ࡱ> KMHIJi  bjbjWW >~==Xh  84!|! l#($:b$b$$777kkkkkkk$MnplQ 76777lxxb$$il<<<7xb$ $k<7k<<Pdl hib$T#U8e0kl0le$q8qTiiJq Zi77<77777ll;T777l7777q777777777 : Apportionment Apportionment is the problem of dividing up a fixed number of things among groups of different sizes. In politics, this takes the form of allocating a limited number of representatives amongst voters. This problem, presumably, is older than the United States, but the best-known ways to solve it have their origins in the problem of assigning each state an appropriate number of representatives in the new Congress when the country was formed. States also face this apportionment problem in defining how to draw districts for state representatives. The apportionment problem comes up in a variety of non-political areas too, though. We face several restrictions in this process: Apportionment rules The things being divided up can exist only in whole numbers. We must use all of the things being divided up, and we cannot use any more. Each group must get at least one of the things being divided up. The number of things assigned to each group should be at least approximately proportional to the population of the group. (Exact proportionality isnt possible because of the whole number requirement, but we should try to be close, and in any case, if Group A is larger than Group B, then Group B shouldnt get more of the things than Group A does.) In terms of the apportionment of the United States House of Representatives, these rules imply: We can only have whole representatives (a state cant have 3.4 representatives) We can only use the (currently) 435 representatives available. If one state gets another representative, another state has to lose one. Every state gets at least one representative The number of representatives each state gets should be approximately proportional to the state population. This way, the number of constituents each representative has should be approximately equal. We will look at four ways of solving the apportionment problem. Three of them (Lowndess method is the exception) have been used at various times to apportion the U.S. Congress, although the method currently in use (the Huntington-Hill method) is significantly more complicated. Hamiltons Method Alexander Hamilton proposed the method that now bears his name. His method was approved by Congress in 1791, but was vetoed by President Washington. It was later adopted in 1852 and used through 1911. He begins by determining, to several decimal places, how many things each group should get. Since he was interested in the question of Congressional representation, well use the language of states and representatives, so he determines how many representatives each state should get. He follows these steps: Hamiltons Method Determine how many people each representative should represent. Do this by dividing the total population of all the states by the total number of representatives. This answer is called the divisor. Divide each states population by the divisor to determine how many representatives it should have. Record this answer to several decimal places. This answer is called the quota. Since we can only allocate whole representatives, Hamilton resolves the whole number problem, as follows: Cut off all the decimal parts of all the quotas (but dont forget what the decimals were). These are called the lower quotas. Add up the remaining whole numbers. This answer will always be less than or equal to the total number of representatives (and the or equal to part happens only in very specific circumstances that are incredibly unlikely to turn up). Assuming that the total from Step 3 was less than the total number of representatives, assign the remaining representatives, one each, to the states whose decimal parts of the quota were largest, until the desired total is reached. Make sure that each state ends up with at least one representative! Note on rounding: Today we have technological advantages that Hamilton (and the others) couldnt even have imagined. Take advantage of them, and keep several decimal places. Example 1 The state of Delaware has three counties: Kent, New Castle, and Sussex. The Delaware state House of Representatives has 41 members. If Delaware wants to divide this representation along county lines (which is not required, but lets pretend they do), lets use Hamiltons method to apportion them. The populations of the counties are as follows (from the 2010 Census): County Population Kent 162,310 New Castle 538,479 Sussex 197,145 Total 897,934 1. First, we determine the divisor: 897,934/41 = 21,900.82927 2. Now we determine each countys quota by dividing the countys population by the divisor: County Population Quota Kent 162,310 7.4111 New Castle 538,479 24.5872 Sussex 197,145 9.0017 Total 897,934 3. Removing the decimal parts of the quotas gives: County Population Quota Initial Kent 162,310 7.4111 7 New Castle 538,479 24.5872 24 Sussex 197,145 9.0017 9 Total 897,934 40 4. We need 41 representatives and this only gives 40. The remaining one goes to the county with the largest decimal part, which is New Castle: County Population Quota Initial Final Kent 162,310 7.4111 7 7 New Castle 538,479 24.5872 24 25 Sussex 197,145 9.0017 9 9 Total 897,934 40 Example 2 Use Hamiltons method to apportion the 75 seats of Rhode Islands House of Representatives among its five counties. County Population Bristol 49,875 Kent 166,158 Newport 82,888 Providence 626,667 Washington 126,979 Total 1,052,567 1. The divisor is 1,052,567/75 = 14,034.22667 2. Determine each countys quota by dividing its population by the divisor: County Population Quota Bristol 49,875 3.5538 Kent 166,158 11.8395 Newport 82,888 5.9061 Providence 626,667 44.6528 Washington 126,979 9.0478 Total 1,052,567 3. Remove the decimal part of each quota: County Population Quota Initial Bristol 49,875 3.5538 3 Kent 166,158 11.8395 11 Newport 82,888 5.9061 5 Providence 626,667 44.6528 44 Washington 126,979 9.0478 9 Total 1,052,567 72 4. We need 75 representatives and we only have 72, so we assign the remaining three, one each, to the three counties with the largest decimal parts, which are Newport, Kent, and Providence: County Population Quota Initial Final Bristol 49,875 3.5538 3 3 Kent 166,158 11.8395 11 12 Newport 82,888 5.9061 5 6 Providence 626,667 44.6528 44 45 Washington 126,979 9.0478 9 9 Total 1,052,567 72 75 Note that even though Bristol Countys decimal part is greater than .5, it isnt big enough to get an additional representative, because three other counties have greater decimal parts. Hamiltons method obeys something called the Quota Rule. The Quota Rule isnt a law of any sort, but just an idea that some people, including Hamilton, think is a good one. Quota Rule The Quota Rule says that the final number of representatives a state gets should be within one of that states quota. Since were dealing with whole numbers for our final answers, that means that each state should either go up to the next whole number above its quota, or down to the next whole number below its quota. Controversy After seeing Hamiltons method, many people find that it makes sense, its not that difficult to use (or, at least, the difficulty comes from the numbers that are involved and the amount of computation thats needed, not from the method), and they wonder why anyone would want another method. The problem is that Hamiltons method is subject to several paradoxes. Three of them happened, on separate occasions, when Hamiltons method was used to apportion the United States House of Representatives. The Alabama Paradox is named for an incident that happened during the apportionment that took place after the 1880 census. (A similar incident happened ten years earlier involving the state of Rhode Island, but the paradox is named after Alabama.) The post-1880 apportionment had been completed, using Hamiltons method and the new population numbers from the census. Then it was decided that because of the countrys growing population, the House of Representatives should be made larger. That meant that the apportionment would need to be done again, still using Hamiltons method and the same 1880 census numbers, but with more representatives. The assumption was that some states would gain another representative and others would stay with the same number they already had (since there werent enough new representatives being added to give one more to every state). The paradox is that Alabama ended up losing a representative in the process, even though no populations were changed and the total number of representatives increased. The New States Paradox happened when Oklahoma became a state in 1907. Oklahoma had enough population to qualify for five representatives in Congress. Those five representatives would need to come from somewhere, though, so five states, presumably, would lose one representative each. That happened, but another thing also happened: Maine gained a representative (from New York). The Population Paradox happened between the apportionments after the census of 1900 and of 1910. In those ten years, Virginias population grew at an average annual rate of 1.07%, while Maines grew at an average annual rate of 