{[<([<[[(<[({<<><>><()[]>}<(()())(())>)<(([]())){<()()><{}<>)}>][(((()<>)[{}{}]){<[]<>>({}{})})]>)[(({([{}[]]
{{[[(<[[[<[<<{()()}(<>{})>[<<><>>[[]]]>[{{[]<>}[[]]}<<[]{}>[<>[]]>]]([[[{}<>]]<<()[]>{()<>}>]([<<
([<{[[{{((([(<[]<>>{[]<>})<([]){<>{}}>][([<>[]][[]{}])])[[{{()[]}<()[]>}<{(){}}>]]]<{(<[{}<
(({(<{(([<[({([]())(<>())}{([]{})[{}{}]})]{(({{}()}{<>()}](<[]<>>(()[])))({[[]{}]<[]<>>})}>[[[{<<>[]>(()
[([<([{({{[{[([]{})[{}[]]][[{}{})]}<([<>{}]<<>()>)>]}([<{[()<>]{()<>}}[[{}{}]<(){}>]><{{{}[]}[()<>]}[{{
<(([<{{<(<[(<{()()}>(({}()){()[]}))<[<[]()>[[]()]]<{[]()}<<>{}>>>](<[([]())]>(([()()][()<>])({()<>}<[]<>>))
[{({<(<[{({{{[()[]](<>[])}{([]{})<<>{}>}}}{{<<{}[]>(<>)><(<><>)([]())>}<{({}<>)(<><>)}{[{}{}
([(<{<[<{[({[<[]{}><<><>>]<({}[])({}<>)>}([{{}<>}<[]()>]<<<><>>>)){({<<><>>[[]{}]}(<()<>>{()}))<{<[
({{([(<{{{{{{([]{}){<>{}}}}{<<()>{{}{}}>[({}())(()<>)]}}[[[[{}{}](<><>)]{<()[]><[][]>}](([[]](()()))<[[]
(<<[<{{{({{<{{(){}}{<>()}}<({}{}){[][]}>>[{<[]{}>{<>()}}<{[]<>}[()<>]>]}}({([({}[])(<>{})][{<>}])[{[()<>]<{}
{[(<<((<[[<{<{<>()}[{}[]]>}{{((){})[()<>]}<{(){})[{}{}]>}>]({((<<>()>){[<>()]{{}()}}){{[()()][<><>]}
{(((([[(<[({({{}()}[<>[]])<(<><>)([]())>}{<[[]<>]><<()<>><()<>>>})<[[<[]{}><<>{}>]]>]<<{{[
[{(<[[(<(<[{<({}[])<{}{}>>(<[]<>>)}]<{(<[]()>[()()])}>>{({<{{}()}[<>()]>})<[[(<>())(<>{})]{{{}[]}}][({{}[]}
{[[<([{[(<<[<<()()>[[]]>[{()()}]](<[()]<()[]>><<{}()>{()()}>)>><[[([{}<>]{{}()})<{{}[]}<()[]>>]]})[([{{{<>()}
((({[(<<{(((<<{}()>><{<><>}>)))[[{<({}[])[{}[]]>}(<[<><>][()()]><[[][]]<{}[]>>)]]}((({<(<>())>[({}{
{<{{[(<<{(<{[({}<>)<{}[]>]([(){}](<>[]))}<(({}()){[][]}}[<()[]><{}()>]>>)}<<{(<[{}()]{<>{}}>[[[]()](()
{(<<({{([<[<[<{}<>>{[][]}]<[<><>][()[]]>>{(({}{})){<()><()()>}}]>(<({{()()}({}<>)}<([]<>){[]{}}>){([[]<>
<(<({{{([({{<<{}<>><()[]>>[{()<>}[<>{}]]}})({([{()[]}{(){}}]<(()<>)<{}<>>>)}<{{<{}<>>[[][]]}}<[{<>}[<>
