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