0.67%. Virginia started with more people, grew at a faster rate, grew by more people, and ended up with more people than Maine. By itself, that doesnt mean that Virginia should gain representatives or Maine shouldnt, because there are lots of other states involved. But Virginia ended up losing a representative to Maine. Jeffersons Method Thomas Jefferson proposed a different method for apportionment. After Washington vetoed Hamiltons method, Jeffersons method was adopted, and used in Congress from 1791 through 1842. Jefferson, of course, had political reasons for wanting his method to be used rather than Hamiltons. Primarily, his method favors larger states, and his own home state of Virginia was the largest in the country at the time. He would also argue that its the ratio of people to representatives that is the critical thing, and apportionment methods should be based on that. But the paradoxes we saw also provide mathematical reasons for concluding that Hamiltons method isnt so good, and while Jeffersons method might or might not be the best one to replace it, at least we should look for other possibilities. The first steps of Jeffersons method are the same as Hamiltons method. He finds the same divisor and the same quota, and cuts off the decimal parts in the same way, giving a total number of representatives that is less than the required total. The difference is in how Jefferson resolves that difference. He says that since we ended up with an answer that is too small, our divisor must have been too big. He changes the divisor by making it smaller, finding new quotas with the new divisor, cutting off the decimal parts, and looking at the new total, until we find a divisor that produces the required total. Jeffersons Method Determine how many people each representative should represent. Do this by dividing the total population of all the states by the total number of representatives. This answer is called the standard divisor. Divide each states population by the divisor to determine how many representatives it should have. Record this answer to several decimal places. This answer is called the quota. Cut off all the decimal parts of all the quotas (but dont forget what the decimals were). These are the lower quotas. Add up the remaining whole numbers. This answer will always be less than or equal to the total number of representatives. If the total from Step 3 was less than the total number of representatives, reduce the divisor and recalculate the quota and allocation. Continue doing this until the total in Step 3 is equal to the total number of representatives. The divisor we end up using is called the modified divisor or adjusted divisor. Example 3 Well return to Delaware and apply Jeffersons method. We begin, as we did with Hamiltons method, by finding the quotas with the original divisor, 21,900.82927: County Population Quota Initial Kent 162,310 7.4111 7 New Castle 538,479 24.5872 24 Sussex 197,145 9.0017 9 Total 897,934 40 We need 41 representatives, and this divisor gives only 40. We must reduce the divisor until we get 41 representatives. Lets try 21,500 as the divisor: County Population Quota Initial Kent 162,310 7.5493 7 New Castle 538,479 25.0455 25 Sussex 197,145 9.1695 9 Total 897,934 41 This gives us the required 41 representatives, so were done. If we had fewer than 41, wed need to reduce the divisor more. If we had more than 41, wed need to choose a divisor less than the original but greater than the second choice. Notice that with the new, lower divisor, the quota for New Castle County (the largest county in the state) increased by much more than those of Kent County or Sussex County. Example 4 Well apply Jeffersons method for Rhode Island. The original divisor of 14,034.22667 gave these results: County Population Quota Initial Bristol 49,875 3.5538 3 Kent 166,158 11.8395 11 Newport 82,888 5.9061 5 Providence 626,667 44.6528 44 Washington 126,979 9.0478 9 Total 1,052,567 72 We need 75 representatives and we only have 72, so we need to use a smaller divisor. Lets try 13,500: County Population Quota Initial Bristol 49,875 3.6944 3 Kent 166,158 12.3080 12 Newport 82,888 6.1399 6 Providence 626,667 46.4198 46 Washington 126,979 9.4059 9 Total 1,052,567 76 Weve gone too far. We need a divisor thats greater than 13,500 but less than 14,034.22667. Lets try 13,700: County Population Quota Initial Bristol 49,875 3.6405 3 Kent 166,158 12.1283 12 Newport 82,888 6.0502 6 Providence 626,667 45.7421 45 Washington 126,979 9.2685 9 Total 1,052,567 75 This works. Notice, in comparison to Hamiltons method, that although the results were the same, they came about in a different way, and the outcome was almost different. Providence County (the largest) almost went up to 46 representatives before Kent (which is much smaller) got to 12. Although that didnt happen here, it can. Divisor-adjusting methods like Jeffersons are not guaranteed to follow the quota rule! Websters Method Daniel Webster (1782-1852) proposed a method similar to Jeffersons in 1832. It was adopted by Congress in 1842, but replaced by Hamiltons method in 1852. It was then adopted again in 1901. The difference is that Webster rounds the quotas to the nearest whole number rather than dropping the decimal parts. If that doesnt produce the desired results at the beginning, he says, like Jefferson, to adjust the divisor until it does. (In Jeffersons case, at least the first adjustment will always be to make the divisor smaller. That is not always the case with Websters method.) Websters Method Determine how many people each representative should represent. Do this by dividing the total population of all the states by the total number of representatives. This answer is called the standard divisor. Divide each states population by the divisor to determine how many representatives it should have. Record this answer to several decimal places. This answer is called the quota. Round all the quotas to the nearest whole number (but dont forget what the decimals were). Add up the remaining whole numbers. If the total from Step 3 was less than the total number of representatives, reduce the divisor and recalculate the quota and allocation. If the total from step 3 was larger than the total number of representatives, increase the divisor and recalculate the quota and allocation. Continue doing this until the total in Step 3 is equal to the total number of representatives. The divisor we end up using is called the modified divisor or adjusted divisor. Example 5 Again, Delaware, with an initial divisor of 21,900.82927: County Population Quota Initial Kent 162,310 7.4111 7 New Castle 538,479 24.5872 25 Sussex 197,145 9.0017 9 Total 897,934 41 This gives the required total, so were done. Example 6 Again, Rhode Island, with an initial divisor of 14,034.22667: County Population Quota Initial Bristol 49,875 3.5538 4 Kent 166,158 11.8395 12 Newport 82,888 5.9061 6 Providence 626,667 44.6528 45 Washington 126,979 9.0478 9 Total 1,052,567 76 This is too many, so we need to increase the divisor. Lets try 14,100: County Population Quota Initial Bristol 49,875 3.5372 4 Kent 166,158 11.7843 12 Newport 82,888 5.8786 6 Providence 626,667 44.4445 44 Washington 126,979 9.0056 9 Total 1,052,567 75 This works, so were done. Like Jeffersons method, Websters method carries a bias in favor of states with large populations, but rounding the quotas to the nearest whole number greatly reduces this bias. (Notice that Providence County, the largest, is the one that gets a representative trimmed because of the increased quota.) Also like Jeffersons method, Websters method does not always follow the quota rule, but it follows the quota rule much more often than Jeffersons method does. (In fact, if Websters method had been applied to every apportionment of Congress in all of American history, it would have followed the quota rule every single time.) In 1980, two mathematicians, Peyton Young and Mike Balinski, proved what we now call the Balinski-Young Impossibility Theorem. Balinski-Young Impossibility Theorem The Balinski-Young Impossibility Theorem shows that any apportionment method which always follows the quota rule will be subject to the possibility of paradoxes like the Alabama, New States, or Population paradoxes. In other words, we can choose a method that avoids those paradoxes, but only if we are willing to give up the guarantee of following the quota rule. Huntington-Hill Method In 1920, no new apportionment was done, because Congress couldnt agree on the method to be used. They appointed a committee of mathematicians to investigate, and they recommended the Huntington-Hill Method. They continued to use Websters method in 1931, but after a second report recommending Huntington-Hill, it was adopted in 1941 and is the current method of apportionment used in Congress. The Huntington-Hill Method is similar to Websters method, but attempts to minimize the percent differences of how many people each representative will represent. Huntington-Hill Method Determine how many people each representative should represent. Do this by dividing the total population of all the states by the total number of representatives. This answer is called the