{({{(<<([({{[(()<>)[[]<>]][(<>{})({}())]}})]{(<[<(<>()){<><>}><<{}()>[[]]>][{{<>()}{[]()}}{[()<>]{<>()}}]>)
([<({{{([[<<[[()[]][<><>]]<<<>[]><()()>>>(<{()<>}<()[]>><{<>()}<[]{}>>)>({(<()[]]<()()>)<[<>()][{}]>
{[{<((<[<<({<{[]{}}[()()>>({[][]}[[]()])})(([{()}{{}()}]<<{}()>{{}{}}>)<([<>()])(<{}<>><{}[]>)>)>{[{
{{([([{(<[[{[{()<>}({}())][[[]<>]<{}{}>]}]<<[({}[])(()<>)]({(){}}[()()])>{{(())<(){}>}}>]{[<{[[]()]{<>[]}}
<(<({<{<<<([<([]<>)([]<>)>]<{{{}{}}<<>()>}>)<<{[[]()](<>{})}(([]())<[]()>)><[{<>{}}[(){}]]>>>>>(<{<[[[{
(([({<{(<{[<({<><>}){{[][]}}>{<([]()){{}{}}>[([][])<{}{}>]}]}[((<{()<>}>)[{{()<>}{[][]}}])]
(<<<(({{{([[<{(){}}>{(()())(()[])}]{({{}[]}<[][]>]<{{}<>}{()}>}])<(({[[][]]{{}{}}}(([][])<(){}>)
{<{{[[({<<{{({{}()}({}{})><[()<>][<>{}]>}([<()[]>({}())][{()<>}[()]])}{<[{(){}}<[]{}>][[[]<>][[][]]]>([[<>]
{{{[(<([[[[{[[(){}}<{}>]<{<>[]}{{}{}}>}]<[[(<>())((){})]((<>()))]{(<[]{}>([][])){<[]<>>(()[])}}>]
(<{[([[<(<[<{[<>{}]}(<[]<>>{{}<>})>[{(())}]]>){<{(<(<>())<{}()>>]}({<<[]<>>[[]<>]>((()<>)[<><>])}
[<{[[(({([((({[]{}}[()()])))]>[((<<[<><>][[]()]>{[()<>][()()]}>({{<>[]}({}<>)})))]})){((<[<[<[<>()]>
<({[{{{<{[<[({[]{}}<[]>)(({}[])({}<>))]><{((()()))[[()<>]{<>[]}]}(<((){})<{}{}>><({}[])>)]][([<{
<(<<<<<[(<<[{{[][]}{{}{}}}{{[][]}<()>}](<([]{})[()[]]>[[{}{}]{<>()}])>([{[[]()]<<>[]>}[<<>{}>{<>
<(<[[<[[[<<(<(()[])<{}()>><(<>{})>)[([{}{}]([]{}))]><<<[<>[]]{<>[]}>{(()<>)({}[])}>>><[[[{<
([[{[({<({(([<(){}><[]<>>]<{()<>}({})>))([([{}<>][{}[]]){[<>[]]({}<>)}][[({}[]){[]()}]])})>[({{(<(()[]){<>
<[<{<[{(<<[[{{(){}}({}<>)}<(()[])>]<<<()()>(()<>)>({{}})>]({[(<>{})<{}()>]{<{}<>><<><>>}}<<{()<>}
{[{({[[(({{{{<()()>{[]{}}}{[<>[]]<()<>>}}(<<<>()><{}<>>>({()<>}[()<>])}}{<{[()[]]{(){}}}>[<<[]{}>>[((){})<(
{{(<[<(<(<{{(<[]()><()<>>)}{((<><>))[<<>{}>{()[]}]}}>{{<({{}{}}[()<>])[<(){}>(<>[])]><<(<>{}}[{}
[{{{[[[[{(<{<[<>[]](()[])]{{<>{}}}}{[(()()){[][]}]{([][])}}><<{<<>()>([])}[[[]{}]<{}{}>]>(([{}<>]<[]()>)
