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