standard divisor. Divide each states population by the divisor to determine how many representatives it should have. Record this answer to several decimal places. This answer is called the quota. Cut off the decimal part of the quota to obtain the lower quota, which well call n. Compute  EMBED Equation.3 , which is the geometric mean of the lower quota and one value higher. If the quota is larger than the geometric mean, round up the quota; if the quota is smaller than the geometric mean, round down the quota. Add up the resulting whole numbers to get the initial allocation. If the total from Step 4 was less than the total number of representatives, reduce the divisor and recalculate the quota and allocation. If the total from step 4 was larger than the total number of representatives, increase the divisor and recalculate the quota and allocation. Continue doing this until the total in Step 4 is equal to the total number of representatives. The divisor we end up using is called the modified divisor or adjusted divisor. Example 7 Again, Delaware, with an initial divisor of 21,900.82927: County Population Quota Lower Quota Geom Mean Initial Kent 162,310 7.4111 7 7.48 7 New Castle 538,479 24.5872 24 24.49 25 Sussex 197,145 9.0017 9 9.49 9 Total 897,934 41 This gives the required total, so were done. Example 8 Again, Rhode Island, with an initial divisor of 14,034.22667: County Population Quota Lower Quota Geom Mean Initial Bristol 49,875 3.5538 3 3.46 4 Kent 166,158 11.8395 11 11.49 12 Newport 82,888 5.9061 5 5.48 6 Providence 626,667 44.6528 44 44.50 45 Washington 126,979 9.0478 9 9.49 9 Total 1,052,567 76 This is too many, so we need to increase the divisor. Lets try 14,100: County Population Quota Lower Quota Geom Mean Initial Bristol 49,875 3.5372 3 3.46 4 Kent 166,158 11.7843 11 11.49 12 Newport 82,888 5.8786 5 5.48 6 Providence 626,667 44.4445 44 44.50 44 Washington 126,979 9.0056 9 9.49 9 Total 1,052,567 75 This works, so were done. In both these cases, the apportionment produced by the Huntington-Hill method was the same as those from Websters method. Example 9 Consider a small country with 5 states, two of which are much larger than the others. We need to apportion 70 representatives. We will apportion using both Websters method and the Huntington-Hill method.  SHAPE \* MERGEFORMAT  1. The total population is 610,000. Dividing this by the 70 representatives gives the divisor: 8714.286 2. Dividing each states population by the divisor gives the quotas  SHAPE \* MERGEFORMAT  Websters Method 3. Using Websters method, we round each quota to the nearest whole number  SHAPE \* MERGEFORMAT  4. Adding these up, they only total 69 representatives, so we adjust the divisor down. Adjusting the divisor down to 8700 gives an updated allocation totaling 70 representatives  SHAPE \* MERGEFORMAT  Huntington-Hill Method 3. Using the Huntington-Hill method, we round down to find the lower quota, then calculate the geometric mean based on each lower quota. If the quota is less than the geometric mean, we round down; if the quota is more than the geometric mean, we round up.  SHAPE \* MERGEFORMAT  These allocations add up to 70, so were done. Notice that this allocation is different than that produced by Websters method. In this case, state E got the extra seat instead of state A. Lowndes Method William Lowndes (1782-1822) was a Congressman from South Carolina (a small state) who proposed a method of apportionment that was more favorable to smaller states. Unlike the methods of Hamilton, Jefferson, and Webster, Lowndess method has never been used to apportion Congress. Lowndes believed that an additional representative was much more valuable to a small state than to a large one. If a state already has 20 or 30 representatives, getting one more doesnt matter very much. But if it only has 2 or 3, one more is a big deal, and he felt that the additional representatives should go where they could make the most difference. Like Hamiltons method, Lowndess method follows the quota rule. In fact, it arrives at the same quotas as Hamilton and the rest, and like Hamilton and Jefferson, it drops the decimal parts. But in deciding where the remaining representatives should go, we divide the decimal part of each states quota by the whole number part (so that the same decimal part with a smaller whole number is worth more, because it matters more to that state). Lowndess Method Determine how many people each representative should represent. Do this by dividing the total population of all the states by the total number of representatives. This answer is called the divisor. Divide each states population by the divisor to determine how many representatives it should have. Record this answer to several decimal places. This answer is called the quota. Cut off all the decimal parts of all the quotas (but dont forget what the decimals were). Add up the remaining whole numbers. Assuming that the total from Step 3 was less than the total number of representatives, divide the decimal part of each states quota by the whole number part. Assign the remaining representatives, one each, to the states whose ratio of decimal part to whole part were largest, until the desired total is reached. Example 10 Well do Delaware again. We begin in the same way as with Hamiltons method: County Population Quota Initial Kent 162,310 7.4111 7 New Castle 538,479 24.5872 24 Sussex 197,145 9.0017 9 Total 897,934 40 We need one more representative. To find out which county should get it, Lowndes says to divide each countys decimal part by its whole number part, with the largest result getting the extra representative: Kent: 0.4111/7 H" 0.0587 New Castle: 0.5872/24 H" 0.0245 Sussex: 0.0017/9 H" 0.0002 The largest of these is Kent s, so Kent gets the 41st representative: County Population Quota Initial Ratio Final Kent 162,310 7.4111 7 0.0587 8 New Castle 538,479 24.5872 24 0.0245 24 Sussex 197,145 9.0017 9 0.0002 9 Total 897,934 40 41 Example 11 Rhode Island, again beginning in the same way as Hamilton: County Population Quota Initial Bristol 49,875 3.5538 3 Kent 166,158 11.8395 11 Newport 82,888 5.9061 5 Providence 626,667 44.6528 44 Washington 126,979 9.0478 9 Total 1,052,567 72 We divide each countys quotas decimal part by its whole number part to determine which three should get the remaining representatives: Bristol: 0.5538/3 H" 0.1846 Kent: 0.8395/11 H" 0.0763 Newport: 0.9061/5 H" 0.1812 Providence: 0.6528/44 H" 0.0148 Washington: 0.0478/9 H" 0.0053 The three largest of these are Bristol, Newport, and Kent, so they get the remaining three representatives: County Population Quota Initial Ratio Final Bristol 49,875 3.5538 3 0.1846 4 Kent 166,158 11.8395 11 0.0763 12 Newport 82,888 5.9061 5 0.1812 6 Providence 626,667 44.6528 44 0.0148 44 Washington 126,979 9.0478 9 0.0053 9 Total 1,052,567 72 75 As you can see, there is no right answer when it comes to choosing a method for apportionment. Each method has its virtues, and favors different sized states. Apportionment of Legislative Districts In most states, there are a fixed number of representatives to the state legislature. Rather than apportioning each county a number of representatives, legislative districts are drawn so that each legislator represents a district. The apportionment process, then, comes in the drawing of the legislative districts, with the goal of having each district include approximately the same number of constituents. Because of this goal, a geographically small city may have several representatives, while a large rural region may be represented by one legislator. When populations change, it becomes necessary to redistrict the regions each legislator represents (Incidentally, this also occurs for the regions that federal legislators represent). The process of redistricting is typically done by the legislature itself, so not surprisingly it is common to see gerrymandering. Gerrymandering Gerrymandering is when districts are drawn based on the political affiliation of the constituents to the advantage of those drawing the boundary. Example 12 Consider three districts, simplified to the three boxes below. On the left there is a college area that typically votes Democratic. On the right is a rural area that typically votes Republican. The rest of the people are more evenly split. The middle district has been voting 50% Democratic and 50% Republican.  SHAPE \* MERGEFORMAT  As part of a redistricting, a Democratic led committee could redraw the boundaries so that the middle district includes less of the typically Republican voters, thereby making it more likely that their party will win in that district, while increasing the Republican majority in the third district.  SHAPE \* MERGEFORMAT  Example 13 The map to the right shows the 38th congressional district in California in 2004. This district was created through a bi-partisan committee of incumbent legislators. This gerrymandering leads to districts that are not competitive; the prevailing party almost always wins with a large margin.  