{[[(<([[[[((({<>{}}(<>())){<{}[]>})[([<>[]](<>[])}[({}[])([]())]])([<{{}()}(<>())><[[][]][<>()]>][([()()]<<>[
<[{[{({(<(((<<<>{}><[]()>][{{}()}{[][]}])[(((){})([][]))[[()<>][[]{}]]])[[(((){})[()])[[(){}]<{}
[{[[<[<{{(({([(){}]<()()>](([]<>)[()[]])}<<{[][]}([][])>>)<[[([]())<{}[]>]]>){[[[{{}()}[<>[]]]{<[]{}>
[[<([([[<<<{{[{}[]][<><>]}}{{{{}{}}}}>>>[([[(<<>[]>({}<>))<([]())<<><>>>]{{<<>[]>{<>()}}}][<{{[
({[<<<((<<<<<<[]{}>[()()]>{[()[]]{()<>}}>[((<>()){()()}){<[][]]<{}{}>}]>{{[[{}{}]<{}[]>]([[]<>])}((
({<<[[{{<{[[{<()><<>>}<<()[]>([][])>]]([[({}<>)[()[]]](([]{})<<>[]])]<[([]<>){[]}]>)}(((<<{}[
<(<(<(([([[[{{[]()}{<>()}}{<{}[]>[{}()]}]{{[{}{}]<()[]>}({<>()}<(){}>)}][[{<{}()><[][]>}](<[
[[<{<[<[<({<<{[]}<()<>>>({<><>}{[]<>})><([<>()]([][]))>}[({[{}{}]<{}[]>})({[<><>]})])>]([[{<({
<([{[[<<[({<<[{}()]({}[])>{<[][]>{()()}}>{<(<>[])([]{})>([{}[]}[<>])}}{{[<<>[]>{[]<>}][([][]){{}{}}]
[([({((<[{{{[<{}><<>()>]<<()[]>>}<[{{}{}}([][])]{{()<>}<(){}>}>}<{<[[][]]>({{}<>}{()[]})}>
[[[{([({{{<{[[[][]]{()()}]}{{<<>[]>[{}[]]}[[[]()]<<>>]}>({{(<>[])[{}[]]}({<>()}[{}[]])}{{(()<
{<{{{<[{[<{(<{[]{}}{[][]}>{{[]<>}}}}[{((()[])<()()>)[<<>[]><{}()>]}<[{<>{}}[()<>]]<[<>[]][<>{}]>>]>[<[
<[<{[[<{<[([{({}[])(()<>)}[[<>()]{()[]}]])][[<{[<>[]][<>[]]}<{<>{}}{<>{}}>>{<<()()><()<>>>{([]()
<[{{({<[<([[[([]{})({}())]]<[{{}}[()<>]]<{<>{}}{()}>>])<[<[<<>()>]{<{}{}>[[]<>]}><({[]()}<<><>>)[(()<>)(<>())
{<[[[<(<[<{<({<>{}}[<><>])([{}<>]<[][]>)><<[(){}](<>[])>[({}[])<<>[]}]>}{{{(<>())(<>{})}}<((<>())
<{(<<[{[{<{<<((){})[[]{}]><([]<>)<{}[]>>>{[[[][]]<()()>]}}{({{<>()}<<>()>}{<{}<>><()[]>})}>}<[<([<()()>{()()
{{([<{[[((<<{<<>()><<>[]>}<(()<>)>>><<[<[][]><{}<>>]>{<([]()){[]<>}>}>))]<{(((<[[]<>]([]<>)>[{{}()}<<
([{{({{<[[(((<[][]>{<>{}}){<()[]>{[]()}})(<({}<>)([]<>)>(([])[()<>])))(([([][]){()<>}]{{[]<>}{[](
[{{<{({[<{<{((<>())({}[]))<{<>()}({}[])>}(<[{}()]<{}<>>>({[][]}{()<>}))}{([({}[]){{}[]}]<([][])>)}}{<{({{}(
