISIqNiM+Jkklc3Vtc0c2IjYjIiR3JSQiKyE0Km9WSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiR4JSQiKzMxXVJKISIqNiM+Jkklc3Vtc0c2IjYjIiR5JSQiK08ub1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiR6JSQiK0QkNCZSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQhWyQiK2M7blZKISIqNiM+Jkklc3Vtc0c2IjYjIiQiWyQiK3F6XlJKISIqNiM+Jkklc3Vtc0c2IjYjIiQjWyQiK1tJbVZKISIqNiM+Jkklc3Vtc0c2IjYjIiQkWyQiK1ZsX1JKISIqNiM+Jkklc3Vtc0c2IjYjIiQlWyQiKzVYbFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQmWyQiK1ldYFJKISIqNiM+Jkklc3Vtc0c2IjYjIiQnWyQiK1Zna1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiQoWyQiK3pNYVJKISIqNiM+Jkklc3Vtc0c2IjYjIiQpWyQiK1h3alZKISIqNiM+Jkklc3Vtc0c2IjYjIiQqWyQiK1Y9YlJKISIqNiM+Jkklc3Vtc0c2IjYjIiQhXCQiKzokSE85JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQiXCQiK1IsY1JKISIqNiM+Jkklc3Vtc0c2IjYjIiQjXCQiK2A1aVZKISIqNiM+Jkklc3Vtc0c2IjYjIiQkXCQiK28kbyZSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQlXCQiK2RHaFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQmXCQiK0lsZFJKISIqNiM+Jkklc3Vtc0c2IjYjIiQnXCQiK0ZaZ1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiQoXCQiK0VZZVJKISIqNiM+Jkklc3Vtc0c2IjYjIiQpXCQiK2ltZlZKISIqNiM+Jkklc3Vtc0c2IjYjIiQqXCQiK2VFZlJKISIqNiM+Jkklc3Vtc0c2IjYjIiQrJiQiK2knKWVWSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQsJiQiK0UxZ1JKISIqNiM+Jkklc3Vtc0c2IjYjIiQtJiQiK0UyZVZKISIqNiM+Jkklc3Vtc0c2IjYjIiQuJiQiK0omMydSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQvJiQiK19HZFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQwJiQiK3RqaFJKISIqNiM+Jkklc3Vtc0c2IjYjIiQxJiQiK1NdY1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiQyJiQiK2BUaVJKISIqNiM+Jkklc3Vtc0c2IjYjIiQzJiQiKyFIZE45JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ0JiQiK3Q9alJKISIqNiM+Jkklc3Vtc0c2IjYjIiQ1JiQiKywnXE45JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ2JiQiK0wmUidSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ3JiQiK3M+YVZKISIqNiM+Jkklc3Vtc0c2IjYjIiQ4JiQiK0xya1JKISIqNiM+Jkklc3Vtc0c2IjYjIiQ5JiQiKy1XYFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQ6JiQiK3VZbFJKISIqNiM+Jkklc3Vtc0c2IjYjIiQ7JiQiKyIqb19WSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ8JiQiK2RAbVJKISIqNiM+Jkklc3Vtc0c2IjYjIiQ9JiQiK1ElPk45JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ+JiQiKyNlcCdSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ/JiQiK1Q/XlZKISIqNiM+Jkklc3Vtc0c2IjYjIiRAJiQiK11wblJKISIqNiM+Jkklc3Vtc0c2IjYjIiRBJiQiKyxaXVZKISIqNiM+Jkklc3Vtc0c2IjYjIiRCJiQiK2lVb1JKISIqNiM+Jkklc3Vtc0c2IjYjIiRDJiQiKzx1XFZKISIqNiM+Jkklc3Vtc0c2IjYjIiREJiQiKz06cFJKISIqNiM+Jkklc3Vtc0c2IjYjIiRFJiQiKyk9IVxWSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRGJiQiKz4oKXBSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRHJiQiKzlJW1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiRIJiQiK21lcVJKISIqNiM+Jkklc3Vtc0c2IjYjIiRJJiQiKyUqZVpWSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRKJiQiK2ZIclJKISIqNiM+Jkklc3Vtc0c2IjYjIiRLJiQiK0cpb005JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRMJiQiKysrc1JKISIqNiM+Jkklc3Vtc0c2IjYjIiRNJiQiKzo9WVZKISIqNiM+Jkklc3Vtc0c2IjYjIiROJiQiKykpcHNSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRPJiQiK2FbWFZKISIqNiM+Jkklc3Vtc0c2IjYjIiRQJiQiK0NSdFJKISIqNiM+Jkklc3Vtc0c2IjYjIiRRJiQiK1d6V1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiRSJiQiKzMzdVJKISIqNiM+Jkklc3Vtc0c2IjYjIiRTJiQiKyczVE05JCEiKg==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NiM+Jkklc3Vtc0c2IjYjIiRkJiQiK1owISlSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRlJiQiK286UVZKISIqNiM+Jkklc3Vtc0c2IjYjIiRmJiQiK1twISlSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRnJiQiKyI+dkw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRoJiQiKy5MIilSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRpJiQiK2Ypb0w5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRqJiQiKzgnPilSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRrJiQiK3JET1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiRsJiQiK3llIylSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRtJiQiK0dqTlZKISIqNiM+Jkklc3Vtc0c2IjYjIiRuJiQiKyo0SylSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRvJiQiK0gsTlZKISIqNiM+Jkklc3Vtc0c2IjYjIiRwJiQiK3cjUSlSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRxJiQiK3RSTVZKISIqNiM+Jkklc3Vtc0c2IjYjIiRyJiQiKzVXJSlSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRzJiQiK2d5TFZKISIqNiM+Jkklc3Vtc0c2IjYjIiR0JiQiKy0wJilSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiR1JiQiKyF6Skw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR2JiQiK15sJilSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiR3JiQiK2lkS1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiR4JiQiK2ZEJylSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiR5JiQiK3coPkw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR6JiQiK0QmbylSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQhZSQiK0pRSlZKISIqNiM+Jkklc3Vtc0c2IjYjIiQiZSQiK11XKClSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQjZSQiK0V6SVZKISIqNiM+Jkklc3Vtc0c2IjYjIiQkZSQiK00uKSlSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQlZSQiK2k/SVZKISIqNiM+Jkklc3Vtc0c2IjYjIiQmZSQiK3loKSlSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQnZSQiK1FpSFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQoZSQiKyQpPiopUkohIio=NiM+Jkklc3Vtc0c2IjYjIiQpZSQiK2EvSFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQqZSQiK1t4KilSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQhZiQiKzNaR1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiQiZiQiK3VNISpSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQjZiQiKywheks5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQkZiQiK2giNCpSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQlZiQiK0xMRlZKISIqNiM+Jkklc3Vtc0c2IjYjIiQmZiQiKzZbIipSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQnZiQiKy54RVZKISIqNiM+Jkklc3Vtc0c2IjYjIiQoZiQiK0IvIypSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQpZiQiKzZARVZKISIqNiM+Jkklc3Vtc0c2IjYjIiQqZiQiKykqZiMqUkohIio=NiM+Jkklc3Vtc0c2IjYjIiQrJyQiK2NsRFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQsJyQiK046JCpSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQtJyQiK1A1RFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQuJyQiK05xJCpSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQvJyQiK2FiQ1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiQwJyQiKypcVSpSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQxJyQiKzMsQ1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiQyJyQiK0Z6JSpSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQzJyQiKylwTUs5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ0JyQiKz9MJipSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ1JyQiK0IkSEs5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ2JyQiK3gnZSpSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ3JyQiKyQpUkFWSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ4JyQiKyoqUicqUkohIio=NiM+Jkklc3Vtc0c2IjYjIiQ5JyQiK3knPUs5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ6JyQiKyhHcCpSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ7JyQiKzJNQFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQ8JyQiK1RYKCpSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ9JyQiK3IiM0s5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ+JyQiK2goeipSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ/JyQiK29IP1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiRAJyQiK1pcKSpSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRBJyQiKyl6KD5WSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRCJyQiKyssKipSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRDJyQiK2lFPlZKISIqNiM+Jkklc3Vtc0c2IjYjIiREJyQiKz9fKipSSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRFJyQiK2V2PVZKISIqNiM+Jkklc3Vtc0c2IjYjIiRGJyQiKzIuK1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRHJyQiKyhbIz1WSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRIJyQiK2lgK1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRJJyQiK1t1PFZKISIqNiM+Jkklc3Vtc0c2IjYjIiRKJyQiKyZRNSs5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRLJyQiK1NDPFZKISIqNiM+Jkklc3Vtc0c2IjYjIiRMJyQiK3dgLFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRNJyQiK2t1O1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiROJyQiK08uLVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRPJyQiKz9EO1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiRQJyQiK2xfLVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRRJyQiKzF3OlZKISIqNiM+Jkklc3Vtc0c2IjYjIiRSJyQiK2osLlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRTJyQiK0NGOlZKISIqNiM+Jkklc3Vtc0c2IjYjIiRUJyQiK0pdLlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRVJyQiK3J5OVZKISIqNiM+Jkklc3Vtc0c2IjYjIiRWJyQiK28pUis5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRXJyQiK1xJOVZKISIqNiM+Jkklc3Vtc0c2IjYjIiRYJyQiK3dZL1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRZJyQiK2QjUUo5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRaJyQiK2ElXCs5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRbJyQiKyVcTEo5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRcJyQiKy1VMFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRdJyQiK2coR0o5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiReJyQiK0AqZSs5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRfJyQiK2JTN1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiRgJyQiKzZPMVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRhJyQiK3okPko5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRiJyQiK3Qjbys5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRjJyQiK0paNlZKISIqNiM+Jkklc3Vtc0c2IjYjIiRkJyQiKzFIMlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRlJyQiKzcsNlZKISIqNiM+Jkklc3Vtc0c2IjYjIiRmJyQiKzd2MlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRnJyQiK0BiNVZKISIqNiM+Jkklc3Vtc0c2IjYjIiRoJyQiKyozIzNTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRpJyQiK2Q0NVZKISIqNiM+Jkklc3Vtc0c2IjYjIiRqJyQiK1JtM1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRrJyQiK0BrNFZKISIqNiM+Jkklc3Vtc0c2IjYjIiRsJyQiK2k2NFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRtJyQiKzc+NFZKISIqNiM+Jkklc3Vtc0c2IjYjIiRuJyQiK2RjNFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRvJyQiK0l1M1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiRwJyQiK0UsNVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRxJyQiK3ZIM1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiRyJyQiK29YNVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRzJyQiK1kmeUk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR0JyQiKyUpKjMsOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiR1JyQiK1ZUMlZKISIqNiM+Jkklc3Vtc0c2IjYjIiR2JyQiK3RMNlNKISIqNiM+Jkklc3Vtc0c2IjYjIiR3JyQiK20ocEk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR4JyQiK094NlNKISIqNiM+Jkklc3Vtc0c2IjYjIiR5JyQiKzphMVZKISIqNiM+Jkklc3Vtc0c2IjYjIiR6JyQiK3U/N1NKISIqNiM+Jkklc3Vtc0c2IjYjIiQhbyQiKyozaEk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQibyQiKydRRSw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQjbyQiKyp5Y0k5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQkbyQiK3QxOFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQlbyQiKzlEMFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQmbyQiK09cOFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQnbyQiK2sjW0k5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQobyQiK3QiUiw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQpbyQiK1JTL1ZKISIqNiM+Jkklc3Vtc0c2IjYjIiQqbyQiKydRViw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQhcCQiK1EpUkk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQicCQiK3Z2OVNKISIqNiM+Jkklc3Vtc0c2IjYjIiQjcCQiK2ljLlZKISIqNiM+Jkklc3Vtc0c2IjYjIiQkcCQiK1M8OlNKISIqNiM+Jkklc3Vtc0c2IjYjIiQlcCQiKzU6LlZKISIqNiM+Jkklc3Vtc0c2IjYjIiQmcCQiKyIpZTpTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQncCQiKyJRRkk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQocCQiKygqKmYsOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQpcCQiK3ZLLVZKISIqNiM+Jkklc3Vtc0c2IjYjIiQqcCQiKyE0ayw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQrKCQiKyQ+Pkk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQsKCQiK2cibyw5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQtKCQiK05eLFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQuKCQiKzJBPFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQvKCQiKys2LFZKISIqNiM+Jkklc3Vtc0c2IjYjIiQwKCQiK0ppPFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQxKCQiKygzMkk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQyKCQiK0stPVNKISIqNiM+Jkklc3Vtc0c2IjYjIiQzKCQiKyg0Lkk5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ0KCQiKzVVPVNKISIqNiM+Jkklc3Vtc0c2IjYjIiQ1KCQiK0giKipIOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQ2KCQiK20iKT1TSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ3KCQiKyU9JipIOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQ4KCQiKyxAPlNKISIqNiM+Jkklc3Vtc0c2IjYjIiQ5KCQiK2g3Kkg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ6KCQiKzhnPlNKISIqNiM+Jkklc3Vtc0c2IjYjIiQ7KCQiK2d0KUg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ8KCQiKy8qKj5TSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ9KCQiKyJbJClIOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQ+KCQiK3RQP1NKISIqNiM+Jkklc3Vtc0c2IjYjIiQ/KCQiK0Inekg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRAKCQiKz93P1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRBKCQiKyd5dkg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRCKCQiK1k5QFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRDKCQiK3E+KEg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiREKCQiK11fQFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRFKCQiK3Yib0g5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRGKCQiK00hPi05JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRHKCQiKyxXJ0g5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRIKCQiKyh6QS05JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRJKCQiK1sxJ0g5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRKKCQiK1NsQVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRLKCQiKzpwJkg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRMKCQiK2ktQlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRNKCQiKy5LJkg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiROKCQiK2tSQlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRPKCQiKzYmXEg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRQKCQiK1p3QlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRRKCQiK1JlJUg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRSKCQiKzQ4Q1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRTKCQiKyg9VUg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRUKCQiK19cQ1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRVKCQiK2ImUUg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRWKCQiK3YmWy05JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRXKCQiK1VcJEg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRYKCQiK3pARFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRZKCQiK1s4JEg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRaKCQiK2pkRFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRbKCQiK3V4I0g5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRcKCQiK0ckZi05JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRdKCQiKz1VI0g5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiReKCQiK3VHRVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRfKCQiKyJvP0g5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRgKCQiKyxrRVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRhKCQiK2pyIkg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRiKCQiKzUqcC05JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRjKCQiK2tPIkg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRkKCQiKytNRlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRlKCQiKyQ9NUg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRmKCQiK3NvRlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRnKCQiK0BuIUg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRoKCQiK0UuR1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRpKCQiK3hLIUg5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRqKCQiK2lQR1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRrKCQiK14pKipHOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiRsKCQiKyE9KEdTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRtKCQiK1ZrKkc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRuKCQiKyFlIUhTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRvKCQiK19JKkc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRwKCQiK2lSSFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRxKCQiK3onKilHOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiRyKCQiK0V0SFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRzKCQiK0JqKUc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR0KCQiK3QxSVNKISIqNiM+Jkklc3Vtc0c2IjYjIiR1KCQiKyUpSClHOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiR2KCQiKy5TSVNKISIqNiM+Jkklc3Vtc0c2IjYjIiR3KCQiK2onekc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR4KCQiKzt0SVNKISIqNiM+Jkklc3Vtc0c2IjYjIiR5KCQiK2ZqKEc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR6KCQiKzcxSlNKISIqNiM+Jkklc3Vtc0c2IjYjIiQheSQiK3NJKEc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQieSQiKyIqUUpTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQjeSQiKy0pcEc