Wonderful Multisets

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Problem

1 is wonderful.
0 is not wonderful.
A multiset is wonderful if at least half of its elements are wonderful.
{001{1}} is the multiset containing 2 0s, a 1, and a multiset containing a 1. So it has 2 non-wonderful elements and 2 wonderful elements, so it's wonderful.
Print 1 for wonderful elements, 0 for non-wonderful elements.

Options

exec is denied

rejudge feature is enabled

now post-mortem time, all source codes will be revealed

Sample input:_

{1}
{0}
{10}
{100}
{0011}
{00{111}}
{{1}{0}{0}}
{0{{{1}}}0}
{{10}{000001}{11}}

Sample output:

1
0
1
0
1
0
0
0
1

Sample input:_

{000}
{11}
{0}
{00011}
{11{01}0}
{11000}
{01}
{1{{{0{{0}}}}1{00}1}{{1}{{1}0{{{0}}}}}11}
{{0}00{{{1}}1}}
{1{{0{00}{{0}{{{0}}}}}}{{0}{0}00}}
{0{00}{{0{{{1}}{0}}}{{{{0}}}01}{{1}{0}}1}}
{110}
{1{1{11}0}}
{{0}}
{11{01}{{1}{0}11}0}
{010}
{{1}0}
{{0}01}
{{0{0}0}1}
{{{0}{{0}{0}0}{10{10}}}101}
{10}
{00}
{0000{100}}
{{10}00}
{{111{{0}0}}{1{1}{{00}1}0}100}
{101{1{11}{0}}}
{10{110{{{{0}}}}}0}
{101{1}}
{{{1{11}}}0{0}{1{1}}}
{{1{{0}00}0}0}
{{1{01{{0}{0}}}}01{0}0}
{{{1{0}}1{10}}1}
{0{1}{1{1{0}{{0}0}}00}{000}{{{1}{{1}0}}{00}{0}}}
{11100}
{{{10}00}{{{{0}0}{1}{{{1}}1}}}{1}}
{{1}0{0}1}
{1}
{1{1}0{1}}
{0{{1{1}1}{110}}000}
{000{{10{00}}{01}{110}}}
{{11}0}
{{101}11}
{{1}1}
{11{101}}
{1{1101}{{{{0}0}0}00{{11}11}}01}
{{0}{1}}
{011{0}0}
{01{{1}}}
{{0}10{{0}}}
{0000}
{{{{0}}{{11}10}0}{0{{0}1}}0}
{{00}11}
{{{0}1}}
{100}
{{0}11{{{{0}}}1}{110}}
{{10}}
{1{{0{0}0}01}1{0}{0{10{0}}1}}
{{1}10{111}}
{1001}
{{1}1{01}{1}{10}}
{{10{10}0}11{{1{1}}}}
{0{1}0{{{{0}}}{11}}0}
{0{01}100}
{1{01}1{0{0}1}}
{{0{0}{{{{0}}{0}}}0}{10{{{1}}0}1}0}
{{11}1}
{01{1}{{1}0}1}
{1{1}{1{{0{0}}1{{0}0}}{1}1}1}
{0101}
{{1}{{{1}}100}{011}}
{{0{0{{{0}}0}1}0{{{0}}{0{{{0}}}}}}1}
{{{{0}00}}00}
{0001}
{1{{{1{0}}11}010}}
{{0}0}
{1{10{{1{{1}}}}1}{10}{010}{{1}00}}
{0{111}}
{{1{0{10}}{0}}}
{0{{1}}0}
{1{{1}1}{0{{1}11}{0}}{{0}1}0}
{01{1}{1}1}
{01{0011}}
{{{00}11}01{10}0}
{0{0}100}
{1{{0}}111}
{{{0}}010}
{{10{{{0}1}{1}}}}
{0010}
{1{0{{10}0}10}1{011}1}
{01{{1{0{{0}}}}1}1}
{{0}10{01}}
{1{10{1{{{1}}1}{{0}1}}}{1}}
