Circles

mapping = {}
mapping["3"] = "1 s"
mapping["5"] = "1 s 1"
mapping["7"] = "1 1 s 1"
mapping["9"] = "2 1 s 2"
mapping["11"] = "2 1 s 1 2"
mapping["13"] = "2 2 s 2 2"
mapping["15"] = "2 2 1 s 2 2"
mapping["17"] = "2 2 1 s 1 2 2"
mapping["19"] = "3 2 1 s 1 2 3"
mapping["21"] = "3 2 1 1 s 1 2 3"
mapping["23"] = "3 2 2 1 s 2 2 3"
mapping["25"] = "3 2 2 1 s 1 2 2 3"
mapping["27"] = "3 3 1 2 s 2 1 3 3"
mapping["29"] = "3 3 2 1 1 s 1 2 3 3"
mapping["31"] = "3 3 2 1 1 s 1 1 2 3 3"
mapping["33"] = "4 2 2 2 1 s 1 2 2 2 4"
mapping["35"] = "4 3 2 1 1 1 s 1 1 2 3 4"
mapping["37"] = "4 3 2 1 2 1 s 2 1 2 3 4"
mapping["39"] = "4 3 2 2 1 1 s 1 1 2 2 3 4"
mapping["41"] = "4 3 2 2 1 1 1 s 1 1 2 2 3 4"
mapping["43"] = "4 3 3 1 2 1 1 s 1 2 1 3 3 4"
mapping["45"] = "4 4 2 2 1 1 1 s 1 1 1 2 2 4 4"
mapping["47"] = "4 4 2 2 1 2 1 s 1 2 1 2 2 4 4"
mapping["49"] = "4 4 2 2 2 1 1 1 s 1 1 2 2 2 4 4"
mapping["51"] = "5 3 3 1 2 1 2 1 s 2 1 2 1 3 3 5"
mapping["53"] = "5 3 3 2 1 2 1 1 s 1 1 2 1 2 3 3 5"
mapping["55"] = "5 3 3 2 2 1 1 1 1 s 1 1 1 2 2 3 3 5"
mapping["57"] = "5 4 2 2 2 1 2 1 1 s 1 2 1 2 2 2 4 5"
mapping["59"] = "5 4 2 2 2 2 1 1 1 s 1 1 1 2 2 2 2 4 5"
mapping["61"] = "5 4 3 2 1 2 1 2 1 s 1 2 1 2 1 2 3 4 5"
mapping["63"] = "5 4 3 2 2 1 2 1 1 1 s 1 1 2 1 2 2 3 4 5"
mapping["65"] = "5 4 3 2 2 2 1 1 1 1 s 1 1 1 1 2 2 2 3 4 5"
mapping["67"] = "5 4 3 2 2 2 1 2 1 1 s 1 1 2 1 2 2 2 3 4 5"
mapping["69"] = "5 5 2 3 2 1 2 1 1 1 1 s 1 1 1 2 1 2 3 2 5 5"
mapping["71"] = "5 5 3 2 2 1 2 1 2 1 1 s 1 2 1 2 1 2 2 3 5 5"
mapping["73"] = "6 4 3 2 2 2 1 2 1 1 1 s 1 1 1 2 1 2 2 2 3 4 6"
mapping["75"] = "6 4 3 2 2 2 2 1 1 1 2 s 2 1 1 1 2 2 2 2 3 4 6"
mapping["77"] = "6 4 3 3 2 1 2 1 2 1 1 1 s 1 1 2 1 2 1 2 3 3 4 6"
mapping["79"] = "6 4 3 3 2 2 1 2 1 1 1 1 s 1 1 1 1 2 1 2 2 3 3 4 6"
mapping["81"] = "6 4 4 2 2 2 2 1 1 2 1 1 s 1 1 2 1 1 2 2 2 2 4 4 6"
mapping["83"] = "6 5 3 2 2 2 2 1 2 1 1 1 1 s 1 1 1 2 1 2 2 2 2 3 5 6"
mapping["85"] = "6 5 3 2 3 1 2 2 1 1 1 2 1 s 2 1 1 1 2 2 1 3 2 3 5 6"