[{(([[[([<<(<([]()){<>}>(({}<>)(()())))[((<>{})){[()<>]<<>{}>}]>>][<{{[<()<>>{{}[]}]<<{}[]><{}[]>]}[
{<<<(<[<[{<[<({}[])>(([])<[]<>>)]<<<{}{}>({}())>{[<>{}}<[][]>}>>[{[<<>()><()()>]{[<>[]]<[]>}}[<<<>[]>{[]()
([(((<<(<[[<[<{}<>>(<><>)]>([<{}[]>{<>{}}]({<>{}}[()()]))]](<({<<>[]>({}[])}<[[]<>]{<>[]}>)(<{
([{({{{[(((<<{[]()}<{}<>>>((<><>){[]()>)>({<{}()><(){}>}<[<>()]>))){((([[][]]{<>{}})[([]<>){<>[]}]
<(({{{[(([<[{<(){}>([]<>)}(<[]><()<>>)]><<([()[]]([]()))>{[(()<>}<{}>]}>]){{[{(({}{})<(){}>){[[]]{[]
[<{(<({<{((<<<[]<>>([]())>(((){})[[]()])>{[[<>]<{}<>>]}){[<[<>[]]({}())]{{()[]}<()>}]})<([[([]())<<
[[<<[<{{[{({<[()<>]{<>[]}>{([][]){<><>}}}<[[{}()]][<<><>>{{}[]}]>)}{<{{({}<>)(()())}[{{}{}}[{}()]]
({<({[{[{(([<<()()>{<>[]}>[([]<>)<()<>>]]{<{<>()}[{}{}]>((<>{}){<>{}})})([<([][])[[]{}]>(<[]()>{<>
{[[((<{[[<<({<[]<>>[()<>]}{[()]{<>}})>[<{<<>()><()[]>}{{()[]}<()<>>}>(([{}[]]))]>[[{({<><>})}
{{(<[{{[{<[({(()){{}<>}}(<{}[]>[[]()]))]>}({(<((()[])((){}))<{<><>}[<>()]>>)}(<<[(())<{}<>>]{[[]]<{}
<{{([<<<<[([<[<><>][[]]><<(){}>[()()]>]<{(<><>)<<><>>}([{}{}])>)][[([<()()><<>()>])(({[]<>}([]{}]){<[]><[]
{(<<[[<{{((([<[]<>>[{}<>]][([][]){{}{}}>)(<<<><>><[]{}>>{{(){}}[<>{}]}))({<(())[<>()]><{<>{}}(<>[])>}(({
[[[([({([<<[[[<>{}]{<>{}}]<[<><>]{{}<>}>]>[({[()()]<<>()>}{[()()][{}()]}){({{}()}[(){}))}]>[(<{[()<>
[{{(<<<[{(((<<()<>>([])>({<>{}}<()[]>)))[{(([]){()<>})(({}[])<{}})}<{([]{})({}())}<(<>[])<<>[]>>>
{<<<<[{[{({{[<<>()><{}[]>]<[[]{}][{}{}]>}(<({}{})<()<>>>{{()<>}})}{[[{{}{}}[{}{}]]<[<><>](<>{})>]})(([{[<>()
<(<[<{(<{[{<{[[]{}]{{}[]}}>[{[[]<>][{}{}]}(([]())(<>))]}<{{[{}{}]([]{})}[({}())]}{<<<>()>>([(
<{{[{[<{[[<[{<[]{}><<>{}>}]{({()<>}(<><>)){[<>[]]}}>{([[<>{}]({}{})](({}{})<[]{}>))<{[{}<>
{{<<{<<<[{[[([[]()][()()])(({}()))][[({}[])<()()>]]]{<[<{}[]>{{}{}}]>}}[[[[([]())]([<>[]][[]{}]>]]
[[<<[({{{(<[(<()<>>[<>])]([(()<>){<>())]([<>[]][[]<>]))>{{[[[]()]([]())]{<[]{}>{()<>}}}[<([]<>)<()>>({<>{}}[<