{101}
{1{1}1{0}}
{01{{1}00}0}
{011}
{1{1}100}
{0{0}1{{{{{{1}}}{{{{1}}}}}{{1}{1}}}{{01}}11}1}
{1110}
{{{10}10}}
{1{01{01}}}
{0{1}{10}}
{{1}00{1100}{{1{0{0}}}0{0{{{0}}1}{1}}{0}}}
{1{10{0{0}0}}0}
{{00}{1}{10}{{{0}}}0}
{{{00{{1}1}}0}10}
{{001}01}
{1{{01}}{{1{{0}0}}}0}
{{{{{1}}0}0{0{{{1}}}0}1}{1}1{011}0}
{{1}}
{1{{00{0{{{0}}}}}{000}00}111}
{1101}
{110{{0{0{0}}}}1}
{{{011}0}}
{{0}0{0011}1}
{{1{{0}10}0}0}
{{11}01}
{1{{1}{{0}1}0}{{01{0}}{10}11}{11{{{1}1}1}}0}
{01101}
{{0{10}{{1}}}1{{{01}}}{1}}
{100{010}0}
{{11}{1{1{{{{{{{{1}}}}}}}}1}0{{{{0}}}}}}
{11{0{0{1}0}{{0}}0}1}
{{0{10}}001}
{{{1{{{1}}{{0}}}1}01}{111}0{1{01}{0}{1{1{1}}{{1}}}}1}
{{0}01{0{11}{{1}}{10}}1}
{{{1}{{1{1}}}{{00}{10}0}}01{1}}
{0000{0{11}}}
{111{01}}
{{0{{1}}}{110}{1{{{0}0}}}1{{01{11}}0}}
{{1}{00{1}}001}
{11{1111}10}
{0{00{1{{{0}}}}}11}
{01110}
{{{{0{0}}1}}000{{01}0}}
{{{{00}}{{00}1}}1}
{{1}0{{0}}0{{0}01}}
{{00{{1}{{1}}1}0}1}
{10{1{{1}1{0}}{{{0}}}{1{{1}}{{1}1}}}}
{0{00}10}
{11101}
{{0{{0}{00}0}1}}
{00{11}00}
{01{1}1}
{{01}{0}{{{{0}}}}1}
{{01}{101}0}
{{{111}1}{1}0}
{{{1{1}}{0}{010}}}
{{0}001}
{0{0010}{001}11}
{{0000}010}
{001}
{{0{0{0}{11}}}}
{1{010{{{0}1}0}}{{0{1{1}}{0}}1}}
{{{00}1}{111}}
{0{01}11}
{11{{0{0}}}}
{1{1}}
{01001}
{{{{{{{0}}}0}}}1}
{{1{0{{1}0}}{00}}{0}1{{0{{1}0}}{111}{01}}}
{1{{1}1}{0{0}}{1{01}00}}
{{01}}
{1{1}10{011}}
{{{{10}{1}0}{1}0}0011}
{1{101{1{{{{0}}}0}1}}10}
{111}
{{{{01}}}0{{{01}}0}00}
{{0{{{{{1}}}}00}}{0}{{{1{{1}}}0}{{{0}}0{01}}{00}1}}
{01{0010}{100}0}
{{1100}0}
{1{111{{{{1}}}}}}
{{1{{00}}}10}
{{1{1}00}{10{1{{0}0}}}{0{1{1{0}}}}0{{{{0}}0{11}}01}}
{1{1000}010}
{{{{01}{10}{{1}}}}}
{100{{01{00}}{1}{01}}}
{0{1{1}}{001}{{00{{1}{1}}}1}}
{10{{11}0}}
{10{0}0}
{{11}{1011}0{{{{{0}}{{1}}}01}}1}
{{{{11}1}00{{{1}0}10}}110{{{{0}}0{1}}}}
{{00{00{1}}}{001{1{{0}}{{{{{0}}}}}}}{{{1}{{1}}}{1{00}}{010}1}{100{{0{1}}0}}}
{1{0{{1}1}}1{1}{{01}11}}
{1{0{{01}1}1}{{1}1}}
{{{0{1}}}100}
{{0}{{0{1{{1}}}{0}}01}1}
{{1{10}}0{{{0}{{{1}}1}}}0}
{{{11{{1}{1}}}{1}}0010}
{00{00}}
{0{0}}
{00{1}1{1{01}01}}
{001{11}}
{{0{1}}0}
{{{1{0{{{1}}}}0}}{01}0{00}0}
{1{0{{11}{10}{1{{0}}}}{{1}1}}0}
{0111}
{{{{1}}{{1}}{0}}0{11}}
{1{11{0}0}01{00}}
{1{1{{{1}0}11}1}0}