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQkeSQiK2FySlNKISIqNiM+Jkklc3Vtc0c2IjYjIiQleSQiK1xsJ0c5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQmeSQiKysvS1NKISIqNiM+Jkklc3Vtc0c2IjYjIiQneSQiKzdMJ0c5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQoeSQiK0hPS1NKISIqNiM+Jkklc3Vtc0c2IjYjIiQpeSQiKyI0Z0c5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQqeSQiK1VvS1NKISIqNiM+Jkklc3Vtc0c2IjYjIiQheiQiKycpbyZHOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQieiQiK1ErTFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQjeiQiKyhwYEc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQkeiQiKz1LTFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQleiQiK0MwJkc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQmeiQiKyNRTy45JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQneiQiK290JUc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQoeiQiK0omUi45JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQpeiQiK0ZVJUc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQqeiQiK2tFTVNKISIqNiM+Jkklc3Vtc0c2IjYjIiQrKSQiKy02JUc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQsKSQiKyJ5WC45JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQtKSQiKyQqeiRHOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQuKSQiKyQpKVsuOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQvKSQiKyoqWyRHOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQwKSQiK3A+TlNKISIqNiM+Jkklc3Vtc0c2IjYjIiQxKSQiKz89JEc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQyKSQiK1NdTlNKISIqNiM+Jkklc3Vtc0c2IjYjIiQzKSQiK2QoR0c5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ0KSQiKyc0ZS45JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ1KSQiKzRkI0c5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ2KSQiK1A2T1NKISIqNiM+Jkklc3Vtc0c2IjYjIiQ3KSQiK3ZFI0c5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ4KSQiK2lUT1NKISIqNiM+Jkklc3Vtc0c2IjYjIiQ5KSQiK2MnPkc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ6KSQiK3RyT1NKISIqNiM+Jkklc3Vtc0c2IjYjIiQ7KSQiK19tIkc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ8KSQiK3AsUFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQ9KSQiK2pPIkc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ+KSQiK11KUFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQ/KSQiKylvNUc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRAKSQiKzxoUFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRBKSQiK0d4IUc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRCKSQiK3Ehei45JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRDKSQiKyR5L0c5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiREKSQiKzQ/UVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRFKSQiK189IUc5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRGKSQiK01cUVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRHKSQiK04qKXpVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRIKSQiK1d5UVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRJKSQiK0tnelVKISIqNiM+Jkklc3Vtc0c2IjYjIiRKKSQiK1MyUlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRLKSQiK1VKelVKISIqNiM+Jkklc3Vtc0c2IjYjIiRMKSQiK0FPUlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRNKSQiK24telVKISIqNiM+Jkklc3Vtc0c2IjYjIiROKSQiKyJcJ1JTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRPKSQiKzF1eVVKISIqNiM+Jkklc3Vtc0c2IjYjIiRQKSQiK1kkKlJTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRRKSQiK2VYeVVKISIqNiM+Jkklc3Vtc0c2IjYjIiRSKSQiKyk9LS85JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRTKSQiK0M8eVVKISIqNiM+Jkklc3Vtc0c2IjYjIiRUKSQiKztdU1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRVKSQiKy4qeUY5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRWKSQiK0l5U1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRXKSQiKyY0d0Y5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRYKSQiK0oxVFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRZKSQiKyxMeFVKISIqNiM+Jkklc3Vtc0c2IjYjIiRaKSQiKz5NVFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRbKSQiKz8weFVKISIqNiM+Jkklc3Vtc0c2IjYjIiRcKSQiKyU+Oy85JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRdKSQiK194d1VKISIqNiM+Jkklc3Vtc0c2IjYjIiReKSQiK2MqPS85JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRfKSQiKygqXHdVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRgKSQiKzA8VVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRhKSQiK2JBd