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