The map to the right shows the 4th congressional district in Illinois in 2004. This district was drawn to contain the two predominantly Hispanic areas of Chicago. The largely Puerto Rican area to the north and the southern Mexican areas are only connected in this districting by a piece of the highway to the west. Exercises In exercises 1-8, determine the apportionment using Hamiltons Method Jeffersons Method Websters Method Huntington-Hill Method Lowndes method A college offers tutoring in Math, English, Chemistry, and Biology. The number of students enrolled in each subject is listed below. If the college can only afford to hire 15 tutors, determine how many tutors should be assigned to each subject. Math: 330 English: 265 Chemistry: 130 Biology: 70 Reapportion the previous problem if the college can hire 20 tutors. The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift. Apportion 20 salespeople given the information below. ShiftMorningMiddayAfternoonEveningAverage number of customers95305435515 Reapportion the previous problem if the store has 25 salespeople. Three people invest in a treasure dive, each investing the amount listed below. The dive results in 36 gold coins. Apportion those coins to the investors. Alice: $7,600 Ben: $5,900 Carlos: $1,400 Reapportion the previous problem if 37 gold coins are recovered. A small country consists of five states, whose populations are listed below. If the legislature has 119 seats, apportion the seats. A: 810,000 B: 473,000 C: 292,000 D: 594,000 E: 211,000 A small country consists of six states, whose populations are listed below. If the legislature has 200 seats, apportion the seats. A: 3,411 B: 2,421 C: 11,586 D: 4,494 E: 3,126 F: 4,962 A small country consists of three states, whose populations are listed below. A: 6,000 B: 6,000 C: 2,000 If the legislature has 10 seats, use Hamiltons method to apportion the seats. If the legislature grows to 11 seats, use Hamiltons method to apportion the seats. Which apportionment paradox does this illustrate? A state with five counties has 50 seats in their legislature. Using Hamiltons method, apportion the seats based on the 2000 census, then again using the 2010 census. Which apportionment paradox does this illustrate? County2000 Population2010 PopulationJefferson60,00060,000Clay31,20031,200Madison69,20072,400Jackson81,60081,600Franklin118,000118,400 A school district has two high schools: Lowell, serving 1715 students, and Fairview, serving 7364. The district could only afford to hire 13 guidance counselors. Determine how many counselors should be assigned to each school using Hamilton's method. The following year, the district expands to include a third school, serving 2989 students. Based on the divisor from above, how many additional counselors should be hired for the new school? After hiring that many new counselors, the district recalculates the reapportion using Hamilton's method. Determine the outcome. Does this situation illustrate any apportionment issues? A small country consists of four states, whose populations are listed below. If the legislature has 116 seats, apportion the seats using Hamiltons method. Does this illustrate any apportionment issues? A: 33,700 B: 559,500 C: 141,300 D: 89,100 Exploration Explore and describe the similarities, differences, and interplay between weighted voting, fair division (if youve studied it yet), and apportionment. In the methods discussed in the text, it was assumed that the number of seats being apportioned was fixed. Suppose instead that the number of seats could be adjusted slightly, perhaps 10% up or down. Create a method for apportioning that incorporates this additional freedom, and describe why you feel it is the best approach. Apply your method to the apportionment in Exercise 7. Lowndes felt that small states deserved additional seats more than larger states. Suppose you were a legislator from a larger state, and write an argument refuting Lowndes. Research how apportionment of legislative seats is done in other countries around the world. What are the similarities and differences compared to how the United States apportions congress? Adamss method is similar to Jeffersons method, but rounds quotas up rather than down. This means we usually need a modified divisor that is smaller than the standard divisor. Rework problems 1-8 using Adams method. Which other method are the results most similar to?  http://en.wikipedia.org/wiki/File:California_District_38_2004.png  http://en.wikipedia.org/wiki/File:Illinois_District_4_2004.png      PAGE 78 Appportionment  PAGE 79 Apportionment  PAGE 75 Mike Kenyon, David Lippman Creative Commons BY-SA StatePopulationA300,500B200,000C50,000D38,000E21,500 StatePopulationQuotaA300,50034.48361B200,00022.95082C50,0005.737705D38,0004.360656E21,5002.467213 StatePopulationQuotaInitialA300,50034.4836134B200,00022.9508223C50,0005.7377056D38,0004.3606564E21,5002.4672132 StatePopulationQuotaInitialA300,50034.5402335B200,00022.9885123C50,0005.7471266D38,0004.3678164E21,5002.4712642 StatePopulationQuotaLower QuotaGeometric MeanInitialA300,50034.483613434.4963834B200,00022.950822222.4944423C UVWXYZl+2345TUV(.0:}.hZh{h{5h{h{>*h{h{6hNshNs5hNs hbhbhNsh{5 h{hbhh{h{CJOJQJaJhZh! hbh{h{ h{h{: Y [ 4a*+CDVXYZlgd{& & Fgdc? & F gdb%gd{gd{gdl45UV%&;Nf{+gd{$gd{gd{gdb  & F ^gdb./Jf3X|)*U~$gd{^gd{+gd{./179CDI wx~,24>?DFMOTrxz?DFOPQ_ d f y ;!A!C!M!N!S!U!\!^!c! h{hNs h{5h{h{5h{h{h{>* h{h{hNsTop 89=PQ|} 5 +gd{5 ] x y 8!9!d!!!!"A"b"c"d"## #####%%%+%,%gd{%gd{gd{^gd{+gd{c!!!C"H"J"a"####%%%,%)'8'''**@+R+,,,,,,..4\5e5l5m5n5o56"6#6$6%666667778.8>8B8R8S8T8^8`89 99999 9ѶɶѶɶh{h{>*h6 hNs5hNs hbhbhNsh{5hNshNs5 hbh{h{h{6h h{5hh{h{5h{ h{h{A,%$'%';+<+,,....2 2444n5o5$6%677T8U8V8`8$gd6gdb  & F ^gdb%gd6gd{gd{`899(9J9p99999L:M:q:::::::;;<<<==4=[=|=$gd6gd{+gd6 9(99999O:U:W:a:b:g:i:q:::::<<<<===$=%=*=,=3==== >x>~>>>>>>>Y?^?`?p???????@@@@@@@@BBBDDDDEEEEEļhNsh{5hNshNs5 hbh{h{ h6h{ h6h6h6 h{h6h{h{5 h{h{h{h{>*G|==== > > >u>v>>>> ?/?W?q?r?s??? @1@S@z@@@@@@@+gd6@@@BBBDDDDEEFF G GHHHHII?I`II+gd6$gd6gdb  & F^gdb%gd6gd6gd{EEFFFFF G G GHHHHHHHHHI#I%I/I0I5I7I?IIIIIIIIIJJCJDJJJLJVJWJ\J^JeJgJhJJJJJJJJJ#K$K)K+K*h6 h{h{hNshNs5 hNs5hNsh{hNsh{5 hbh{ hbhbFIIIIIIIIIIIJAJBJfJJJJJ"K=K>KKKKKKLAL$gd6gd{+gd6KKKKKKLLBLCLkLpLrLLLLLOOOOOOOSSSSZTcTjTkTlTmTU U!U"U#UuUvUUUUUUUUUUUUUVVVԵԱԍhNsjhPxhPxEHUj>T hPxUVjhPxUhPxhh{6 hbhbhNsh{5hNshNs5 hbh{ h{h h{h6h{h{h{5 h{h{h67ALiLLLLLLOOOOOO5Q6Q7QNQRRSSSSlTmTgdb  & F^gdbgd6gd6%gd6gd6gd{+gd6mT"U#UUUVV{X|X}XXXXX#YRY~YYYYYYZZNZzZZ+gd6$gd6gd{gdb  & F^gdbVVVV)XUXeXiXyXzX{X|X}XXXXXXXXXXXXXXXXXXXXXYY#Y$YFYGYRYSYrYsY~YYYYYYYYYYYZZZZZZ(Z)Z.Z0Z˻˳˦Ϧ h65h{h{5 h6>*h6h{>*h6h6>*h{h{>*h6 h{h{ h{h6hNshNs5 hNs5hNs hbhbh{ hbh{?0Z5Z;Z* h{h6 h65h{h{5h6h{h{>* h{h{h6h6>*h6h{>*DZZ[1[O[P[[[[\-\[\\\\\\\\q]r]s]}]L^M^j^k^+gdb$gd6gd{+gd6M^N^e^g^h^i^j^__2_4_5_6_8_I________ `%`H`d`e`f`}``````[a_aaaaaaaaaafffffgggg۶۶۶۶۶휕ۉۜhNsh{5hY9 h{hh{jh{h{Uj:h{h{U hbhijh{h{Uhih{5jh{hNsU hbh{jh{hNsU h{h{jh{h{U5k^^^_7_8_I____e````aaaaabbbcceegdR gd{+gd6+gdb +^`gdbeffffgg^h_hhhjjj)jwjxjjjjk"k#kkk+gdR $gdR gdR gdb  & F^gdb%gdR gd{ggWh\h]h^h_hhhhiijj'j)jzjjjjjjjjjj kkk!kkkll6l8lNlPlnlplllll2m6mBmFmZm\mfmjmxmzmmmmmmmn nPnQn`nenjnnؼصذ hR >* h{hR h{h{H*h{h{5h{h{>*hR h{h{ hR h{h{hNsh{5 hbh{ hbhbCkl\lll m2mmm,n^nnnnnnnno0oZooooop+@`@gd +gd $gd gd{gd +gdR nnnnnnnnnnnnno*o=oCoooooppppppppppppqq$q&q(q,qRqTqdqfqhqlqqqqqqqPrVrXrbrcrhrjrqrrrwrxryr~rrrrrrrssEsFszs{ssssssww h 5 h >*hh{h{>*h  h{h{h{h{5 h h{Rpppq8qxqqqHrPrrrrsRssssLtMtttvvwwww%gd gd gd{+@`@gd +gd wxxxxxxyyyyyyy{{{{0{2{3{4{5{6{A{B{J{V{c{e{{{{h|j|q|r|t|{|||||}}}}}}h?dhB(jhDQ0J"UhDQhDQH*jh 0J"Uh h H*hDQjhDQUmHnHu hhjh{h U h h jZh{h Ujh{h U h{h h{ h{h{h /wxxxxyy{5{6{A{i|j|k|l|m|n|o|p|q|s|t|}}}}+gdDQ$gdDQgd+gd $gd gd{gd }}}}}}}}}}}}}}}}}~~'~8~O~_~`~W & F gd?d & FgdP sgdgdDQ+gdDQ}`~YZÁā˅HĉȉωӉىډ܉PkOopÍǍŎƎǎȎ ļļ䠘jhAWUhAW hDQhCi h hCijhCi0J"Uho@ho@6ho@hX\}hQcheH heH 5heH h~hhCi5hCihh#lDhh^h?dhP s; $Ifgd?dh^hgd?d & F gd?dӀրڀ0''' $Ifgd?dkdz$$Iflrd VBz(88 t0644 lap2yt%ڀހ'kda$$Iflrd VBz(88 t0644 lap2yt% $Ifgd?d&'ā12sf & F ^gd#lD & F gdP s & F gdgd^gdgd^^gd^ & F gd?dh^hgd^ & F gd^gd?d˅҅[kdH$$IflFb&Fbb t0 6    44 layt~h $IfgdCi & F gdCigdCi  hkd$$IflFb&Fbb t0 6    44 layt~h $IfgdCi (/6qhhh $IfgdCikdX $$IflFb&Fbb t0 6    44 layt~h67?FMqhhh $IfgdCikd $$IflFb&Fbb t0 6    44 layt~hMNW_gqhhh $IfgdCikdh $$IflFb&Fbb t0 6    44 layt~hghig'qldXXXXOd gdCi & F ^gdCi & F gdCigdCikd $$IflFb&Fbb t0 6    44 layt~h ډۉ܉pqƎ  & F gdW:h^hgdo@h^hgdX\}h^hgdQc & F gdeH gdeH h^hgd#lD^gdeH  !@A_`_kdx $$Ifl0*pF t644 lapyt $$Ifa$gd$Ifgd #!#145;<>?STZ[]^boߏ (12;DENWZƐѐې*6@KU`juvxՑ֑hc?hCiB*ph hihCihAWh2 h 0J hCih0J mHnHu hCi0J jhCi0J UK_kd $$Ifl0*pF t644 lapyt $$Ifa$gdc?$Ifȏɏˏ-_kd $$Ifl0*pF t644 lapyt $$Ifa$gdc?$If_kdb $$Ifl0*pF t644 lapytˏҏӏՏ܏ݏ-_kd $$Ifl0*pF t644 lapyt$If_kd0 $$Ifl0*pF t644 lapyt $$Ifa$gdc?ݏޏߏ nbb $$Ifa$gdc?wkd $$IflF Ek FF t6    44 lapyt $$Ifa$gd$Ifgd{ uu $$Ifa$gdc?$Ifwkd$$IflF Ek FF t6    44 lapyt!(1uu $$Ifa$gdc?$Ifwkd$$IflF Ek FF t6    44 lapyt124;Duu $$Ifa$gdc?$Ifwkd$$IflF Ek FF t6    44 lapytDEGNWuu $$Ifa$gdc?$Ifwkd$$IflF Ek FF t6    44 lapytWXYZ`kqyznnn $$Ifa$gd$Ifgd{wkd$$IflF Ek FF t6    44 lapytyz|oi]]] $$Ifa$gdc?$Ifkd$$Ifl\ k t644 lap(ytoi]]] $$Ifa$gdc?$Ifkd$$Ifl\ k t644 lap(ytoi]]] $$Ifa$gdc?$IfkdR$$Ifl\ k t644 lap(ytƐϐѐoi]]] $$Ifa$gdc?$Ifkd$$Ifl\ k t644 lap(ytѐҐԐېoi]]] $$Ifa$gdc?$Ifkd$$Ifl\ k t644 lap(ytojhbVVV $$Ifa$gd$Ifgd{kd)$$Ifl\ k t644 lap(yt oi]]] $$Ifa$gdc?$Ifkd$$Ifl\ k t644 lap(yt "*36oi]]] $$Ifa$gdc?