1VKISIqNiM+Jkklc3Vtc0c2IjYjIiRiKSQiK1RXVVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRjKSQiK0UmZkY5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRkKSQiK2tyVVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRlKSQiKzRvdlVKISIqNiM+Jkklc3Vtc0c2IjYjIiRmKSQiK3YpSC85JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRnKSQiKzBUdlVKISIqNiM+Jkklc3Vtc0c2IjYjIiRoKSQiK3REVlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRpKSQiKzk5dlVKISIqNiM+Jkklc3Vtc0c2IjYjIiRqKSQiK2ZfVlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRrKSQiK04oW0Y5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRsKSQiK0t6VlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRtKSQiK29ndVVKISIqNiM+Jkklc3Vtc0c2IjYjIiRuKSQiKyNmUy85JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRvKSQiKzhNdVVKISIqNiM+Jkklc3Vtc0c2IjYjIiRwKSQiK1NLV1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRxKSQiK3EydVVKISIqNiM+Jkklc3Vtc0c2IjYjIiRyKSQiK3dlV1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRzKSQiK1MiUUY5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR0KSQiKywmWy85JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR1KSQiK0FidFVKISIqNiM+Jkklc3Vtc0c2IjYjIiR2KSQiKzg2WFNKISIqNiM+Jkklc3Vtc0c2IjYjIiR3KSQiKztIdFVKISIqNiM+Jkklc3Vtc0c2IjYjIiR4KSQiKzlQWFNKISIqNiM+Jkklc3Vtc0c2IjYjIiR5KSQiK0EudFVKISIqNiM+Jkklc3Vtc0c2IjYjIiR6KSQiKy5qWFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQhKSkkIitTeHNVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQiKSkkIishKSllLzkkISIqNiM+Jkklc3Vtc0c2IjYjIiQjKSkkIitwXnNVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQkKSkkIitYOVlTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQlKSkkIis1RXNVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQmKSkkIisqKlJZU0ohIio=NiM+Jkklc3Vtc0c2IjYjIiQnKSkkIitpK3NVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQoKSkkIitUbFlTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQpKSkkIitFdnJVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQqKSkkIitzIXAvOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQhKikkIissXXJVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQiKikkIisiZnIvOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQjKikkIisoWzdGOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQkKikkIisqNHUvOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQlKikkIismKSo0RjkkISIqNiM+Jkklc3Vtc0c2IjYjIiQmKikkIisnZncvOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQnKikkIislXDJGOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQoKikkIisjM3ovOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQpKikkIis5XXFVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQqKikkIitkOltTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQrKiQiK1hEcVVKISIqNiM+Jkklc3Vtc0c2IjYjIiQsKiQiKz9TW1NKISIqNiM+Jkklc3Vtc0c2IjYjIiQtKiQiKyczK0Y5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiQuKiQiK3NrW1NKISIqNiM+Jkklc3Vtc0c2IjYjIiQvKiQiK1F3cFVKISIqNiM+Jkklc3Vtc0c2IjYjIiQwKiQiKzkqKVtTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQxKiQiKy1fcFVKISIqNiM+Jkklc3Vtc0c2IjYjIiQyKiQiK1g4XFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQzKiQiK3dGcFVKISIqNiM+Jkklc3Vtc0c2IjYjIiQ0KiQiK21QXFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQ1KiQiK2gucFVKISIqNiM+Jkklc3Vtc0c2IjYjIiQ2KiQiK3doXFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQ3KiQiK2R6b1VKISIqNiM+Jkklc3Vtc0c2IjYjIiQ4KiQiK3cmKVxTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQ5KiQiK2pib1VKISIqNiM+Jkklc3Vtc0c2IjYjIiQ6KiQiK2s0XVNKISIqNiM+Jkklc3Vtc0c2IjYjIiQ7KiQiK3pKb1VKISIqNiM+Jkklc3Vtc0c2IjYjIiQ8KiQiK1VMXVNKISIqNiM+Jkklc3Vtc0c2IjYjIiQ9KiQiKzAzb1VKISIqNiM+Jkklc3Vtc0c2IjYjIiQ+KiQiKzVkXVNKISIqNiM+Jkklc3Vtc0c2IjYjIiQ/KiQiK1UleUU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRAKiQiK28hMzA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRBKiQiKyE0d0U5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRCKiQiKzsvXlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRDKiQiK1tQblVKISIqNiM+Jkklc3Vtc0c2IjYjIiREKiQiK2FGXlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRFKiQiKzs5blVKISIqNiM+Jkklc3Vtc0c2IjYjIiRGKiQiKyMzOjA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRHKiQiKyU0cEU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRIKiQiKyt1XlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRJKiQiKyN5bUU