{{00}101}
{1{1{00{00}}0}0}
{{{101}{{0}0}}{{{1{0}}{1}0}}}
{{0}10{00{11}}0}
{{111{00{01}}}}
{1{10{{01}}0}1}
{1{1{01}{00}}10}
{{01{0{11}}}1111}
{{1001}}
{{0}00{10{{0}1}{{1}}}{01}}
{{{00}{0{{1}1}}}}
{{1{{00}{11}}01}{11}{{{11}1}{10}0}0{{00}110}}
{11{000}}
{0{0{0}{1}}}
{{{{1}{10}0}}0}
{1{{0}1}{0}0{10{0{{{0}}}1}1}}
{{01}00{0{00}}}
{1001{0}}
{{1{00}}00}
{10101}
{{{0{1}1}01}111{10}}
{{{01}0}0{1}}
{010{{111}01}}
{0{0{11{00}}}00}
{{0{101}}{1{100}00}01}
{{1}101}
{{{{0}11}10}1}
{{111}{0}{00{1{{{0}}1}}{01}}}
{0{10{{01}{0}}}}
{10{{00}}}
{01{{01{0{{1}}}}0}11}
{1{11}0{{1{0}}{{0}}0{{1}1}}1}
{{00{11}0}}
{110{{011}0}{0}}
{{{11}110}0{00{10}{0}}}
{{01}{0}{{{10}{{0}0}{1}}00}01}
{01{{{01}1{1{0}}}0{{{0}{{{0}}}}}}0}
{0{1{0{{1}}1}1}{{1}1{1{0}}1}}
{0{1{{{0}{{{0}}}}1}}{{10}{0}{00{1}}1}{10}{00{11}0}}
{{00{000}{{0{{{0}}}}}}00{{11}{{0}{{{{1}}}}}0}1}
{{00}10{0}}
{{{{0}}01{1}}100}
{0{1101}{1001}}
{1{00}000}
{10{{01}}{{01{11}}11}0}
{{1{{{1}}}{01}0}}
{{0}{0100}}
{{1101}10{1{{0}{0{{1}}}0}{00}1}{{11}0}}
{01{{{0{0}}1{0{1}}}{0{0{1}}0}10}}
{10010}
{{{{0{{{0}}}}}01}1}
{{{0{{0}{0}}0}0{1{{{1}}1}}0}0}
{{0{{0}00}1}}
{{10}0{{1}}}
{0{{11{0}}}1{10}{0{0}}}
{{10{1}}0}
{0{010}}
{01{{0{{1}}}}}
{{{{11}}1}{1{110}10}}
{{110}010}
{11010}
{11{0{0}}01}
{01{{1}0}}
{1{11}{0{01}0}11}
{{{0}{01}}01}
{{1{0{0}{1}}1}{0101}{{0{0}}}{111}{1}}
{0{0{1}}}
{1{1}01}
{{{10}{1{0}{{{1}}}}0}{001}10}
{{00{1}0}1}
{{001}{0}10}
{1011}
{10{0111}}
{{000}}
{10{1}}
{0{011{00{1{{{{{1}}}}}}}}0{{0{{0}{{0}}}0}01}}
{1{11}00}
{1{1{{0{{{{1}}}}}}}{000{001}}11}
{{1{{0{0}}0}}0{1}0{0}}
{{1}10{{11}1}0}
{{1{10}{{10}11}1}{00{{1{0}}}}1{0010}0}
{{01}{11{11}}10}
{{01{101}{1}}0}
{{100}{1{0{{0}}{1{{{{0}}}}}}{111}}0{0010}}
{0{{00}0}{{1{1}0}{{0{1}}{00}0}{111}0}}
{{{1}1}1}
{{{0}0{00{1{{0}}}}}{110}10}
{1{{{1{1}}}00{01{0}}}01}
{{0111}{{00}1}1}
{{1111}{0{1}}{0}0{1}}
{{011{1}}101}
{0{1{{{0}1}0}00}0}
{{{{{{{0}}}}10}{{1}}{{0{0}}}{01}}01}
{{01{{0{0}}{{0}}0}0}}
{{0{{{{{1}}}{1}}{0}}{1}}1}
{{0{1{{{1}}{{0}}}}11}}
{1{0101}1}
{{01}{1}0}
{{{01{1}}{0}0}00}
{1{{01}{1{{{{1}}}}0}0}1}
{11{11}{00}{000}}
{{{{0}}0{0{0}}}01{01}}
{{{10}01}00{00{1{1}}{100}}1}
{{{{00}0{{1}}}00{11{0}}}10{{0{1}1}}}
{0{{11}}0{0{111}10}}