$Ifkdk$$Ifl\ k t644 lap(yt679@IKoi]]] $$Ifa$gdc?$Ifkd$$Ifl\ k t644 lap(ytKLNU^`oi]]] $$Ifa$gdc?$Ifkd$$Ifl\ k t644 lap(yt`acjsuoi]]] $$Ifa$gdc?$IfkdP$$Ifl\ k t644 lap(ytuvwx~ojhbVVVVV $$Ifa$gd$Ifgd{kd$$Ifl\ k t644 lap(yt Ƒɑ?9--- $$Ifa$gdc?$Ifkd$$Iflֈxs \n t644 lap<ytɑґՑ֑ؑ3-$Ifkd_$$Iflֈxs Wn t644 lap<yt $$Ifa$gdc?3kd@$$Iflֈxs \n t644 lap<yt $$Ifa$gdc?      $$Ifa$gdc?$If50,0005.73770555.4772266D38,0004.36065644.4721364E21,5002.46721322.449493 College Rural College Rural    ' = > G \    hhAWhCihc?hCiB*ph hihCiU    ' 0 2 ?9--- $$Ifa$gdc?$Ifkd$$Iflֈxs \n t644 lap<yt2 ; = > @ G 3-$Ifkd$$Iflֈxs \n t644 lap<yt $$Ifa$gdc?G P R Z \ ] 3kd$$Iflֈxs \n t644 lap<yt $$Ifa$gdc?] ^ _ g h n o w x ~     & F gdW:gd gd{ F 00PK&P1h:pjM/ =!8"8#$8%8 DpKn$hsN\@8HPNG  IHDRyWݷbKGD pHYs  tIME 3x IDATx}{\Tc"W 0H)i)fʼfbT:GE9 B;h"Ihxf5~k; 3ϧOg_^{_{{{;((((((ghPPPPPPRBAAAAAI % #  P!jDe] g0 *PPt 71-'dUΠvSpG [R {kb~=sʜvE[ ?lm-]+a .=[91 |l>W&!N9F}0Ӿ!kE* w$7$%'@5Ra$Ҙt_H;La=< %W}eUSyض,.AJ7(Kcұ4&]%il>8Ytݒ{mrr c6=3MMX=ޘ1Ƥc_?U:7ywAV^EES ~'N%~+l}mom7tzciiK*hk{CW%}m}moc/*_oW7t_|k%AUc3Z|kQ)j_e ;:ש:N{PJ8Q1õ&wZ=G;MCBȨ4lR͞荩ɽV,9+-y&ȟ0k`5bG2}G,DȻ}; >m FRysM,d笮dSěO VO3X()>S7BjNq`7+ ~Y{ d2l*rKj1kXOlLāBvN>μ6л7Jh]qR]{F[D>DQO*}׿W. qgWt.tU5Dս;kK{{{Q)J y7w70wWor}sɷ&=oˎ>qSwl溺X}>O@Yg vIPվ7R-@%. Uې`v{_)>r$瓝't'Wֵ0;5>% &CGGJVO;OE"~1½eFi 3rM+ȻJ$,+s| cRv<[CٻuQ'c/qձReJu;ڎ6}{iJaYI{"Ǣ)^ϛ>#. amYy`Y5w(tG}Afc6"gDD#_>:xbUsH@*ݕ}3JTKTEʌsS-~n}qA%H#=! ue$ީ#*{a=rKjƎo ۷]e(ӊ1$C*5f.rܒZp:EJUawLf%.eQPQ,oLX2RFCH]=@y<''c*IPg[{7F)yi,|0,ԐV*$q!UٽUI _Adl&qEXϨ&8Ƹ"TNEA@YN_;:PLpA nĸ"WX =ԕ:UW%7yj=7w86gO+VLѱoNBu߿g UUI궓^.\:[P[V|>B,ZYV8 E@jGT$3\޻ENN`EY: Wϓz"+zdUy :k ']3x:SCKv#JCe ӧD4k%3z glΐ#|ħ3Yv5k:Tzx/2TI]NAIW0{7㖙SpGcc}G,iͼ1 Ae6^+"c3ETFڞddqr ̨1dHf[Yyg#R* {׆7y j1x@THaEl (|ںN˲2y<㴲M:@ Gו\5 \g$%U*> ݂;}gF QQ,pdQC,.zӷ=\V%Zwk}Gb)pB Fc"qȪH[dtʂ3.{]Eػ:.1 |!:Zg3/ܽ+| QҜh@Eq {G7KOUܢ)^ v~e)%"xF~sƮ1\,rY$ZҘt@6U^GE튰a[9INpUfw$m!d2{C2?i?1-go$fQܑt7$3MNG"GD28OG+zFrKj$\w")+1ّt{w! ԥ"fCt#DJʫ@N?2^ҾՓ3W⧬D!H%^k:ҏ]U/1\;xs)F2(] xs)+DI3gOƢ)^O+fE_kooo5gمbUI*Č51+"5"!o]CE쓶wCxMcJvٴd;oܢx<s+ޙ< P+sgm]:C_;Fb!:{cR'mW,Q٩RQPPPԦbd8V1\$𒂂S Uʒ{}T(@b[d2{C2(((z PoR[פ % UQPPPPPRBAAAAAI % J*T(((((((PPPPPPRg땦i3Ep`«'Q>1a]|Bq5Ί쿙7OFtPh&.Q8'H_9:o-Y);񗟍7C=W'ƒEb~?Gilmn_cGpz\P8;dV P f.+"EIqk3/'">t%ͥ\, S [gW Ϝ~tjq" A^y]m2ꑈ+0h{]<HEڌ[ jiZ!۸-M|xhv;ZOBfl z[z>8s20s` % T“UUpwFs1Ҟ{tuBVf'$OTϢDňB;B{\FS JEl'!R Dk0V id'L xas8@M-0&zOT0'o26ך/iZm!~eU{B2ҖVANh !ξVMǍ:!vI dU@S?9v=PF #- ?/,yE0ٹݤvCߌdCȱ`S{B8[^3<Irx\G+[yah'dٹ)I@*sFO03y̿WgQR0R!J}^@b#*fH܉(4޿|DG6B'rfQp{mEV"3@;S\f& Qb6Y ^lH-R>|r`h5,cK@Ua"V|v\whNǩ)G@򝩛Y|YC,{OY1( TȤNjKfYU^+DJ)#츽'H7ۉ&$Cs/7cS8;0QZ̘Em8ol\]y@Tfrwj"? ޙ׫jJ2s#xjA'\ qAiS9^qp9۸ߎ0Q A=\8q m-H)ckB>*kRLx&[WETkf<Q 3ۻV(}l#0へY<"*cFq!0+Ɂvud3~[RNY5؊P_Jׅ > +PpO 2逊]M&c2$Emv5V(gtu{.Rfn-~i6 Y)_GXG7}R5.4@I(4ν0+&:v>eOǂM BD_ND Syo a%8\o2Җ{wV0<[UU\xcA. {rd!p<| ^v( TXϋї"m8`8們Ć۸-/) . GfQۤ)_ <K;W8s jn:!U #&ЙME“`mjb ֱqhZ_M\gShu߁mf3=c`T&yEOjШ8A/'bMXM7ѻ +b1{OY)ˉU)b6㇛(-/Kx/]{>20Wɱf׺H>t.rϔ_Y(hzY(jN tY*A{8>3PSG+[x DF(_ޞtW ^?43ٜ{lUd"{U$ %{M)¾Egw}F[f]wyB ї Y:!P*~,Dƌ(5i)_Mr9vhwsB?QV TTu, m^֦]Jb)F",Ԋ g6=,M,cU>vx`|ؑ,Pa:ʚ6ضBȺI.dD=?w7>m 3+Դuv0Q+mݻ^*SrꔙWUv\jKrmhka\3<}9anzL(/hK Hx+-prވ%O#q[x7cTO¢;s<'mfn 1h4UH^ʄH*FfGlXa%F~[I(}Xȱs{$M2_y`m^g]A&E  B6z^^cTpwNU;Abhl-+QPkJ=} ȬЂqFRIowċ'6b b_Xg񜠰pwA;([֌v\604D̒ф(A&-ئ``EWX7zRYantZț팤l̉[qYU"r\r<J~y+去. /'*dq()VPQKZ6иAXpf;VDtUU\޳O?u1tL/m7ri09"ӎI w&JjxN\NG-ˉZ+,c ? 7aEVcw^ /'t8 ^T:5㫉KUnC[ L6Ю[b)X*cN{:Fh+R<[}9^Z3d~ZLWdQCSDPڌ Cn]$5pcrEҤ\vx-R$}W*`zLP;/[3}]!̭[6`[.e%ؕ BVr^g}YU؟Yq=  V$ӒJ" nkFLbr3y)`Z Xϋ[DkNB>i*ϭbuVCWb&g;97D'MM9I)h,JZƚ|phZ 2BNu1B|:W:v> Fmӛ'HCVUžS:U 8lRǿoƊ x! _Aor'PP@.ѫwa[&4ذ1s3f3vMR!c2A nm=⫉K*crk RJj5NXܨ*!hZ/Fj5S R?յ#>t%"ւܺ2dV Y)yNbЛrJr} $Xϋ@o@;:+ ,s!jn/䌕qs<'M-vFTwWد+9T$M}|F}>1d\=.G ǣ2K>W^3&xَ`'W` V3!ξ͍:!#W /08p{$, kR&_Rǂ4ع)3/Q1܌36eٕdά`Nd`n[+Dc[3Fr@G/ۚGBW !5~T} [֠ ؇y)r#츘a8ئ(jBD?m*lAMiKT칈;ze3i9“Ńx >5[ nm{RI Ζ碨yuB&@ w!r\䈊1q?: IDAToJ[8 nknߏ]lґc26M@U_ELbZ#*ԂI "kEJ)Uams8Z٢Mw^}&)`'%c"*RC#z&0EJ%5rG]I7X3vq(!|[gJ*=H[;RمEK6q Xsk񜀿O;ˁ1 O¬/KºŚˤiY BB_+FLWyM;ї}9Q`G?>f5)Pf i"J*ksKzZqk3ܬ$m Cixb#l$ D_NTkwEӲ>@}i-ĭZ/(G@J 3Z?% 9prxNX`0Ģ"kv홴WI*f2?/H߃4Դ@;]!|EfނHRxsk8Z*Mzb)?!fV+HC\A͢/'[ǿEgw"<9 rR*ɇ8Z4bDT߻i{#FxrM-UU+mĞ14<qxmdjq>Iݘ~Bc?eEm^E6wA&|+ cVj2-i7ĆFq{r!P*F`Yb ? rL7C݄'G񵇋20{"'_>ԠoŸֱ`n :VmRoOߗJ'e?;U'6={&bKY) Ijējy$ 8\7EE`CPQ |\E-_\bXϓ^i[<\]$Z̬EHG2cz r'ϸTbv' ʖSv0 9ul&vL0%*+ߣbȬt;3LMRM3ͬFzH綕RI v8CS G+[?X1b:秢~lɲ6r#y4[Fv4]؋. GT #aDHf!O* UAhTR 6Bl'!k}GR>7C33!:/;F >> c6";vjIeE oyO qvv~"`v;`݅ 5K*BJ5b|yC'RI 2+e="LI E6"Z,]Ί;.C.l'W<\0Q6Xϋ`< _yJA NjhH>wd?G&Sp"¢)^xp lWñ ^˱5VVpr҇H.5r2xL /L-ۋicvn ^ oS\}uАf9׀ uMcw;e`I.”5 g8/Ǣ)^=on>; #ͰQ `Y30a~Cȩ.Fq Xxy,henP%us]R!9H@xOYreBCE?ys2/)ReFZ~ m\. {OS{Qa_vS!4J^4 ?ߜc,]ኰm[D: eMux%)YZ. 6eU2y 1^eX`nm4^t[b ? e(xJk5v們\ն{+"OSyd$QЪ/^+ >1QNAD|s0ؖvvE/cT*5TJ%5X=.DѹR*Q0 F%< 3~>@͟7]3 9w`dUꥲl@j[9 5+Ί ޫ?H(D3Rɭ"GT@쥩wBNu1irE Uz82vt4*LYUrv cDhY>|1^q{׾qD|ZߧE>IV̜&_6G"Jո}w y6^ >l'1r(-w=Wiv_5e7dв}N>Lm\oDž7۹[?mM/Mp'2o`(oaY. zZ0KSVWBvI%NjRM-dM31:!Y F "5/> GB$b{B6F){@@5p+^_= ;'Apu 1]po++Nze*i% k-mDu>&dd)έ"xBm m y)O1TROld 4ɂ3ۙviWM*c_"if0\$0gWE_|,,aJ`nvY HAO>H4Cq@Um skp<2 u[ieT꺜;<\*?GέbU>&oU_F/ ҐTMl"rZKC qu@BMD[3o Sk24/qNukPM|Z{>@qFjWTVX*f`#5'ħk5b%p8Dϱg_?6wLRUnJVU:oRS㮼HƏ~:eUjyr(yMSLby0=Ki%R/ҏbkxoV<Pv1t$8_Ǯxd0M2!P#R) TAf\+;, 2Pxm~TLy޻-/WWj!e߄,ѯ#25EAy4V/ {P$b<𜜍› > ~&Q'j&X(d3ZV==p@T^~2[R&zaz4Thi\xW#89>e4^F 'P/RDu0AK?UFqP:q*H2~֍͔9D'(l{p0ҵ8$an0fE]u} _xAT_[=R)%qk3RJ}a;%{愇C<7Z+i?% # RE̬p@Ysp'gR}}uNҙ#C^~| Oc ?fee RwȈn=_Cd't +?GX؈hf^&7?|76tUwPZxh!VY)_SdK?#% L˥1[)Dtڕ GeK;-ͧpEXAܽTeMu`ZDrcr ;j~F܋M<3_reߡ&)gkh5ʣ^IYUJ<0_.GU/2 i%٘:ƤrP/_ 6ʚԖNٌ;6Zڙ\ئ}N$FVIKrWb% >I^ +kJFڧ }-[<W>ǩ"1S82u5|@yٯxrD%(|;mRf~t=9v ߌνZ=DχP|?rMJ<@!9T{UUs -{gɡn^v3bQB(=I$r@;.yjf;a ?Iqghn/R6GT?/○uFBĭЩ=Lz*QҩC.UNYc<\Ȭ` ?ƙtmWV7چCuxxԃL;B _fݽ7l,m[8kV.3H$9I[ Y9b`n+2kq[hiC u8Ke . ̸: |7鸘_+DVUIN>i˅% +ӆ'޺ҞBɏ&<+0R2"Cэu!ݦn*#{h .!ξaŪ}w!f2x)4A1j0? /jL.2!YU^Ƿz/UV[MYr>QGA,&fD@hHN&Ijp(ehe;7_*AfYUaEMe $L*FG]H 3;V1ߥBvLM3\֐?wZUƶf4(T 6#_CNu1xN| ȩ.lG +{*Lu/ Y^w^ϋ xM>]:5R}մ1wIGvW{C>:\ Im N:BRB ks8.Ɠy0H+V#DF".مA\ %C~u_#)'H8VNG`Qh/7+Z!I~G# wiedw^ejȠ%H.$MqT:ۭo+(;ZAB*\<9v{~u ޟ+Q~W='bP`Y"YGxr_ 2+p0]RI ̭1T\G=Cϒ Bԋ++8D:s59[F{A <Q1fқȪ*@Mֱ5[?LM2C>([ݮE`] jzT 1 >m(4'zȬ*=(`ѝbej!](GRb[|>)wLeٝp}*l(g*=gU)Dյ-T[r*!N3d!Vz Cwf!*{?n eno.K=$~T2kϓ̾Vo'!l8S3AV|vgGDuN;`hD*3(pa:d}<`޿; q4`'9CRLU y9FXH-\L-Qw[j ʹSt{.۸`W)K+vڳ7?IMCcFRWߙ4Qt71&MP?QLϕN@ZL'Y`Kd{/'bň鈾i3R>2mR`$k%^kOv?<vPiLӶyXϋ;1Ýg4.iY+-pv%? G/3Wݞ>3DjEˑ d[+£ I%93Oe3H҉ wZ!`ḵD@$'aU>\ΧB>Fqar8t޵yX@G.JG*I }95bpw"q0ɗ7UsrgYX=p L IDAT39JR@kd$Hm]Q_ Ww )eDFiJbIx]}BtW(\whp|{$m-T`'2x?<ѺoEx(>)Ck2E=ǧc(o z[ކe ǂR>D nゔRAM*LGIa~.z޲QsS]/ADL;f颒9v.6_S>FLbTz;ssk5.)-U]ǵ| Mցmƶc1os(0rgd$ai`$n¶cEolWxwvl7v~+ƍV.L&c<߬ݪ~hCdzOi.IENmmY70ؽ8A +Q+ Ұ<} pG_D-5|t4TRR>^(Kjpcd;ᛰO[W(4dgj5|5q)atv4 g_x0^Hck ?I?'%Xmaok8=΍?͉ ",X7F:'N1X6Y3"L:%_`8D*8+dz)I!vl7.]ڝX?0vT Du8v m u}ˉ5i2I ]of)Қ#.TeD;q>xo6L-q|ύ0ۚ1h .XBrp cE' xF9ɺ~3݉(dV nmƬ/lIώöcn)UVQ>ۚf=]R^ *,&M@ūsOAZwFohbt=*]AڌUĥ7l;M!QX-@\A2+OEΩd!9&FJ`PHo.Ƌ'6"r\PdUpU{xZXW Y{}<?<&.UHo٘?Egw uXr@QCS]=ًkv/1Hޥxv_-EBdDI\οuJ E T̒/WWlD_NDQC3$޺@G^CZlXHsNdI-|G{]LVM(ƟO2#,>;YqXϋP+qgHP/Q7#GTk"nmƴH+6z^[4.Y(m9Ycۯ%aƲ9ȽxQKi9>@끰hq"&Ϝ=/ִa44iZNXQXϋGr)$bV r1JL.ӝlDž$uTN#kSKFh(n<|"~.V;.]?bv";rtv%D_ns2 1~J%Z ~ljBtCAIū q 2 nޅèd78):{c_x^ǿO#!h7lPƖK*fErdž۸hdiJjpN/'}72mtk`, ~8vs᷋:IɢBNt&E@(%:CAG췳ǥnm nB$;v l'lBCs-Yz> 񳐏7N!&xS#o NύV::s:q3d*ugMW ?̓<djzv\8Jpwq묢! Vm ŨLŰ9nKf=!?ٌM%QWQxg2fH 8=G渇;bb'{*R45pu9O2 5JfV+nmƮSHqN-C6>ICٮx%} ȳ8C*ϔ+DsYeJ~#@}Jv פ]>ST;bQn?ZHΟPJ*\ǯ`_Ϗ |8+= omgpugw=PEvʿ!4w93?EizXJjM-u[FgǻP| x&n 6~u_C^YTd醭_(߼~厅8"-$ƍPRI ]s<'0PX-@XVcquškQn*zh\p^DyJa4Cї2l6VT߮ܬQxm\kr#/N1Ov펎UrPiDp?0/b:B]Ej_:DxЙIR!X[}6JPX_9H39?*cs}=ǵ|liCسl71]c5";hC;qʂ0amns腋Z!La6~垹5mV_=ύMlTw۞bФt Y?`'v֬\w`Pxf7#Cz;L/^w{Դ1EWQKQeu#†Çc~:~.up`{,P/mY^}z>^J0_$`:|o| ^<_.XmwKΨ:Ba6C?*zSQ*F;l3+|9nK.B>v祠aCᛰOٺCWJ&:JeJB=E\_OF$d-^\6JyM ǬE+ Ȭr"8Zjq tZX;JGAւ& c }TTA/v3CC꓍A;0wQoDlldU1ξJDR]}?[cW}z#*ƪ}z_wNPaZ`PdV3+pc9w["D՛tە>+u  cL]xjrSa#m*-&ւgdW BLūο-$, hY["eFl'!|,=PpO"M Y*cR*AYO>cb{G?_ _@0#]xȺ w^\-1wxZS +S]H.[2'HCRI6 +he^N[I8\pwi"'O65q[vZŨ{j($ "rܧ"]S"3+aǕfC^MDLb$d//kt3x=;,sm?iҔH5XhXXEcb!IDS%XXш JY, K};R\:(u;;03>!|iExTQj_)QqPK򳸑.j y: <"L:tHIz66or:Ks$ٜ9O(>݄Yb;*mm9iߟ \|Eןx\QC:aZr>ՈdK9ydKcXFm_"\AH~ W!>AQ8(hX0H@R pkW!WURsj8:2=S;Ѯn^@z-N$߬8Z$?/~I׹zGt6fEz3vژ&.a6ձC{d]9?TB躙ӴC Hng Ϣ6r@yn.iH, }*x3/ջq?6vⳋݧ߷l<[q$GE!3(נ8~LW:WmIg4VQ-QWw3Gn'e7`%@XgfľA975+Taj5*寔ˡe[mY]\((RRsx\` _nOi50m!)8[9p1GVQQ:h+X&% ]Υ^ %'NE8B_)QLPnU>᧫><&5^~|eBU5( /AKL؟1ѾO⸫kMb nfOӱ?cmz {˸uU} ShӑN 85 i?ߤOX8ǽٿ`8r;S#'+ɮ4|p-F&4;W5UtmߠͥiAOl ;8E8VogІތ:Z χ)(ǼU1( /Aũp5(`iVI k̭<}W]NtRT(Yy SIz*-3M8lTJ\2AFZ!ydtC[p?F۔OߔE1>*-ꙋڱ',*v(f'/X$Ԟڻ;z-p)+d Y[3m"9&$UBZ]9z R>C>rڝq$s e`Es{aLX/6{Yr*&(9OXN-=m U~TɨLu|Bk©5OXSϿU޹wbڍ%>sIvJe3|<%¨ xTrl=u CX8b4~^0c< ,ٸXOv8vNؤ;|3z<1gԄ[+!ǃڻ;ѱGҳ[w!=%Kg0j[qGLV 1'^#uz5Ib"XˈJ`e'>K3=hVdi|i*LcOzsh<R㿞L^rKaWʨhl_Kb V|(‹>z }gtC9``kCLU$2T 'LOIcۚ?[vV°ؤt ʶ`ʺShߔިi<+HG(!,X.Ggi=f,XS{fBa/d-QK/mr08~tSn^^ͽo%)Qv iA^1c3~ʙ0ǩ=J`SkRhM²Kڲgec 't:dK13o=,fj %h2(#M/AƔ34\z EI#JfYbo` t2ע [rLt ~k\ʖ ls7^VL?2s-^?Lf^:t7P?zHzݫArA퉉!gDQ¸d\0K).mƃ$yVaf^y%bgAN8zD~f N$7Gc!Y3g)#̌T %1Sz3S!a_|0%E|H٫=/Y>DI=t*O}ǚ9Ki#߾l9\Y뗑*+ [DaE WmoU˖b?o+irY9Poޥ/k穪 T%U򼖓^Xoٹ$XP` kв-6< yռR(@DIFˉzq=y{K5/‘%1R۵ZcOVQd  /AC" S4W|i^UߕdKϊe929زgn(2g.E^S˻Ҏ- ?];U6( 4JonvR5g w5BoDF%l{]m=/ ʢEUP1&glފ$z0,>*ut dd}XQWVJ'>P.cכ~{m s]Yb3DDgʓ&pfͰ70+3-%WGP}>b%&ZI__2OׁdX_ IOüƾB ^HSY3#Vc yq/_`Jx¢^SKn|Kc2iN+lPnXMf|~a <KYaq#]BLWiܽ_|0-g橖iT"RK8W^M=YNǣ߭.?3h˖|kZQ&@$zu"&+ߋh٥xy,DYYE v%@,/P$Vaߚh{Y80(fmD͢54*zl0)g1¥^VN:Gjí]yuGiڭ6?qH P,Ѧc=4*NZDQtHRO/?"=% 6Ƽ?i"]¦ׄUSȔ񽸉iN\viA?G(DC+@] K hSK7(B~Q0PvVJ˃=cכE5XqιX^Ӧcj]q12._<+h˽84|sGRӅ'&L0FỚy2-2خʫ1ldMv RiMl~eʱ8s}pWÇEl`kޕɫ*P Gg-SM2!s+zs eÿeWˉylGϡpklT IDAT9OFC1-tX6^ߏa ]Ft1`u{ۼ*{V`+{TU 765Ӊ*+CC1J!  |HUSݴ}pU;Zhk5wL2rx?>sR5g;{{V8 sh~8GO&qpJ/RLV J(~eI2Lk,Ǥ-G˸Fao`FxY3в oHSboІ)gamP0˫&dxeE/H-\ٞJeܖ^JG8px? 6i0&d;s2c씩]tMZ=l c{2ebS#oL#ꍥ![d7eA_ht +eP>:FwřUȭ-5|X.K3De?V/7]-00)_$!<2Sƣ5]4|W#Jj}S#-)Δ9B?˚_NX8(y&Q`-XR4xۺ FbʙuqUr }+5KL^eW{X)۬}qX) v:$ JZ=֢\z y{1'rʱpZ̒7JM@UBCc{DA9SnbYTF-Zв-7E%NB_kw t]H+{UI՛|VQ~O{Ե_bT,M8ul>< n<`ZEÜH߱OlYbRf뀙e wԱ>Etj$쏹>ؚ#~JĔ.FP]  Ə 4Z&-gUymY>F߳gzF6ghld@b‹eTض5;vau@wFV&<fbEԾ_I}DC˶eVܸ/XSfdK;t+7^ L/AQA~*,'j4M}y$ [;+ VT߬dPn] }6CH my S dhkѠ3hç&>۪rl@MRH9ßX=7G=jxNsćߡk0o2<ïbXiQ<'yZ;ѡ E)џBJV< y2JrkXđ}.c8㏱^WI`Jsq ˡ'/Ŭ!*Ԩ4ߺM{q#-ZU64M[1hT.^Hh~8GĤr+|6 ^bn1yJߙc3Q[E.EVEid1qecK=,(->u-uYQ>L9Ėx*/d*-#2L/]RÀ7ܫ%/-ccJz+RgQXPUj>zRcmXcF&kX󗘑R%|l)>]Ƽ$"y[ЈxC#1ߺR{)g/͹̿16.#3OK&5;E1a}gS|8uBzNE-6zPGYƚz jFcz}2a U3ڜZ'ƱI}_ږ])idKY>bYkв-Άt4uzDaP*rCL\26,ƒBs3& 0hM~=R+a&0(Y&y8OL\2NvJD~g/ FXx4.+ah0IL\2;qyLLlqAb'<" վQy{J-vei^CC6S;$}=eh߇!& r@۰v <+`T*k{'@w3s<|剋5fLu|WoBǭВvVw2_G'Ckz3՛ ,6"ޱoC^U|,]Xq dT&U*Vu3dTikiVHJ,B[2i NV ejxۺ:n@W*y)/g6n=\X8Sriyl޸.Wشر`KZY=1YFS p:WH.yYBlYXX|0h;ښM11iSy7B]7&+G=Q;@.QZpiWB,/ɖ \Kt~[Xibe@QBa%ӜК/l/>lb_團x4ﱄaX^ @n.DE'uX!'W}g4uu'ڳj+x&%&⸗A|\,+@sr*زҖwcq[(ʛcttp|~ccSf-p}͙?ob'қ T9@K;gy k~=+.4{-BiHzl2TMEz*;NūtݝЋW=u"ozsqIM,_9G& 0 ĹGWx[ +d܊o3Ќ(>7O4h͓{4hg;íI*- ,mq#YyWy)W߷HҳI\E=Y11'6.Q/)akILе^XOVh()1Y3fظDkb`#>,Q/zF{VPt۫rO3G\ -=zR_0ma"p53"@l"3p—KR^iNK^ǥ(U 0z0hn.x/S*m-g -碞!(`2 ׃lܲ(>qD90m$0ݯ1-M롳=O3ժ<*t'u;߬+2YQ>73D޺;~G#ߪ.aG}KՌ$}GAW]K(/hE* E{.̸4O䟀4d*1*KNJ`^OQcΘ#xXFy|46 /Ikgs3pKc;Zz ˼< Ur)"꼤GOo׮UbV3zZV^hEZ&x:Z /uӤ$ k0C!_uSjEʂ1C\Ym'uTWtutIIɳE@VV2 |0?1d$1Aedl^$]|q_Tb{`J4ΘUR^ MkP[[xF-,PTm<yVKзFί /|*W|](ݬWYPzв-(_<hхFVɠ(u0ozUghǭ"cJh /K^{Rxy3/\DDD_3rx?/&1zNKiTXzA]rscKYAU ϊ_tũvLui V^ዙߠ͵UVm+(H3A/sSa[HSY3+_|? Z+j`!\V.,BpnKYWi46M֪%!&+`q^nTJlWTUsbhɆkzԗ5.47h;c.Qױ5N!S?Gè)}dCz`R]3S=R*ZiV(硳=cM"k_dEA5WR,kxDF{o,[ʼ'C-t?] V]ztֽt-+-]25G6L^JQ<jL;=:*#>t6/¢F˱UA8Zí] iQ}KP=My|_И/ iR:n꩗ҘKi`F塳=Mj-78tsyz*x4 -Z1QH|-V 4^aN<˂nc-tYyܣk4=Mm:9gi^ ̸'S*O?"z 4s5vݾP+WvU'+ =uᵼ K-mDPx EzNC&?Y%cLxlYy4s= SpL/l,mR=#}l>c IDATΏߑ)9Lpѵ%&+r& yc ^7D vQt6+tmѩ sQAFR)xZڵ) g S (dBǭ5˯czDAsɔ㿞_&HYsHYՏڍ5V_]:K%ڢNpK̼NKk4((:3b5* վ:P>cV\_8!Jƹ+ז'@@u멡qѕS{&>:Vv 1vX>5G fh}L(K@Ȣk;:s:Mbn{y̑d o 0lw/;""˜;kZw&jZlcxs fr<_Zj򉿉roohWx+WE]ˤ="G@OE_,%l _Q&vùi^N$H}i>:n}ơ{053>j+5Y̭*UsnϽd1=%`kNg՚܊?~G7.]ycZ-Ws/s 텡)asFCdٕ:j͛׾Q)}&|1U04=;DELߞi^N^tK3{S'kW֊-QgdsnO|!Qoka3ڻ;i^vd4xkLzChzg__Uyza$훒/kcE]dhͩ69`g$!< [XYgesWq4W׬d F: iNYstMJ{D 4i"ʣZ3HN%^'@F3u>=MmN%]f-ZڵԊQQ_}C䄑cr52 EC07Vb2ܳl^Kl{lῄ&Z->5xYO=Sᛱz9Rcޘ2ˏQ$21ҧ`[<͗(IL W-(HfM/~`&Z5c(Du? Ju:%GN쀉K{{>kߴe7}zu{!=j&Fm]=Lִۣn=޳.gQFhժ%v ʨd?xYb_ީ-gx0_Þ؋h\ 4iҤZ騷7VUfݒ}Y{@^>(S{ֺdZ%_AVQ>ĖRVEZnÃƕ n80ձ"NͽϖB7FW]g lߢzKKKƪL/&6.T!6.ܦ.>rr;1Yy% ^b_M8kRl/~lM ?N%qj8ys2AWUA)pqvcw04|f2gfb༌9ˁK쌾L2 d*1Hd#-JSicۋ6=0Ԭ{R+ʄI^,9u]y^6ܕd ^H'SʻP$c;#wqYeyDOS 0Jl ,U}p}>?9 ʕTQqh1=XirIz6K }{X41ij ۍMIJNO+q0p!(:!lO899!¸1pvrsDDDN -Xt.W8|^CÅ+fű}>:Ksq?mUhҤ n=pMbEIL4Shozd6q>mhׂ5k7r9_~LB]̹z9hg Ơ< fLzʲc_iyRB|e؆ =h\itd:4Wzju7ՊQf&?OroKqLr`iLtժP\BȚƲ>;yWf9_u6G&SLT&)h0,]Dv|(m=WB 6.5%CW¸w/>@0$7FXX~66GD#f0*ńqo=Zdgg ҂/$Lt0u$@J,Z]χL:m[Vz׳ED0Oaccyͦ-zsAgGg::dܗ3bq*F[/.)Oq]1qɠBN8|˂*!8cIL}^[ֈ7޴iS}dPs~=fFXY\&rvr`Gӿ_O23PCxv6y~E1Vq#,eK4jˑ1yL{[Ƭ!;ϔ#!73(~lL\2ig|+(|fXRS.luiڤag<|"><s2tLoA*y/?&(GO?['>( T`hݒ:hӊ&O=ɢǏ^lu Y6I]',]DBn: H\~)x O5U)0%JriK]cu{We#͉}8u&)$YZ0qOz!ylE֮x(,vVi xN$5UGM;aW`$/ pԙ Ξ|0׹x.wƕ|FxS>9;;C<_sq63KaB><"Z8Vaiij .ű 'QC+vDq;45,-8>x˩wKt k]#&{pGs#]DLv ̝P1b{"j퀍^k>y!tOZL%\ckXEfaPK5ñ k_ FǕW/j=G`D2 lM; FsU& 4.̏˖Hy sz5.{YQ>I!>+"zi9đj 1N߀_ubˀ[1ascttP(N}vw|woUy'n* wmb 5Dq7>7E遹bHϗY(u3'.F"3/Ehie CKy t AM+)>4߻+W9nnnU7*O"U1,)z'@k~S G2:n+>ƦarNTMVk;μ[mF@?ƮwN "5<Ņao^kۨd:Ht#;o^%3Et45y'rp+.MhI|k=VN wKnQ!-Po'k87謻:` h F[gQkڌ6=i[ͤy'zTШHu٨ -^aIѲy2)\*UnlV{жeEmƳMj5 4>=Zrw7tԶQ8{ Fld@h|:Y>9MCO]GQoڜ,t^Պ.akY~}\ރB6iBB_H"?Df=~LZ}u-*S GbmYwjw:70R ]踵 IS|oÃ)r^9+A2yQwEsfݍ; F0-vq';GE! ",#QģqN4OJCmZsعs;K̆q7HGɺyЦ59rPk΁@~ ;κs^4c,4}Nrd@ lv ( 8ZUmkom=)2٠BY>'#!}]\9ys?sz?n&OW *)N߿C6;-Nאmѓ&ҕۊM[#99tjx)HJ!d4ʲ8ld7SQϜ1$56.6Uuz/wrP6F#>zs{duHeZQ9eXLJVeYJ")&Ɵ&IG~JOeIܴkڨ8"׈8P)Z`ّՈ⼿;.ǔ?2ty\Hh2' v:rK]O,aI4ۿU L,\FE'U`[%b^v&j‚ٱ3# -H`\P,6J; -e$Ntc[Yc3+^i(%2"|SL^cttY~ oʭ@澣l߹M"+R{X7)N]WZ!8JL #ZZb$gꛟfe>-C tޯ#~)C hjӌ'LEoauQ?`xKE/Pfl}\I4K냯5eFp63OK\V"C%<-G{ePLI>vKׅGX\.dקәsTO+Qp\ QpJ̠a{1YM@ZI L&ĩ^3KGz}?a_x'g ~uuzs2+@?GX^R.L{]Ѓzu9t-H"|>d捷?a9(2J˪hhl FF"I1cs:WyI`D[ 6svXMawm>OYZ^Ͽarp~]ΡC6>Դq<ڹ+y:u!oN1|z&wģsx.k ڷsY^ g}"B[[=U]W(l,Kq\$eְnSC&`,o'eɶi/vkOagkUv{MM-TW پ3c}22p;4H hJMA)av8X̼qz=͆I7.'GKp7f]6TrKB:&2BF]w% "<o/O.Oe+)T̎WcSec^P©&I|apQ23@_W?rbucodȋb/R^{M G\Sn.C$2;fׇh u<8եx:x;&6Tdqw/%f_I>/;T$a^XFys;).bxyYxxXv;w"/۹6 olC!4~ R VR|;GCbO$'_qGl2~UJDrL=m̰5}g80v 3jr:D{ckU6i # urfRՊL$_F֨IEz`-e|UC ݷU崐br>Z{m &"L@ TCFh r򷡕*9Xa%Jͻ9XDw"c6;{1i9r8]]> IDAT|IDb&ǡQsӉB;d{DZ{xCJNy-gz+]M4x:G}}N\ Be`,nkEO'7\34r -=@uW+>NsLP ^={kO Q{b> ÅVA"`9#JGF(WgFP0MOivmv12 nxn9'Yz˩ЩCe!*tVZ&ާ9ԸZpUK^מڿxj5 I )?D}l1nvUSy{?fbgZsM =0!]ڪe<qSQ>@h&D7oS]SS4tb0())ˋ骦N̺:xFS1|XF֏:s;冦27dWngT$R1ii,j;Bˌd@@?eKeՉ:]+7b?m;)lgc6\=vh^ 㾑 h4w޷Iv&vf]&y%ӚZ:Xt BsKǰ2I_E%B1U-{ ],YfZ=6VKK91nDN Ht0? [ˏى=̉V"熰1T[xzf%#Pe*t񉼨&EGF%%Oss#bٕy,F$.'"cK1vV2) Or^Lg5ĵ>kҶMYãoóێUFcQV`_UKڟ҇IRwKĕHWLpvo Dh.ܘ-_C<i$= [e~X~ 6/~ʢL*MČvU$ou_s+ ីz6b3Uh}?h/o0* vVe,I?G.~uW}\g |,WS=ƴk,N;Q:sVRLd5"H99  {Qnh䓢FUu[̚18ld˦LD!{OfM~pwK(څ^aˊ#(DR$"S.F.`s9.eyf M)# h!YgPDWL}A>_^aE0*eGV/Owoq]F3#H$Mfk<㦑C)HTo U{m'9t#J{ \nZ?xԄk}886.[7N/rSXLv vN9y}/(_̣؂nc|b>r/{<ug z'ykj:[Q715ǫ [.'ŝJ"Rw^9Swe on* MDj٨zMAS+ O[y'7 xvz:͔5,? ;ձK8V/_n3Qil湬5\IpMvSFnGt|/PHG 29VR}xE#FKǾD#U0#0_'MUGS[@EW3Vű(To2wbՐ<;&J;ˑy]zn" }cY4]qREܰ4~&˲Cw^EWtkyN>+K]/}6: nlfh-t9RJ;>)CeFa{-" -ze3(ps8*/~1IHEbb)gYb<=z2 "'`rXU|%g{hZ֖ RGƋۣi3p9cs88P 2_rxnNᮘ o(*׬Țxu@}^!l>Fŀa~{*3=_7ꜿ O}A:C]lf慧j$pN] vT k .h*f}狍[vj:"#o}a?(8ס䏇V1@Zocƛy[鴙i⍈B4ffp,ԅ/p<FB>G+FBP4ӃioG oneUq&*=ut[U:j >=t;b<=inn!#YZ槏ko~B|2fp埮IrJg2`"ʦ(? i@`aZ]*d/omfϭ.ZPJ TPVCΟ坜 \īo|D*aލl Bn#6 wkXv3f1MwS}>6TCJw8}Hbb=kQCΏNo92-rX`#cYZfLsh{ WuW eW =,ΫKw/>G̠D֗,/yQojg_>mM NʳZxX0?y66l^ϧ5II:]N6Vjfoe^WŨ|AŲ#`1i}+KL0M'|z}g6-Vt:9;XBiA.o,F: Fr92iqDx"/MhUH $Xn,,c[9j` oБDkPg0JG+kW{pǢy44NkkC?; x r[7GJ6CnF<zc7u*t{M(=ӃE)ELfTj9=RAMW+ϸڰ2*γ8o?gó1k`13bQn-z}+Y,*ן(0"fnSHQG{O#C*-|>PsYkk +{`1yd*y~+ffTF^[2,:m1el(5-6TJ"G%/it17@';.r OXA݂&AP(=M[*)74${e?D j1e&q$&0kV fvHul3=s\^ŜN"pwA$Vlb\ܑ<0be5(WŨ/;?Ղgyr߇dkSɬ?Af ~1ߕm̃/{UO->[SW ꯑ^[ Yc0FM䕏_3W.VG/RH NkȘjN6F|W\:+[!p$c;8 'sGrO4f~g=MһjNͧ{谚xr-R-[yr̭jNS%5wXz>gj<>$D}(5]lQx5ZY7̈́b Hۿfboj(h"juc7Eh$ DB!.>+ُH(B*2AƇ%qw9nv~;6zfb?{D>Ci ƛ~Oz`B_xvkNkUآ)8\N y6d"1F BZ8`<eRilfWm>z1|dH(h.n""<N)G v+K? hP~?P㸄r`s9Y=qp+`_C_ZN 5 tiU̎"4~lbFP2J"TAڋ&T/laO!XgZP"F,2/h'j8T| >Vc|T1ۭ]NNEy5׼T~rZ*U(\X^?ϠmHѽ}w&W; WesZ]{'w@l:^v+RYL$،Nr1& oF({b9B>N5J҃h|xާ0tv$E5Y_rR|"i ;c7{OdpB H"vE+ײ0>s䶨I/?&4&J3?^OR~ѧ["K_7 IJdnh*Q:?kMTv_q e5r9~y\'Eױ j n M}25 %-7^3Feّ<1 .>b(iZ:%3|ydZf~gy{_|TF )Ɉ =|&qPhtR%[sp$$ObK3S4ܛr''7'!BǢɼ_OУ:r..+%U8N #eUt=~f)qk}Y]*,!oԤ! ZTH(!\ȞViG-r ]+<Ш71vt2:}G3@(2bt"Y_Hڋ۷@F(tR%aJD| mTwp9p]LJw=N?LCÆ8k"\\X7%q}r(GJ{W ],싅+A֔&B*H|zK/UJ}y Δ%,rnh}_3A\zm$@+ӰEPelKdŢɨ$r J wy2o0w[鴹0R(?Nۀ O%D&-Ō@G_ ͌D(#\wV5`'_(Xx&fd ԒMl8҃A)tYژWq% ߂ۍj2 +r76Fĵ4mxw:dʷqjOohDd-]V +0#BRR|qKGG0$ow LfMۊZ"E/WeؑFt8F$GNg杙??'v+בRƴb[J nT9;j{oMwƤQihd{&(عyofz#+>G S]wXNR@2" y4~Z0&|~\P^]JUe K$A2=|+WHܢA{TF5=Jc3@/kj9WҞ:U ZV!4uwSiW:L tjJ Fl"!RncvSHK\=PH @%Q8fu$r5_䲳&XI>{ cg=fT(dY?E( g9@f)&͌i$B۪rQs7>'FkjGA1>\Lѷ0⒓J ɶc݉Cr1'xϠ~ͅWx*t4;n)4b{~o0$탆nB]RΎ愥 ,ǫ >yŌJg{ꗟW\Yr_M($|R$- rm71K˞NFx(o73Ym"B#'P)C$1: oZ))H&e*M%,LZ:~JEs51ըHl7)WFw8Zǘ$Jګ/W3?bSbi|NΗv NǮ0'# DΌ^J|Lv+bk.*r>6@ݳ)kq}r!~xn_/ASqo3ܰ/YeGVaK nXzWLCNaXlF%sf١n'R#w#yd=m'QcSM +V;f1z6_UH|&!3DIe[ IDATvsgR#~{@8e\Ny.g_裥pxWuڋJOnR(搋\&3+0CzrZ*kMvrM"f(2t?v1z5Qj9V.n+nMq`NAJP*Gp\* Yډͽ,n#G܎B,K`C1N/?.Kǿ䵜;@_'.FXL [l㳒4:mM&?XEQq{uv:kHMmU! 3+ddO84N"Fj3o21_~9хoʞko"=05H[۫6@/@H >BT2|VaNAz=eL0̇pفHffvDVgbs,Tqj>;GvL<73RoPcQ1%"1 &˔yH"e)KD! A8{s=A*=vTz`_K/:D{FJ)?YʸԑZ5:sTumTcXhlj M5%l<׵? un)ϋ^R`,nkYodtad^6r'  H \ kI S}Dڷ_1hbK 3$5Ϗ8auG=@N Ÿmt6f$h5jtZ 'ȱRԒ!U{}cf<ɁI\6DB9N0?gANڪxplz. vY*PYUˆ[ɘ9b)-bo"Oӣu6x/@T(!:_W@@.M۷Oǖe.Frn72|ʙ΋?2tpuPbƐT W>$W{5-kj#G<N"\nH B-9{$h;MyD^ɋ6K:?yjijl7 (+w[a#A+UK FwGH E&[?M(IJO@q~1aw]>6WnhskX;_zd|~1RWCl57\7X@G/kicvH2/M"`u>$Bu+zNH\cV ӂ*z4X~HO\ B5 K?`^?{^x{ iv6pװ,VY NBHJctt]"b</ݨ f\X2J};Ye ݌$p6Ty*ユاzY=#ȈHxa!^ѡ̺e\ۗ3Wڃzm<.I;72v]VR*v;}u,/j D%Rn0߃̦N&iCv%CԚ-]nv5K%X]np;To60tnB*ˉL fwEhJZ-F*:QL L@+Q.-${a[$Vy.j:JE  1aVJi5hWk@^l^-[:(-dD$1.KJuAW/v?u|v?D2sG.ř6C繜JW>ΣI7 *h4]8tZ6OHPd}FF_ h #XX^v㪚&;o`%΂A@Fh sDZD D%%CV"^iP/$BIJb3*{23g R^K tnW#3%S͘bqӋSrU)ݳ꤃/- P,SHk)ͩdu3hii#/ !᭿>úL*iЫoh>{܁b+˗VJy6l#&tl`|N8~=@uW o#Zm='^'`J~kyU}E MnaxzpUղ;~lSyƴ[h7uPgjcVȅ@_vBSE*?zG:8mO%3 xrG9tGX]=3D55YS s.OH cٷ-1iVzW{(=MD\入$ @cMMu}wuhm"Ba{-EEN] 0rڻ;ˠM0w^ƏImMm81+h]Gۙ5}Əe 2n3OVm/+2'HÔx`Z]ҶF*sHQ!j9(2աkH`_ ?O.[7~s:Qil#<%r%\Jګwt5򢡱{?_?*)*.'1WC+Њ 9*ޏ^ i=x'S*O"J ӏUo=ª7xYSOټb= |ʻ__xg 0/|n14Xr׌C}>jNt{qg7f ARFn{tu~^JON4g¸눉oxQS_oX6i !!wr"#RG59,s$ =sUJDB!gNF}zHd F{gYT;n:_N6|Zڭ&V WI^8sRY7y᩼UhH ¨}i\%s/8Věv {SGcTYy թN^GCt[u՗!46yWC_iI?rHƭ=s?>AxBξ,Xzw{na݄'Dsx^蕾Ʒ?;}[7eϫgq[$;ԝuKA["!z>jaUM v]X1y")9m;ver] N敜M=aO> ʯ#7RM`MݼXc(hsU=ٰr;!A!X,VٵqȎGpI}\B,bVIdz|-]x5";TqUGɔ5QtP do4md|* H\l&%$HD\\4Ʀ7p l0wHD"2BG(:l&>8Aʛeu~~~yp/DnyFh ?ID}~*=[;< z[c-d\Ն !={u'i_/ߤmуħ$KkC}iiAH3MJ|t<-ƞbocz7z?=GW9-n*WYJtغQZ0ٝԚmx$4v[i1 oMF=.p-#_c4N"Cٽw>/LnHG&YDN J϶c`O$Sy;\+'116\.! k!x b@zFƇ c!joB2ggb=q?:)X:b&lF(2% ;I =CUȥ \Wz{.x3/`[`iTN&YdPQ߷@z=8*zMm;\pg%{jWAJ ;7#9T};_p >//xt=,Z?z-}sTDA1iV:/=

