{"text_format":"1","workbook":"xlsx","n_sheets":1,"sheets":["Question 5"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":0,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Question 5","index":0,"n_rows":1048576,"n_cols":28,"rows_kept":4500,"cut":true,"hidden":false,"merged":[[50,2,51,5],[8,3,8,4],[9,3,9,4],[10,3,10,4],[11,3,11,4],[28,3,28,4],[40,2,41,5]],"bounds":{"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0}}
["RETFRC Fall 2023",null,null,null,null,null,null,null,{"$f":"A1","v":"RETFRC Fall 2023"}]
["Question 5",null,null,null,null,null,null,null,"Question 5"]
[]
["(12 points)",null,"Your client is establishing a new non-contributory defined benefit pension plan that recognizes past service.",null,null,null,null,null,"Answer question here:"]
[]
[null,null,"You are given:",null,null,null,null,null,"A)","Candidates answered this part relatively well. Some candidates were not familiar with the AAN method and calculated the UAL under the PUC/UC method. "]
[null,null,null,null,null,null,null,null,null,"Other candidates lost some marks because they calculated the NC individually and then added them."]
[null,null,"Plan provisions:",null,null,null,null,null,null,"Initial UC Actuarial Liability"]
[null,null,"Retirement benefit:","$100 per month per year of service",null,null,null,null,null,"Member A ",null,null,null,null,null,null,null,null,null,"Member B"]
[null,null,"Normal form of payment:","Life only, payable monthly in advance",null,null,null,null,null,48,18,null,null,null,null,null,null,null,null,64,34]
[null,null,"Normal retirement age:","Age 65",null,null,null,null,null,"Age","Service","Benefit","Decrement Probability","Survival Probability","Discount Factor","ä65(12)","AL",null,null,"Age","Service","Benefit","Decrement Probability","Survival Probability","Discount Factor","ä65(12)","AL"]
[null,null,"Termination benefit:","Accrued pension deferred to normal retirement age",null,null,null,null,null,48,{"$f":"K10","v":18},{"$f":"100*12*K12","v":21600},0.04,1,{"$f":"1.05^-(65-J10)","v":0.43629668761085727},12.5,{"$f":"PRODUCT(L12:P12)","v":4712.0042261972585},null,null,65,{"$f":"U10","v":34},{"$f":"100*12*U12","v":40800},1,1,{"$f":"1.05^-(T12-T10)","v":0.95238095238095233},12.5,{"$f":"PRODUCT(V12:Z12)","v":485714.28571428568}]
[null,null,null,null,null,null,null,null,null,49,{"$f":"K12","v":18},{"$f":"100*12*K13","v":21600},0.04,{"$f":"N12*(1-M12)","v":0.96},{"$f":"1.05^-(65-J10)","v":0.43629668761085727},12.5,{"$f":"PRODUCT(L13:P13)","v":4523.5240571493678},null,null,null,null,null,null,null,null,null,{"$f":"AA12","v":485714.28571428568}]
[null,null,"Actuarial assumptions and methods:",null,null,null,null,null,null,65,{"$f":"K13","v":18},{"$f":"100*12*K14","v":21600},1,{"$f":"N13*(1-M13)","v":0.92159999999999997},{"$f":"1.05^-(J14-J10)","v":0.43629668761085727},12.5,{"$f":"PRODUCT(L14:P14)","v":108564.57737158482}]
[null,null,"Discount rate:","5% per year",null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(Q12:Q14)","v":117800.10565493145}]
[null,null,"Decrements:","Beginning of year"]
[null,null,"Retirement:","Later of: age 65 or 1 year after the valuation date"]
[null,null,"Termination rates:","Age","Rate",null,null,null,null,"UAL and NC"]
[null,null,null,"Prior to age 50","4% per year",null,null,null,null,"Member A ",null,null,null,null,null,null,null,null,null,"Member B"]
[null,null,null,"At or after age 50","0% per year",null,null,null,null,48,18,null,null,null,null,null,null,null,null,64,34]
[null,null,"Other pre-retirement decrements:","None",null,null,null,null,null,"Age","Service","Benefit","Decrement Probability","Survival Probability","Discount Factor","ä65(12)","PVFB","PVFY",null,"Age","Service","Benefit","Decrement Probability","Survival Probability","Discount Factor","ä65(12)","PVFB","PVFY"]