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRKKiQiKzIoPjA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRLKiQiK3pXbVVKISIqNiM+Jkklc3Vtc0c2IjYjIiRMKiQiKy8/X1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRNKiQiKyc9aUU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiROKiQiKyNIQzA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRPKiQiKy4qZkU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRQKiQiK3FsX1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRRKiQiK0l3bFVKISIqNiM+Jkklc3Vtc0c2IjYjIiRSKiQiK1EpRzA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRTKiQiK21gbFVKISIqNiM+Jkklc3Vtc0c2IjYjIiRUKiQiKyc0SjA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRVKiQiKzdKbFVKISIqNiM+Jkklc3Vtc0c2IjYjIiRWKiQiK1hMYFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRXKiQiK24zbFVKISIqNiM+Jkklc3Vtc0c2IjYjIiRYKiQiKyVlTjA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRZKiQiK0snW0U5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRaKiQiKzl5YFNKISIqNiM+Jkklc3Vtc0c2IjYjIiRbKiQiKzJra1VKISIqNiM+Jkklc3Vtc0c2IjYjIiRcKiQiK04rYVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRdKiQiKyI+V0U5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiReKiQiK1pBYVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRfKiQiKyYpPmtVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiRgKiQiK11XYVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRhKiQiKyl5UkU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRiKiQiK1ZtYVNKISIqNiM+Jkklc3Vtc0c2IjYjIiRjKiQiKyt3alVKISIqNiM+Jkklc3Vtc0c2IjYjIiRkKiQiK0YpWzA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRlKiQiK0BhalVKISIqNiM+Jkklc3Vtc0c2IjYjIiRmKiQiKy01YlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRnKiQiK15LalVKISIqNiM+Jkklc3Vtc0c2IjYjIiRoKiQiK29KYlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRpKiQiKyE0SkU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRqKiQiK0RgYlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRrKiQiK1EqR0U5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRsKiQiK3N1YlNKISIqNiM+Jkklc3Vtc0c2IjYjIiRtKiQiKyV6RUU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRuKiQiKzYnZjA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiRvKiQiK2dZaVVKISIqNiM+Jkklc3Vtc0c2IjYjIiRwKiQiK1Q8Y1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRxKiQiK01EaVVKISIqNiM+Jkklc3Vtc0c2IjYjIiRyKiQiK2lRY1NKISIqNiM+Jkklc3Vtc0c2IjYjIiRzKiQiKzwvaVVKISIqNiM+Jkklc3Vtc0c2IjYjIiR0KiQiK3VmY1NKISIqNiM+Jkklc3Vtc0c2IjYjIiR1KiQiKzQkPUU5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR2KiQiK3khbzA5JCEiKg==NiM+Jkklc3Vtc0c2IjYjIiR3KiQiKzRpaFVKISIqNiM+Jkklc3Vtc0c2IjYjIiR4KiQiK3QsZFNKISIqNiM+Jkklc3Vtc0c2IjYjIiR5KiQiKz1UaFVKISIqNiM+Jkklc3Vtc0c2IjYjIiR6KiQiK2dBZFNKISIqNiM+Jkklc3Vtc0c2IjYjIiQhKSokIitPP2hVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQiKSokIitSVmRTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQjKSokIitpKjRFOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQkKSokIisza2RTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQlKSokIisnKnlnVUohIio=NiM+Jkklc3Vtc0c2IjYjIiQmKSokIitwJXkwOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQnKSokIitRZWdVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQoKSokIitBMGVTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQpKSokIishei5FOSQhIio=NiM+Jkklc3Vtc0c2IjYjIiQqKSokIituRGVTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQhKiokIitcPGdVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQiKiokIisuWWVTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQjKiokIis7KCpmVUohIio=NiM+Jkklc3Vtc0c2IjYjIiQkKiokIitKbWVTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQlKiokIisjcChmVUohIio=NiM+Jkklc3Vtc0c2IjYjIiQmKiokIiteJyllU0ohIio=NiM+Jkklc3Vtc0c2IjYjIiQnKiokIit3Y2ZVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQoKiokIitqMWZTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQpKiokIitvT2ZVSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiQqKiokIitvRWZTSiEiKg==NiM+Jkklc3Vtc0c2IjYjIiUrNSQiK287ZlVKISIqWith a thousand terms summed up the error is less than NiMqKCIiJSIiIkYlRiUsJiomIiIjRiUiJSs1RiVGJUYlRiUhIiI=, which is equal to evalf(4/(2*1000+1));NiMkIisrMCsqKj4hIzc=Since the odd subscript partial sums are increasing and the even are decreasing we are certain of the first two decimal digits. Unfortunately we are not certain of any more.