yWSyj ԟGK̏ \J/ȵ4=mH(_B=)BDJJAµFj:*0غ9VLB[awe[8 ?Z93Q~2X"P9N'uM:QNbL7sPT(fO*OKue9\AJ )tП_٬*ًN<@eK!@y^i@lZj_-no| M9,o7>d_UW PbytW/Xz{7c8PQѧX*263?jt6Xȩs8_= m:+煢LqZMShT7[_yTIDGkzΆNTR?Xs sb1~r͙o[nhw>hF.bs9ۄʕh57S.F!#ѱ8SFV 22__=+๔r2 c|I["#iVOAV$"1Ӄ6wQi㾧LʤB BbǂkYsu}6V,A i@zd$! Iȹ"gΜ99yW{X̟v}²IRrrh(4 e|mxX./ڙw'`~+n*:֥p%Le67Џ@~|Y{}\0oѮuLlr+frSߒ{JI'1MGr7p=G}Pu7yBQ*;˲ȩ/%ԗ3Ed+Tf&Ļ.uDZk=ϵUêB`oU#4PgknGޖ9awkYky~j|Ojkۨ55cs6R*8\Ig00w4zD" Jn(žM0s7ptAlF+D>GTho`UnB>9TiX2zܼn z3B9GzD"<֋^s(lu4ZZʦCj}XjS>J]β,ou//y^ʊ b޺`a}/HdE'?;0;K;piyqO[sɩb_~[!`_eFN})oMY|BZ~_l2(ZZ~O@]pGxz 򠬥kt"&K+ʤ8´>,IgpKtgdPMJ,PUDF~cr!Kg^D(-L]A5`Sm:&lN 7Z9ޕ1VS@և27P úNG2737bE0Z:Ɩ4j R#v*+s*L>5c˩/G!://Bv{.Xwx.ܴgR`-3xMsʯ7xJ_90Za);*ip)%3(r0ƍwޏB,bEN߽'G1\NFg9y`;&cO _P=q͸FD"頼\EoV8x(bf>Bfi35hxt&(#ñ;l+ֳxtdw#IbH㽌TF^n意Ȩ+t-(27< ԇ;sY[k _)^290]z+lpr*8`g'ԥ_}ʕ]hKbOm ~n^[wMMKJ=3JADr2!7 3wl" GJk*gU.N'Zof"#zK+o\^Ϋ#ZGvm ys ;ZPta^ls3Vcw:kev a=xK\+?.SRa#qWXtJg .}dD[9_bk/ysF؄NF&PRGՄB"bxS%{+q)graGV4=qq1/]5DŽ/LT׊鼃%eJkTNXYAi)?7㻼:U:Uy{o_N3Id Fi_E2[IAĺ24* 5Ӄ!TZI;NēYʬa,|~jp0&h9PN:s3Q(uL 찤.v%aJ#b=WT*39R_,q~M}y4[" Ut=(o#X?B10* IDAT!>1noe)Yԛ&41~Qx2- 7MM GwJ`;哛|>u]HWUYY WVbnt<N_M]oJ6 [M :s5\2& hhl!D'͋ZĈ6['T}-T,fO4C8\y?*yG5z ?|O̍e& ɚ:OrX?B5ބjY[FBRXR#URn?*"u~,NƁ¦*,:{Vה eTV~'RNޛ0Oj[3WJBjl F_ -=c>S/7C&]L, G$X4Do(![;l.Xڂ$RxGA$?f<kx/c=J"^0X)d1?ʙ2yZP7fD)s8L6 HߒX.Rel<=qO=6K)th{eM}7;[2l"WMqє,GB_}NbyfA p ӇLąwW] veĸX7e^u~ 2@n1k#'Z}֔\1[v{*K!b3syʣg\ўQ[Dv]1=*a>Vw2ԇ1$\x#.G{X~'^u6Œgyz,_xjg|~ZCH0X,V `D@[2 :@{{bCM{DD\c fFH-:<+AήJ@Nw7x[,yB&ß[-:nTQ1β6'g(MHfty滃]GKO _XFh,d^[eN.s)V3Zwyۚ&#ŭ tV)DfD^cu]2QXT>] E,Q?v$IgG8U|{N̰9X(qܭl,>DHp䒞%b1C +svkMc3hZ8GғlwV\O)&t-\8JZ-($"eN'Y T-he,v+8($8N򛌨TR)"10DU:#Нf1ja'_c2imm!p.Us8= aZ"w'&e٤1,%7Of%QR֒a'#yQqn+JeY,«\9P<9ET_5>:`e+%LP*Inc+6G[W";L j%X-jX"bHmCHD>kcfĮϺs%i ӥ?dht$U8^XۈFyJCbZxdNЇ)ϸPo#j3ɑ=&@B>u'NsA[[&S+[ Ymf& ~> E\b>[5-M>I=\W@|N _wZmv2[XJFFJ*A&㫔smz/jsw#+џT2P쟙B?>*w"&kK^c9KR>Uû[kAzf #\?H`U6몮"^NtM\X$_ Zj),Fܤ & k,P-uG>xveێ{:PgԏI eԹr>u}c6 AT,"Rd=3XZMV-JTQJyRHWFvº8n0RوڛF߉LĦ<V'^KNCkXC%7d-s~LˢE h5im63sTʶ:\M#37BI)?Y[SqLuZal)I#;G߃z--$ ;YzR {m囱/.,27q`@Iz}oQ7~4uG m%ĵ6 A6Y#goM3sHŝangp8HEm1/s6s,~Ō=B"c_4n=ctZ : N4>k2G&씲fu<8WSWRsDQvkskU ׾_^';X sWQ?c}1OB E55ꮢbcci= k)i1Z>˫b#MFvMV>:IbJcYWLnM̋E2ob*1XM) R{Kyl/;˲Ȫ;q+i}/IYW[d~D*[ O@|kĿ_/̩/_J͉%($b4;b( -($"y$RH4#g_U>Y dhp~v} CPQt:q8l/Z}TAgp#TĤԇRP*uru--όY ^_ O26T$ġ-ʖC\X|C9T{Q=}s F~x{_^}S_fî/b9GEi5^:xwJۣ|PJ$6& qj"4 ,6T,B"Qba\J"fÁN~E*xy頠}eYWxγVޡW 7p+r>k@%UV[@֛pKFp|/s#?R\$='A-G)jpbZKTDUUJОW%c=LZMHGO+ Sk9\Sʣ.MO(, U%i>IOw2ןKj- YrAgm+Y?i$ϚCy*Jї^r`rI/-.g#l&&t$ȉGd۱ӻ, ƒFտnR˅*2w37i?1ezFDRڀLɾ<6FW`.ٜC}d5VX7e0܇bv6=[hfnZyfu[x1]ol0 taw >Z-Y@Xw5&+MFJ6JZhڈѩ(kddF'ٍ-Db&w]8%|:J0ӏpn*hfPܺ_DIs-W"_0.Hs嵉wskdE^E$a8XAΗ"R92F0_*"smK)vxd^Rg.2\ڂUmXf'+KNk v|a^<+=C/[j!oMY,N:4Z$lB)aui(h6a (1z-V;*62_Gَ`'N)o8ή# b :N {6#Ǝd鹞U}"7V"{GO&PE \R˴ԛU{`i8 &R$[Ȩ-b+J8wyY^U*^C=ȩ/ĕqr`} %_yݶMn2ן#If^FJe#r):+y&!=M)8 alv2kc?k$D½}e~ _+Ȉ #3 ̯Ƕ^S/ʽp:(n)=.@b<Fڏ5Ԗ`[Rj u-{tN,K冯]10)߃xj659j^xwLfi*gcn?ul2J4XdԶJzp z{dh0,6$MII,1۝f°9$yas>XN"ɻ}rXmM$BۥvG>"Dx(ܺU b/do[垡W9MiĻ7_N_=զ&WL-H,\o_0IHR`Oٿ |u풶gAۦL$){e] LɉB##f!W{@QiU"*Uۉ̦d߶\"&\<ɂrBJTRQ;C&PonfKq3GQۃ!ul{U*fy^.I{dRʳvzuawW<|+i}+kRRwtIoO#fgb4[O_X '04ܼ>UR9yzg fGՓ>妥k|:nKNM-4T_H.={x//ӺE%?k ]޿GN_=_wY-?<ԥ[nCy*  9OLXIaseа}Njiin%8=)qn'}_M9\WG\IFNG#rt߁`onio~jpÕ#9;{~=r||:tlbzl_4Ok Y-~(]ږ5H[^`s"lTeoodCZJ|PI)˦ՀT,!wahO@9b0yfJZfuRFQxlf_w%5յTTT5ґ㳞Oweu֗okpC"]mD _GkvSv9 ? mVMM#6ȡj].кbvFw,WKyRX*Zj q̺b&"4^4Rel3ϻwEm-߭ѣSYYM3Ws[/R阁 @,XS̍q3g?~gNUM#6oDOF t.QU-ރ{tgϾ̟WG"+.b2T`n%}B e@!̶;njbO$"a^!yKA6ZZ1,T,T2 !#ݕ`? ^a'Ӷe0/XLo*nu<WMDaQ fV3uxq؝h>@ #˳ ~g_O696w¥@~O]go%_oA79}8]]UM#>%'JA,ݵm3jּ'F|0"7cGӑ$z# 7&fdW.&<ⁿv̅j̕JZMT|}G䆕,XD!)+rc~U1>nzfD]iۤT*4['e4[8lT6d#p˰9*b' :yOrx4mXβ,RʳYQ6#4!<4DvKkyژڵv|ΖgmaUk<~:j;׫ۺa'ǍbD@ϐj fFA3D"Pl⋼<0gp)Ho[`؟_MɩpOԟj4 ȗc2j gr@&2=$sGl&)/ž슳*m{mߠSel T1mbc2DFt|IO$4$iYGT9=LŞTQ# ("]_PNPM/jj}(:I,:ME,~s;>>Cй)xm| ߤ/S)KݟRdfr`kQgox3|V8Y<]֕,]." N%;ϯm]N1psS36q Դ\ 'UrGF^QV B$Hr("m/KPS>rI)F|~/':?mF=ŰƥX^ ^wk}E$=iJ 3Gd(ݑOiU# }}Y6-o\ Kgh߾Zt8#S+Bd mDY}eެm3 Ær!L }G/X4aAXj/4;W3t*m> V*=']ELEjW;GuXH/d0}5uU,#Ww$DSXaCvG۪囹̢W7r`v=O9όYI*;fMm3+xcA-IXbL?٦s x]X+Qb0`wi48[oKKK+j`tZ7rs!7v/Kɗ_2:t2|l%rfLx}4oc_$ ~`"L~IO?x#!JVf7gemٞ߾Lǧȼ?aw~y*[z4N`ZU;Q8IX ǸqFFpM*2#40˥0띉D`[mNl+'<,ITdАm}CvFR{3 W| KVK8VJ&k_J]m3:ܓ0-m9eFg@ru4ZY[VLCƹӰ:{5|,-'揢K~%270?7/1n4ɁޙFabTԱ46&BR &:d\*ƈѬ^KnЎ7Z;Ӣ⦍kig\_X)Ɂ'$X#yT>x--oR٘Zlzs7=eNq `֣/ݜ IDATyՠLUSoY0%&`g܏Wr:xeY& t2#-%$CR,Fίg? u1J1W D,bGy>WƢRQ&X)(j8s%]Nj7wږ׌dwz*?4_/4TEN6b]:9y/66b87;ju0):̊,حԙ x)(6+ &tRyJK ÎX"$ǓZfcőm<2ځTD?UR8x|nwvlANدowy֔ŗo̓/@]3o"7Qj7gm)_ ({~&0.ԏS?`*% KF#bXKV|[d‹סXU|j<,Wh9/Yf骴N b8I*zcNb3vԬEև,fnVqZ9x :WýIP\CjU6Sf"$_K3>Rg;˲pu֌NfwqCn~H9IX  +y`B2~PveQ&t OΔlhf7vqNP ɚ/3rKw ,DjdAg`JD6Dv} C.WQ[SNFm%w3&'O`rjj4dr5 y.MVm~g,WbGsa~I$){P.^['dhi%<Q#卛܍ W7/>;nIZ$/t,p5(j&'O`¸׬z O Ѓ=y<_GWrWbhw<= =ysGMt  ??l(:ܧ-"c̯Uƿ3֓wtr5ԫXurK QXr' 0P$VonH])IS*b̗0{%O]]hfSѡ.y ۈkO ;o&?(|U ,o8_x{xv=*:%i>WuηiMKil/q9V"[*Ɔ^AJ!´p&K+k'PKZ* SY^QX%c}#f #…S+ 1h a)_#ݶCՓޫUH1MD"ch% CD}ܟ R9XO"ڵY$e$&]cgД/ e#A:hn]t+Z.y.^,aTBFI^D|Pz] V;}&54YcUL᫺"V; Fv*f"1#< ȩ;M]1ýBh4Rej܂FD,13f 7ⴊdP`&SϏ=do.&ݶK*W׻@G/OxoÃ+4T:t1}:*IfnC.*LEO%#B!jcYnRɾ:mD/ :\1P\Knz 7IY[\"rA!pMd6岣,w`nt*^lή23,|5z8!sFozm`}ԮH-bu :8b~.E^;*#LD-z~)mu--׊FAd*vD"6muS$"l`mq SȻ*TƲz6hc [J*i(3iSja[y#_dtZl-d;Ʋz֗s_J.fKveXkj(__7cu f_4ةw5n^wH25FOb>[.[泟#..^~+ŧ/_1$Zl;* (b=^n`TR FJjELѲh-}:^MI$DzÁXvT,&MEFW*PH$ԚlNX3vW#E%!9 cq=^nmȨ7U.+3G!Aq;Xk#.72<RLvZ#*XhVѳSBYk#*Y來⇙=J;?WT);˲xh_-b%C)h6QbSk!3 )vINvz$xe8iZbs oNF+!n38&k-,ؖßF3͵OņwՒddNծ8yz"u%5DiU7r"ԛ-x*i0/tr F 9NkDNW$5Zͨe'd)}8@O~)Pr"GV>6?7/2yd.OY~I=yoF"1ZFN: & T: "<Ȫ9JqK'&DqQJևusob9i=T,ơX풤~[,'%BMag<\6e1ƻkۇbJ:ߙ6bq'zx+e,9e&-w?uIXqC5*vnׇLԻoS@ 'Y=c}N\ܐi^ƜOTz3TS:eVD?tI\_@L>iek)TMf{⭔ x<7ZA3Z*uxp.!Z\XhA=9LaRP ~m#>٤\2ry8 '7̙?N\\4Ͼ7;R깂rl*>ČDA=H;#  'A!j:mW>JKK3w>Rjj.R;kE+L嵉w n'7<G(UZ7®b/**Ccp:E|HNEP qtJT\WڂT :meXϮܜRb<;aHRq7o U)%J%J ňV;@O||47%A_r8Z:[ zֶE*sh}%.@/=_M8+ DjjgA --DFʡÙT7t!AO)wtL0ᄥr( pԛ-|F&c Q7CI$Oi1I_PXp "{ iY7 Thx˸ &*#uzH@do,ĺiaO>A0Lpj-fz* S$DeN;wDO@~A(ZW]zJE@@2wPj2b5!#hct*wr-VG@dSj<9^_(βQ*;v)cvAfnA dbwQQeK/vz -N^zE2ri[Uޡ=3B}Ha;o4;/N1$6իW3,)A'?m۶r` rլ9{< a_vٿw?|eoӵmͪ{l۶iVn۶յMecq:&:?İ`&YN?UT>?,[ ocG<0ż‹u^O>'w_㚵'۫!Cٳ˺vfMtdǎ],>]K/xFHw qf(I[@oaJ RS4JO5VvOYZ5#.Nlݶ QNI,{\9u*=ؠMɔ)S:  &44#lvB֬ZR,Q^g.gռ‹,{dez '|7xCx01\55Ș4cUYԚk?2/f&OEt[MvB6*wuv6*̐//kXj% n~z ҋ46nr Lr >$!p 'U] bP{Rhrrߤ_eZZLX" Sz0\~w#!2LÐIx{{= 7&ԜXK@@"K cb$ZD>LyKrVP\Ѻ<\C*=#z,FW.L^e|"^qc =ڋaPy,m "G~W> @[{>C] NO_4N}7v˪]6zsUn2w9e7w6JE@@ãnKܕp3LsO% 7SDڃv4[Ti4R\\/^DF,Ȧ+7 /'3cfQ˄go1%8:z3+l4Anz$b19*>HXT~!=D,M/qWjU(6Tc[*=C%j"E[Vު4֗w:PK@2on 8omFq-H374ϕWN@# JE@@@@TZjDIENDB`n5=t\c} 3PNG  IHDR|{<@PLTEZzt΄yyƢ wnABAøĘJs,XE7eWoSO Bxiif>bψYJDh1b8pgrԳ¡D*ZmclpBϐswYP{ά/s͸#UYYWʢı~oon*,-ywn?5^rʷ>{Erz|q*̿2`ڽ|{wM]^IgbE?z7Zsd{k/1a[awpwvr W֩5<a{T[J콿ŲE# pHYs  tIME 9xZ IDATx흍w3%)$mƪ 0dZ?:,j}k\v._#_@MP8-m!_vg}!FKKKKKY__R𗲄oE 7 M&7 2zf% hF_4-㗶ߪVϢQÃJV,mj_&ѩĵZJ4Jg!f /A:9 LIJtҟ윕gcUTuTDYv}Ã]Ydk%7M=(lJf2UltϪdb:MvFxd6♤QO'F!FnQpF3L % n&nhdR2𓓪rZ,{{n$p~EU荫GM=/KEWBq6BUgGJ2-l27̜5>ۑF1|LQM}zG_F&=Jѓ@)S~f6.$vy(QKbWO8MJ~ծ~q(7- fZ*kNO:-G3☁aߘN.4#NOG z Y}ʥDTP"Gؚ{Z$dSߢӔ.jhz}iGǣM" @KGW(ϥґ;E sұUݎb_xM) RxՄ< 47KKkD05>iF&@1`ׁQY9j =EHwE uZS߶z㿞Ja3ߓןi |-$7C bO'`U`ljּ͇Gg0Nƶ 0H9:l^*G6H=hWiK谊Gߋk |fL&#yF:(f@E$k]%v)ZK 5TU֘iT =dd;AQ 7mI~}T zZcSc.#Wx]#]QF5Jn;LI;⫪MɇU.*ƔBLxpFQU4QL?mWT<&s 2<i6L 71*F5>9:޶qz&×Q1}9BۉOI8l`KLV[P}CTHi _=k 8;&8=)ȠUVjSXh4ioQZD HU<CAw7KPÇ)DuF Ķ,MN59BTweoْh}&dҷ's_~rD%EW@oS_:RFR𗲄Kybw*?ӧy%wo?lwS]6nBt)[~f"?$H#z$ ֟O#=~$@#?fz/%|zN\՟C_҃:^ekWdr&<= T Iaw`zRΊW >-Y9bMMO$C[zi$ _cI8W"Rv4hz"Mzi/O[/zjxȊ!|juX 0\ 1M';owI$:^z'_ Q|nF. o/'4%".c/e_wbQz.…'] ~5`5o9`̘O4r}OҧOkv^ܹ?]'R{Y.yxבP??|cP*۪; f&'X">0=`0n~~K۞aū9 ~u,l3~nhy2 FC#|8IH?d#Y 6 tu_u~$htt(5n˙ٝp'yR_/evPnlFFwtKOrQapxduNX9IOݻ!`?8<,}cY|oFHr;|<]3|J$W#ߐXaЙ֣}YqW>|Rᣢ<>L7 xC R ל2eih:+YQ x\vG][w?z)NP5S=(b,i O sk0c(G .k910Yb&gl'<2r5Q>-4[!H~V`]}gSSj ߎRYKS@YL7t>aY]vS!0o~"# qsf)AhiXF:9 Q11AzE$ޯ_~Yr9Q<6r 6$_ղ|Ν7QHT~Ys)A\ի_X'l"Hԍ)יF >hk%eׯt _]/owݡEVv֞z&x唷N\e>$| &*<*lnASgW)0U0.s4,g<7J֜ٚLt:'aEW@%pU#Y<0ۭg7em.S(Fy&r<叿8/5^1(2O$uqPi<%x:A'|tI-8鲗IRZʚ#XO>ǝ |c&' "dhfWЉGsb|ͥX52r=Fv$m0#NӜTW}G 7oȾQO︃/>͂x)c鲸"WO'Aji">QxK`4ϐRO>+̮Fr+h T`Yh8cȂG:]e{>)Ѐ;I6/Ձ?'(Vx #0䜄2ڤ/Q>G$|F]-Y-Hs|ljIbvzBIy_sSʺ|<Ѕ8U4UB~OuG>xݰIu19qVG]?Mҋ <|?O/{T;`w>8!t;d/?R~i$+9H..*|叱y#=k)r/,wNO?H:^@( >:XC>??IzETzb+v 0/$-S Ï{n 'e#g:A]xՌT#~@)<LK]yyRlezpt3jW%KޤVW=zB(<+7 , zyg3v˥8# `iǬ$Ɵ~-R ^%$GO7dtmz`YK'=ocaC|UŔMG=6,$8pfT?eZbz%.k_USq`w4a+?]p}es| ]RH!G).!k'\K89.{y> 9^[I,vfr&|le1GԳ&]KnaRgFScmMz#܄|4L*NiVb~=bwp^S?&rޣ^.Jk k?!qn'bVtp0(6  &ҟ+m[k9vx79Ʀ`iG%L~29h%Ϣ و>G1YgE z.?#-#:g5Fi77?V2:ئmh"%F+:~i 2}^L#߶5A\= _OXS2T~ ೼yeLH}ݭjFz S[۵xxZ~[KRwdbOڵpNФ=c紳o ^ݼC!Ϳ(o5ŧ)tIy ?Ob6hkMH'6ࢽ5>$ouhW[:3=bR{@2)O}ǟ>}KY{L Rl:Ӆy7>0>$m_yN]k(dT>J6;idR*|'iB1E9IMG2yf>]k9ËE  k"4=|x)R.ab[~CITq.+iC>;Uۮj5x*|)j^kID-g>I;TxWvH%ܳe;_ Xda"xDC?JÁ-#f\BmGwB|,۝ªeAie#`qF\Q|_-~  L;p*~dvAߕӬ]c+!k qRo;"&am?發 8:_A]wn5OAZRmi)Mu_½s;!ι,b 8i+-zG< @]ĝpυNՇgŝ+, h5r>89VĠ",囁9dN&{Ȁ;;':p96dREabC '|ӃVx';|fGx#b(\eƊ~|B Cҕ;Ͷ;;e*qh"BXF>$7_S ҷ3ݥCݾZsVp7C .Z@Ƭiq~z7wvoi^>Ư*%8O=%yfҰg݆rE ?f>.0>')EAxr5/A>_yYjdŒE8w,i_ĜI~}˫UѾ)N#܀r:3Oŝ*|ݵe[S 7T`Ʋ'π_~~>IX¯ 1<4#*s 4scg2VU߭e3c$9 B r҂RÄ_ag?gE5;LʤNQih0h 5#s'/嘊a 1h8;ߩ)R#_7;7#rW>XOl5ÂDE, b,/PԊ^6&D4c3 oI,G3$,6|Tha*coRۚpfYk$Q~~(tf>^z\*8niXo;٥f&%џ'|Lx'ko: &plJ7DRNy LLzT%%o~?g}^_}wC;6㼸~_~iZSO}/5mV ᷭ%| ruq}k0k]ܧ۟)ܦ:4;322_xM|zeI-ǹrn~'<7(  j6h7kqA5{&_|E毶~[[rb`P-ۡo|E^hiu[W^৞>o`Yl& Y(>lg\Y_[{gqoM˾8*ϊb$F ,?w¯1Nꬿq=o|(D;cY5ӈAnس?ŽKɅp‡朗މ޼3")R2Pj;AP,~L~J& pscdaq=:@ykQ B:8FO/+[{@_:^oe,oBXߧ3oo[o7v~<P:+G+bxEN"YQ XC͔-7u8PnrePV^*[/^PJondew,Sҧb=eѶ#z_T"||{f?Xyw^-ѣu+낤oOo?lYѲ=> <:m #()c =# %7v [7'GpM=u#懎%y͓$i&5| Ȟxk4@#znK 9yڷwNj@6DkUɼ eck甦qoUɥo=]_n+/y|3J/K,aflI̯6<^Ꙝ~m>163|k;(3{tmNdY fyJi He4?uwx\ p%CӃ5YPa=Oy'8[sq16@G{]"Z²Rx<|P[߭v;zu0l3^p˚lE@!焔v}sfmM{`qB[ _z0 X=7?]c6ÕkھaFfysN7>ik4)l ÏT~GJ7 qТ}f&=S7HSwG⮼C]y |7w[ ttcL`xBMTƣܜ3ΌNy&| IG@d')çƲ8j%y Otf×B-yC]o~S*&Iۇ?6 @waG(4MȸhB_͜lw=!WXқ|~' Aa9|w52|nB'TA=, G7Am1joWly}gpvj#_!Eߔ.9ӅxhYh~cfц/i~у߭5Gl֨F; z{vd-XnkGxR;͆Y`HnR}'׌ lF7.!qbab'u4KFVڟ>J%i^|]ڲD8g!§Hd颇:vr(}:WF1f6qPpkuqRT _PaBc^ xH=7SEZU78.