[null,null,"Actuarial cost method:","Attained Age Normal",null,null,null,null,null,48,{"$f":"K20","v":18},{"$f":"100*12*K22","v":21600},0.04,1,{"$f":"1.05^-(65-J20)","v":0.43629668761085727},12.5,{"$f":"PRODUCT(L22:P22)","v":4712.0042261972585},{"$f":"M22*N22*(1-1.05^-(J22-J20))/(0.05/1.05)","v":0},null,65,{"$f":"U20+T22-T20","v":35},{"$f":"100*12*U22","v":42000},1,1,{"$f":"1.05^-(T22-T20)","v":0.95238095238095233},12.5,{"$f":"PRODUCT(V22:Z22)","v":500000},{"$f":"W22*X22*(1-1.05^-(T22-T20))/(0.05/1.05)","v":1.0000000000000011}]
[null,null,"Asset method:","Market value of assets",null,null,null,null,null,49,{"$f":"K22+J23-J22","v":19},{"$f":"100*12*K23","v":22800},0.04,{"$f":"N22*(1-M22)","v":0.96},{"$f":"1.05^-(65-J20)","v":0.43629668761085727},12.5,{"$f":"PRODUCT(L23:P23)","v":4774.8309492132221},{"$f":"M23*N23*(1-1.05^-(J23-J20))/(0.05/1.05)","v":3.8400000000000045E-2},null,null,null,null,null,null,null,null,{"$f":"AA22","v":500000},{"$f":"AB22","v":1.0000000000000011}]
[null,null,null,null,null,null,null,null,null,65,{"$f":"K23+J24-J23","v":35},{"$f":"100*12*K24","v":42000},1,{"$f":"N23*(1-M23)","v":0.92159999999999997},{"$f":"1.05^-(J24-J20)","v":0.43629668761085727},12.5,{"$f":"PRODUCT(L24:P24)","v":211097.78933363719},{"$f":"M24*N24*(1-1.05^-(J24-J20))/(0.05/1.05)","v":10.909688426654514}]
[null,null,"Participant data at January 1, 2023:",null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(Q22:Q24)","v":220584.62450904766},{"$f":"SUM(R22:R24)","v":10.948088426654513}]
[null,null,"Employee:","Member A","Member B"]
[null,null,"Age (years):",48,64,null,null,null,null,"Total"]
[null,null,"Service (years):",18,34,null,null,null,null,"AL",{"$f":"Q15+AA13","v":603514.39136921708}]
[null,null,null,null,null,null,null,null,null,"F",600000]
[null,null,"Additional information:",null,null,null,null,null,null,"UAL",{"$f":"K28-K29","v":3514.3913692170754}]
[null,null,"Market value of assets as at January 1, 2023:",600000," ",null,null,null,null,"PVFB",{"$f":"AA23+Q25","v":720584.62450904772}]
[null,null,null,null,null,null,null,null,null,"PVFY",{"$f":"R25+AB23","v":11.948088426654515}]
[null,null,"Annuity factors:",null,null,null,null,null,null,"n",2]
[null,null,"ä68(12) = ",11.6,"ä67(12) = ",11.9,null,null,null,"NC",{"$f":"(K31-K30-K29)/K32*K33","v":19596.479195561245},"(PVFB - F - UAL) / PVFY * n"]
[null,null,"ä66(12) = ",12.2,"ä65(12) = ",12.5]
[null,null,"ä64(12) = ",12.8,"ä63(12) = ",13.1,null,null,"B)","Candidates answered this part relatively well. Some candidates were not familiar with the AAN method and calculated the UAL under the PUC/UC method. "]
[null,null,null,null,null,null,null,null,null,"Other candidates lost some marks because they calculated the NC individually and then added them."]
[null,null,null,null,null,null,null,null,null,"UAL and NC"]
["(a)","(4 points)","Calculate the unfunded actuarial liability and the total normal cost as at January 1, 2023."]
[null,null,null,null,null,null,null,null,null,"Member A ",null,null,null,null,null,null,null,null,null,"Member B"]
[null,null,"Show all work, including each step of the calculation separately, in the workspace provided to the right (in Excel).",null,null,null,null,null,null,49,19,null,null,null,null,null,null,null,null,65,35]
[null,null,null,null,null,null,null,null,null,"Age","Service","Benefit","Decrement Probability","Survival Probability","Discount Factor","ä65(12)","PVFB","PVFY",null,"Age","Service","Benefit","Decrement Probability","Survival Probability","Discount Factor","ä65(12)","PVFB","PVFY"]
[null,null,null,null,null,null,null,null,null,49,{"$f":"K41","v":19},{"$f":"100*12*K43","v":22800},0.04,1,{"$f":"1.05^-(65-J41)","v":0.45811152199140021},12.5,{"$f":"PRODUCT(L43:P43)","v":5222.4713507019624},{"$f":"M43*N43*(1-1.05^-(J43-J41))/(0.05/1.05)","v":0},null,66,{"$f":"U41+T43-T41","v":36},{"$f":"100*12*U43","v":43200},1,1,{"$f":"1.05^-(T43-T41)","v":0.95238095238095233},12.2,{"$f":"PRODUCT(V43:Z43)","v":501942.85714285704},{"$f":"W43*X43*(1-1.05^-(T43-T41))/(0.05/1.05)","v":1.0000000000000011}]