([[([<{<[<((<(<>[])(<>[])>(<<><>><{}[]>)){<<{}<>>>({{}{}}<()[]>)}>[{{(<><>)(()<>)}[<<>[]>]}]>]<{{
{{{((<<{[[{<([[]{}][{}<>])>}<[((()())<()<>>)[[[]{}]{[][]}]]<<<[]{}>{{}[]}>(<<>()><(){}>)>>](<
{(([[{{<[[<{(({}<>)[<>[]])}<{({}{}){{}}}[[()[]](()())]>>]([<[{()[]})({<>}[<>{}])>{[{{}{}}{(){}}]{<{}{}>}}])
{([(<{<<({[<[{()()}<[]<>>]{<[]{}>}><[[<>][()<>]]>]{<{{[]{}}<(){}>}[({})]>{{<{}{}><()<>>}([{}
{{[[({{({[(([{{}()}[{}]]({{}<>}([][]))){({{}<>}[[]{}])<<()<>>>})]{(<[<{}{}>{<>()}](({}())((){
{<({{<<{{([{{{[]<>}{<>{}}}((<><>)<()<>>)}[<[{}<>][()[]]><[<>()][<><>]>]]{{[[()<>]<<>[]>]<(<><>)
<(<[(<<[[<<<[({}())<[][]>](({}<>)[{}<>])>>[<{{{}}<()<>>}<(()<>){{}{}}>>]>({{<[<><>](<><>)>[(<>{}
[((<{[{{(<{[({{}[]}((){}))([[][]]{<>[]})]<{<{}[]>[{}<>]}[<{}()><{}<>>]>]>)}}]}{{{(<[(<{{()()}}>{[<{}<>><<>[]>
{([<<{(<([[({{{}<>}<(){}>}<<()[]>{<>{}}>)((<[][]>[<><>])<<[][]>{<>()}>)]((<{<>[]}{[][]}>[[<>()]{<>[]}]]{{[
[<{(<{([{{(([<<>()>]{<(){}><()<>>}){(([]{}>)<(<><>)>})}({({[<>]{<>[]}}[[{}<>]])}[{<[()[]]<{}<>
{[(<(<{(<<[{[<[]()>(<>[])][{{}}[()[]]]}{{[[]{}]{()()}}<<<>>[[]()]>}]>{{<[<{}()>([]())]({(){}}(()<>))>([(<>(
{{([[([[[<(({<{}<>>[<>[]]}{([]<>)<<>{}>})<{{[]<>}{{}<>}}([()()]<<>[]>>>){{[[()<>]]<((){})<[]{}>>}{<<[]<>><()
<({([[[[[({[[{{}<>}({}<>)]({<>[]}[<>{}])][([<>[]](<>()))<([]())[{}{}]>]}(((({}[])[()[]])[{{}{}}(<>)])(<<<>
[({{<{[([(((<{[]{}}{<>()}><[{}<>>{<>[]}>)){([<{}{}><()[]>]<([]{})[{}{}]>){{[[]]<[]{}>}((()[])[(
(({<[<<{{[[<{(<>{})([]())}([[]{}]{{}()})><[<{}()><{}{}>]<<<>()>[[]()]>>]<[<<()[]><<>()>>[{{}<>}[<>]]]>]
((<[[<{{{[({<(()[])<()<>>>})]{<(([()()][[]]))({[[]()]{[]<>}}{[<>()]})><<(({}[])[{}{}])>>}}}[[[{{{{[]{}}({}[
([<[<{{{{[<<{{<>[]}([]<>)}><{{()[]}[<><>]}{<[]>[()<>]}>><{[{[][]}<()[]>]({[][]}(()<>))}<{(<>())(
{((<(([[<[(<[{()[]}([]())>>[<[<>()]<[]{}>>(<()<>><[]>)])<(<{()}>(([]<>){<>{}}))<[[[]<>]{[]()}
[(<[([([{{{<([[]<>]<<>>)[{<>[]}{{}<>}]}({(())[{}()]}[<{}<>>{<>()}])}([<[(){}]([][])><(()())