{+L &va $yb0lAgoƎX<e|erN K(AOD]-|9y|^ wۨ1f-٩} tGÞTX`lbE ?rD@I;=?7p7ts*b%\+ EMu61D4V8ԜA;YoJq&3ܨ5/Ɠ1 Yǵ R_B"6*2 O2ПTo(.$"O`Y 6oj}ehޢl V(ߛl#ݘ> =FG;3϶[?d*bHY%/9R{qG^=ny.s"-(I]ÏόW2|hj|٦N$*kwRKM J"sc q~zڅ0bwD!9%(f)|1|Rj4NMuxY?b~Pc.^+Gf-tS<N5Gzkpw19H}$|]ӳDWZ6AiLf%z z>ZTzԣۦa1'[|w𼄯TKqgtxMKQ >Fr{vdiwFUONjKa}e\?8?26_]0~>F5<s<6x^OV Y1OO`Qf^|BDNǒsbZ1O.=iw!u _D İxh+Q>~>KTïL+~?>831#=9y #!ٛ]Đx/5CVz5#xlوov*|q_u85C+zT_[% |]w*KaCocb xcJCqzFS'v\4Y'7H r=msnzӒMH<>| Dvd&|` gx|pCN>Z9o\۝hWztg#/+Mvﳯc&z)c?\`P?Ѱ$ }&E&* 𩝹w=4G^>%B-uŝE?5}׎*r^*Fy ?2e/6%s8bw3ZW;MG󿝘H"a4Oih|}.g[{V[fÙ 8fcYlf;NGOga73~nH=.'T81gWhp#f|zAvBP÷w#4ښl:)yy|FX# ,P+WVhF:tLJwo¢f ӑ- ^{?=76qi_looዽr9kl _l,5Gf=ҎFOX`f%~m˪5+o^\KOFof'oǖH]NAyEK5A//rK\r{9%du"rkx b(.ednlGvkkoPD/Sq!:̎Ԋmw@sv hDf1|pjp4G5(x /*3k+J>թw3ez}}{.\~|.O8l}2۶s[x;ƨَ}Px.aa+|~*ڱEDӊ ࿱¶OwQi1~¿  Aك_#/L=&%rVio)Ah^{w^K6$ i1D @U89`9[/eL4¯&"6Lc,셦*K=%\C5⬯a~8 zY|OD)YM?+BFA%Se9|y OECY' &.0;|)镆2Ta  4?7İp3ZT}] J۶SGS]سT)he{C/lN /?)5`woZ@ !V3$+X3ya؈d/fog-=0OmQP)ѻhsRz Tօ\;م/nVQlj8Y q_|[mRŸCYս>}XZoa(%3 |e k.["yر_~l`§1IzoT%= )FNAz6"7Ko@Ϯ:t.Er;뷭6 w>^5\>j*67|b[3;(SAy{?HmPיר:V(I8_J5 Gr{_cR=dG0G I}2;AÏ j ~:B\SͷgWC."heE/R >XnZ);">iOA_jhGZdJf?6 vuTȉ]Bqo;#u@x T~bC$GrO\·?|m{b3a|QU@_;{+B ?=H`{!drS)?=Er|0O+^S 0/ʍ,MR&KKKKY__RPnY ōܦPB  gЌ_=i\+7Fa| /~\ۣB}.54ƍѕ+!߾2jq[ A|ŋ@Nkϩf2Q0e {,H͍F?, \b3VFoq7 {͐o཯4^}5d'+{ =[4A(}˲d-//e  l,/c,///////O%R𗲄%oK?b\ rIENDB`Dd b  c $A? ?3"`?2uwd,QwD sMDG`!uwd,QwD sM ~ hvxR=KBa~sW!IaTCDCsKAؠR@%.-B[C45;QK?hKv } p|Wzz0k1N6nK;RSQDlU V&|shDdxD  3 @@"?DdxD  3 @@"?DdxD  3 @@"?DdxD  3 @@"?Dd"RD  3 @@"?DdU D  3 @@"?DdU !D  3 @@"?$$If!vh#v(#v#v8#v#v8:V l t065(558558ap2yt%$$If!vh#v(#v#v8#v#v8:V l t065(558558ap2yt%$$If!vh#vF#vb:V l t0 65F5bayt~h$$If!vh#vF#vb:V l t0 65F5bayt~h$$If!vh#vF#vb:V l t0 65F5bayt~h$$If!vh#vF#vb:V l t0 65F5bayt~h$$If!vh#vF#vb:V l t0 65F5bayt~h$$If!vh#vF#vb:V l t0 65F5bayt~hs$$If!vh#v#vF:V l t655F/ pyts$$If!vh#v#vF:V l t655F/ pyte$$If!vh#v#vF:V l t655Fpyte$$If!vh#v#vF:V l t655Fpyte$$If!vh#v#vF:V l t655Fpyte$$If!vh#v#vF:V l t655Fpyt$$If!vh#vx#v9#v&:V l t655F/ pyt$$If!vh#vx#v9#v&:V l t6,55F/ pyt{$$If!vh#vx#v9#v&:V l t6,55Fpyt{$$If!vh#vx#v9#v&:V l t6,55Fp  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?ABCDEFGPLOWZQRSTUVXY[\]a^_`bcdefghklmnopqrstuvwxyz{|}~Root Entry  Fm#NData @WordDocument >~ObjectPool  y#m#_1413353622F y# y#Ole CompObjfObjInfo  !"#%&'()*+,-./013456789:;<=>?@ABDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrsuvwxyz} FMicrosoft Equation 3.0 DS Equation Equation.39q* fc  n(n+1) Oh+'0 Equation Native F1TablejrSummaryInformation( DocumentSummaryInformation8 @yt{$$If!vh#vx#v9#v&:V l t6,55Fpyt{$$If!vh#vx#v9#v&:V l t6,55Fpyt$$If!vh#v#v#vk#v:V l t6555k5/ p(yt$$If!vh#v#v#vk#v:V l t6,555k5/ p(yt$$If!vh#v#v#vk#v:V l t6,555k5p(yt$$If!vh#v#v#vk#v:V l t6,555k5p(yt$$If!vh#v#v#vk#v:V l t6,555k5p(yt$$If!vh#v#v#vk#v:V l t6,555k5p(yt$$If!vh#v#v#vk#v:V l t6555k5/ p(yt$$If!vh#v#v#vk#v:V l t6,555k5/ p(yt$$If!vh#v#v#vk#v:V l t6,555k5p(yt$$If!vh#v#v#vk#v:V l t6,555k5p(yt$$If!vh#v#v#vk#v:V l t6,555k5p(yt$$If!vh#v#v#vk#v:V l t6,555k5p(yt$$If!vh#v#v#v\#v#v#vn:V l t6555\555n/ p<yt$$If!vh#v#v#v\#v#v#vn:V l t6,,555W555n/ p<yt$$If!vh#v#v#v\#v#v#vn:V l t6,,555\555np<yt$$If!vh#v#v#v\#v#v#vn:V l t6,,555\555np<yt$$If!vh#v#v#v\#v#v#vn:V l t6,,555\555np<yt$$If!vh#v#v#v\#v#v#vn:V l t6,,555\555np<yt 8 D P \hpxVoting TheoryPierce College 107temp.dotWindows User26Microsoft Office Word@8@+@ll>@ii՜.+,D՜.+,D hp  Pierce CollegeF< Voting Theory Title 8@ _PID_HLINKSA ,Shttp://upload.wikimedia.org/wikipedia/commons/d/d3/California_District_38_2004.png1_Phttp://upload.wikimedia.org/wikipedia/commons/9/99/Illinois_District_4_2004.png K0* pHdProjectQ(@= l Q T{ J< rstdole>stdoleP h%^*\G{00020430-C 0046}#2.0#0#C:\Windows\SysWOW64\e2.tlb#OLE Automation`Tem plater>F FmpJaAOePrQjEMacros##VBA##dir$OThisDocument21 cT8*\C;MSFQrms$3@ByD452EE1-E0D8F1A-8-02608C4D0BB4YyFM2.0L'B\0&/;&1B“ A00}#0#G 50 B32fF8-33A4-4823-B9DA-A7F799E55 2CIhAppData\Local\\Word8.0d8.exde=@#.E .`M ||d"rThisDocumentG`*Tri6D6cu 8ena2` H1"n`b,G"+0^7dG',wDZyFsx ޷`v@uBxME (S"SS"<:1TemplateProject.ThisDocument(%H0h %" %8p@xAttribute VB_Name = "ThisDocument" Bas1TemplateProject.hGlobaBlSpac~False Cre atablPr@edeclaI"dTru BEx0poseDeriv$Cust0omizC1a  *\G{000204EF-0000-0000-C000-000000000046}#4.1#9#C:\PROGRA~2\COMMON~1\MICROS~1\VBA\VBA7\VBE7.DLL#Visual Basic For Applications*\G{000209_VBA_PROJECTC PROJECTtPROJECTwm{)CompObj|r05-0000-0000-C000-000000000046}#8.5#0#C:\Program Files (x86)\Microsoft Office\Office14\MSWORD.OLB#Microsoft Word 14.0 Object Library*\G{00020430-0000-0000-C000-000000000046}#2.0#0#C:\Windows\SysWOW64\stdole2.tlb#OLE Automationp*\CC:\Users\dlippman\Dropbox\107 Book Ed 2.1\107temp.dot*\C107temp.dotB;R4*\G{2DF8D04C-5BFA-101B-BDE5-00AA0044DE52}#2.5#0#C:\Program Files (x86)\Common Files\Microsoft Shared\OFFICE14\MSO.DLL#Microsoft Office 12.0 Object Library*\G{0D452EE1-E08F-101A-852E-02608C4D0BB4}#2.0#0#C:\Windows\SysWOW64\FM20.DLL#Microsoft Forms 2.0 Object Library*\G{032BFAF8-33A4-4823-B9DA-A7F799E552C2}#2.0#0#C:\Users\dlippman\AppData\Local\Temp\Word8.0\MSForms.exd#Microsoft Forms 2.0 Object Library.E .`M  Q T{dThisDocument2s540c51f0#ThisDocumentG 圩3L+4`$'WordkVBAWin16~Win32Win64xMacVBA6#VBA7#Project-stdole`TemplateProjectEOfficeuMSFormsC ThisDocument< _EvaluateDocumentjMTCommand_OnRibbonLoadedr#MTCommand_OnSelectedIndexBrowseType a` # ID="{BD7459C5-5C07-4000-8E38-9698D76A13AB}" Document=ThisDocument/&H00000000 Name="Project" HelpContextID="0" VersionCompatible32="393222000" CMG="1614D1CDF1F503F903F903F903F9" DPB="2C2EEBE317F818F818F8" GC="424085119A129A1265" [Host Extender Info] &H00000001={3832D640-CF90-11CF-8E43-00A0C911005A};VBE;&H00000000 &H00000002={000209F2-0000-0000-C000-000000000046};Word8.0;&H00000000 [Workspace] ThisDocument=0, 0, 0, 0, C ThisDocumentThisDocument  F Microsoft Word 97-2003 Document MSWordDocWord.Document.89q^/ 002 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p8XV~_HmH nH sH tH D`D NormalCJPJ_HaJmH sH tH h`h , Heading 1$$P@&^P#5B*CJOJPJQJ\aJphOh`h - Heading 2$$@&^#5B*CJOJPJQJ\aJphO``` . Heading 3$<@&#5B*CJOJPJQJ\aJphOb@b q Heading 4($ ``<@&^``5CJ\aJf@f q Heading 5% <@&^`56CJ\]aJ`@` q Heading 6% <@&^`5CJ\aJRR q Heading 7% <@&^`X@X q Heading 8% `<@&^``6]f @f q Heading 9% 00<@&^0`CJOJQJ^JaJDA`D Default Paragraph FontRi@R  Table Normal4 l4a (k ( 0No List jj ' Table Grid7:V0~o~ Definition BodyE  %d&d'dOp0Pp0Qp0] ^ LoL HDefinition Body Char CJPJaJ2o!2 Bq7Example 5B*ph4@24 Header  !4 @B4 Footer  !B'`QB Comment ReferenceCJaJ<@b<  Comment TextCJaJ@j@ab@ Comment Subject5\H@H  Balloon TextCJOJQJ^JaJ>@> !q Footnote TextCJaJB^B q0 Normal (Web)dd[$\$66 qfirstpdd[$\$22 qparadd[$\$*@* qTOC 15.. qTOC 2 ^.. qTOC 3 ^.)@.  # Page Number<< HFootnote Text Char@&`!@ HFootnote ReferenceH*6U`16 H Hyperlink >*B*ph\oB\ Example Header$P&d Pp^P B* phpoR )Definition HeaderE%  $d%d'dNp0Op0Qp0] ^  5B*php0D@bD { List Paragraph &^m$NorN * Try it Now'$d Nl  5B*phl LoL Try it Now body(&d Pl \o\ %HDefinition Header Char5B*CJPJaJphp0NoN 'HTry it Now Char5B*CJPJaJphl FoF  Example Body+%d OpToT Heading 1 Char5B*CJOJQJ\aJphOToT Heading 2 Char5B*CJOJQJ\aJphOToT Heading 3 Char5B*CJOJQJ\aJphOPK![Content_Types].xmlN0EH-J@%ǎǢ|ș$زULTB l,3;rØJB+$G]7O٭V$ !)O^rC$y@/yH*񄴽)޵߻UDb`}"qۋJחX^)I`nEp)liV[]1M<OP6r=zgbIguSebORD۫qu gZo~ٺlAplxpT0+[}`jzAV2Fi@qv֬5\|ʜ̭NleXdsjcs7f W+Ն7`g ȘJj|h(KD- dXiJ؇(x$( :;˹! I_TS 1?E??ZBΪmU/?~xY'y5g&΋/ɋ>GMGeD3Vq%'#q$8K)fw9:ĵ x}rxwr:\TZaG*y8IjbRc|XŻǿI u3KGnD1NIBs RuK>V.EL+M2#'fi ~V vl{u8zH *:(W☕ ~JTe\O*tHGHY}KNP*ݾ˦TѼ9/#A7qZ$*c?qUnwN%Oi4 =3N)cbJ uV4(Tn 7_?m-ٛ{UBwznʜ"Z xJZp; {/<P;,)''KQk5qpN8KGbe Sd̛\17 pa>SR! 3K4'+rzQ TTIIvt]Kc⫲K#v5+|D~O@%\w_nN[L9KqgVhn R!y+Un;*&/HrT >>\ t=.Tġ S; Z~!P9giCڧ!# B,;X=ۻ,I2UWV9$lk=Aj;{AP79|s*Y;̠[MCۿhf]o{oY=1kyVV5E8Vk+֜\80X4D)!!?*|fv u"xA@T_q64)kڬuV7 t '%;i9s9x,ڎ-45xd8?ǘd/Y|t &LILJ`& -Gt/PK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6 0_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!0C)theme/theme/theme1.xmlPK-! ѐ' theme/theme/_rels/themeManager.xml.relsPK] qr|DHR|tsrqpy~HR|), 999X.c! 9EKV0ZM^gnw} IMPSVX[\^acehul5 ,%`8|=@IALmTZk^ekpw}ڀ6Mgˏݏ 1DWyѐ6K`uɑ 2 G ]  JKLNOQRTUWYZ]_`bdfgijklmnopqrstvwxyz{|}~MMMMVeVhVW2W5WWWWeX}XXYYYoooq0q3q|:_______ ,36KRU!!!QQQQ/Xb$$hsN\@8HH,b$=t\c} 35@H@ (  : &c 3  "<?Z  S X?&c*h a  "[P   "`a  r@ABNC8EFN88@`"`G Y P n  C "` ]    v@AB CpEFTp p @`"`Pa  t@AB CpEFo pp@`"`PaV  # o"` a  t@AB CpEFo pp@`"` (an  C  "`m)    47 u3  "<?Z v S X?47h a  "G vB w  a x f@ABNC8EFN88@`G Y P ` y C y ]  H z # o aH { # o <a | j@AB CpEFTp p @`PaH } # o<a` ~ C ~mu    p C @@ c"$?  q C @@ c"$?  r C @@ c"$?  s C @@ s"*?  t C @@ s"*? X  S A Jhttp://upload.wikimedia.org/wikipedia/commons/d/d3/California_District_38_2004.pngFile:California District 38 2004.png3"`?F  S A Dhttp://upload.wikimedia.org/wikipedia/commons/9/99/Illinois_District_4_2004.pngFile:Illinois District 4 2004.png#" `?B S  ?fV3WW~XYo1qAqqr|txtsxtrxtqxtp"Rtut~t!!TNx##AT$$RGZGxGGGGGGPP ?ABKK@LmLMMQQ^^__``t`tXuuYvvwwxx \>c?f?o@_C#lDJ7EFGGFKv8OxRAWG7YZT[N'\{aib1Nce d0d1d?dfbg2h~hCiPkfJm@quqP sNsss u8wPxY{A2|X\}b^g98=jM2DQ,%n+(dIO\m-<a^iDh9n:j I sbDir;Y1qm$ov{Tq'Y9\yXZC\ #Au[QXH ?7b6{{K6@$$$$Ldegh|H@HlH@HpH@H@@UnknownG*Ax Times New Roman5Symbol3. *Cx Arial7.@Calibri7@Cambria5. .[`)TahomaA$BCambria Math#qHhg.s'fiiFiiF!p24<< uq 3QHP ?'2!xx 'C:\Users\dlippman\Documents\107temp.dot Voting TheoryPierce College Windows UserT