[null,null,"You are given the following for 2024:",null,null,null,null,null,null,65,{"$f":"K43+J44-J43","v":35},{"$f":"100*12*K44","v":42000},1,{"$f":"N43*(1-M43)","v":0.96},{"$f":"1.05^-(J44-J41)","v":0.45811152199140021},12.5,{"$f":"PRODUCT(L44:P44)","v":230888.20708366571},{"$f":"M44*N44*(1-1.05^-(J44-J41))/(0.05/1.05)","v":10.92447171665337},null,null,null,null,null,null,null,null,{"$f":"AA43","v":501942.85714285704},{"$f":"AB43","v":1.0000000000000011}]
[null,null,"·      \tA contribution of $20,000 was made to the plan on December 31, 2023.",null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(Q43:Q44)","v":236110.67843436767},{"$f":"SUM(R43:R44)","v":10.92447171665337}]
[null,null,"·      \tThe plan's assets earned a rate of return of 5% during 2023.",null,null,null,null,null,null,"Total"]
[null,null,"·       Member B did not retire.",null,null,null,null,null,null,"AL",{"$f":"(K28+K34)*1.05","v":654266.41409301723}]
[null,null,null,null,null,null,null,null,null,"F",{"$f":"K29*1.05+20000","v":650000}]
["(b)","(3 points)","Calculate the unfunded actuarial liability and the total normal cost as at January 1, 2024.",null,null,null,null,null,null,"UAL",{"$f":"K47-K48","v":4266.4140930172289}]
[null,null,null,null,null,null,null,null,null,"PVFB",{"$f":"AA44+Q45","v":738053.53557722468}]
[null,null,"Show all work, including each step of the calculation separately, in the workspace provided to the right (in Excel).",null,null,null,null,null,null,"PVFY",{"$f":"R45+AB44","v":11.924471716653372}]
[null,null,null,null,null,null,null,null,null,"n",2]
[null,null,null,null,null,null,null,null,null,"NC",{"$f":"(K50-K49-K48)/K51*K52","v":14052.969972194707},"(PVFB - F - UAL) / PVFY * n"]
["(c)","(5 points)","Calculate the effect of the demographic experience by source between January 1, 2023 ",null,null,null,null,null,null,"NC",{"$f":"K53/2","v":7026.4849860973536},"(per member)"]
[null,null,"and January 1, 2024 on the normal cost for each member."]
[null,null,null,null,null,null,null,null,"C)","This question was answered very poorly. Very few candidates knew the structure of how the gains/losses were calculated under the AAN method."]
[null,null,"Show all work, including each step of the calculation separately, in the workspace provided to the right (in Excel)."]
[]
[null,null,null,null,null,null,null,null,null,"Member A",null,"Expected","Actual",null,null,null,null,null,null,"Member B",null,"Expected","Actual"]
[null,null,null,null,null,null,null,null,null,null,"PVFB",{"$f":"Q25*1.05","v":231613.85573450004},{"$f":"Q45","v":236110.67843436767},null,null,null,null,null,null,null,"PVFB",{"$f":"AA23*1.05","v":525000},{"$f":"AA44","v":501942.85714285704}]
[null,null,null,null,null,null,null,null,null,null,"PVFY",{"$f":"R25*1.05-1*1.05*0.96","v":10.487492847987237},{"$f":"R45","v":10.92447171665337},null,null,null,null,null,null,null,"PVFY",{"$f":"AB23*1.05-1*1.05","v":0},{"$f":"AB44","v":1.0000000000000011}]
[]
[null,null,null,null,null,null,null,null,null,"Total",null,null,null,null,null,null,null,null,null,"Total"]
[null,null,null,null,null,null,null,null,null,"Expected","PVFB",{"$f":"K50-M60+L60","v":733556.71287735715},null,null,null,null,null,null,null,"Expected","PVFB",{"$f":"L64-W60+V60","v":756613.8557345001}]
[null,null,null,null,null,null,null,null,null,null,"PVFY",{"$f":"K51-M61+L61","v":11.487492847987239},null,null,null,null,null,null,null,null,"PVFY",{"$f":"L65-W61+V61","v":10.487492847987237}]
[null,null,null,null,null,null,null,null,null,null,"NC",{"$f":"(L64-K49-K48)/L65*K52","v":13804.630798657277},null,null,null,null,null,null,null,null,"NC",{"$f":"(V64-K49-K48)/V65*K52","v":19517.999797468357}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L66/2","v":6902.3153993286387},"(per member)",null,null,null,null,null,null,null,null,{"$f":"V66/2","v":9758.9998987341787},"(per member)"]
[null,null,null,null,null,null,null,null,null,null,"G&L",{"$f":"L67-K54","v":-124.16958676871491},"NC lower than expected due to member not terminating",null,null,null,null,null,null,null,"G&L",{"$f":"V67-L67","v":2856.68449940554},"NC higher than expected due to member not retiring"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"PRODUCT(K1048576:O1048576)","v":0}]