{1{1010}}
{11{{100}{{0{1}}}}1}
{0{0}{0{01}0}}
{01{01}}
{1{1}0{{0{11}{1}}0}}
{{{{10}0}}}
{{{{{{0}}{1}}1{{{{1}}}1}}{01}{11}}1}
{{010}10}
{{00}10{{{00}10}}}
{00{0{10}}}
{{{1{{1}}}{{0{0}}{1{0}}}1{11{{{1}}0}}}{{10}0}01{00}}
{0{1}{101{{0}}}1}
{0011}
{{0}{{1{{{0}}0}}}11}
{{0}10}
{101{1}{1}}
{10000}
{00{{10}01}{0101}1}
{00{110}{111}}
{0{0{{11}1}}{{00{{1}0}}{11{1}}1{{{0}}}}0}
{{{00{0{1}}}1}}
{{{{1}00}}{00{{10}{{{{1}}}1}0}{{1}}}1{{0{{0}{{1}}}}0}1}
{1{01}01{101}}
{00{{{{0}}}1{{00}0}}1}
{0{{{{{1}}}}100}01}
{{1{100}10}011{1}}
{{{{11}{01}}1{011}{01{{{{1}}}1}}}{0{1{{1}1}}}{0{0{0}}}}
{0{000}}
{{000}{{{1}}1}{01}}
{{{{0}1}1}{{11}1{{{1}{1}}}1}0}
{1{0{{1}}}}
{{001}{010}}
{0{10}{{0}1{001}1}}
{10{0{100}}0}
{11{10}{1010}0}
{{1{1}11}001}
{111{000}0}
{{010{00}}0{01}}
{0{1110}{{0}0}}
{0{0{{01}00}1}}
{0{{100}{00}{1{1}0}}0}
{{{111}}00{00{{{{0}}}}1}{10}}
{{0{10{00}}{10}}{0}}
{0{{10}{{0}{1{0}}}}1{1{1{01}{0}}11}}
{00{0{00{{0}}}10}}
{0{1{11}}0{{101}110}}
{{00{11}}0}
{0{{1{{1}{{1}}}{00}}{{0}11}}0}
{{00{0{1}}}}
{0{11}}
{{101}}
{{{1}}{01}{{1}{0}}01}
{{1{1{1}}0}1100}
{1{{0{1}1}{{0}1}}}
{1111}
{0{1{0}1}000}
{{111{0}}1}
{{11{1{1}1}{0}}10}
{{{0{1{0}}}}0{0}0}
{{11}{{{{{0}}{0}}0}{0}{{0}}1}011}
{01{11}10}
{001{{01}{01{01}}{1}0}0}
{{1011}11{0}}
{{1{0}{10{{0}1}}}1000}
{{{10}}1}
{1{00{01}}{1{1{1}}}11}
{{111}0}
{{1}{{0{1}1}1}{{10}}}
{1{010}{0}{01}0}
{1{0}{0}11}
{10{1110}{1{0}0}1}
{1{{0}00}}
{01{{{1}}1}1}
{{{0{1}{1}}}}
{{{11}}{101{1{00}}}00}
{{{0{01}0}10{1{1}1}}0{{0}}}
{{001}{001}1}
{{1{000}00}{001{{00}0{1}}}}
{{0{{1}}0}}
{0{{1}}}
{{{11}{{{{{1}}}}}01}1}
{{{1{11}1}1}{{1}1{10}0}}
{{111}01}
{1{0}11}
{{{{1}{0}}}{0{{{{1}}}1}10}{{1{{1}{0}}}1}}
{{0{00}1}1}
{10{00}}
{{0{1}1{{0{1}}{00}1}}}
{0{1{{0}0{1}}}01{{{10}0}{{{0}{{{{{{1}}}}}}}}0}}
{{0{0}0}10{{01{1}}}{1{00}{{{{0}}0}{1{0}}}1}}
{1{{0}01{10}}{{{00}00}10{01{1}}}{0{{01}{1}0}0{{1}0}}}
{1{1}1{10}}
{1{01}10}
{{{01}101}{{1}0}001}
{0{{{1}11}00{11}}}

Sample output:

0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1

Sample input:_

{11{{11}{01}}}
{{{0}{{{0}{0}}}}}
{{0}10}
{11001}
{1010}
{{00}}
{{0}}
{1}
{{1}}
{10}
{{1{00}{1}}1}
{{{10}{{11}01}0}0{{{1{0}}0{0}}1}{{{1}}{011}}}
{{{01}{01{{0}0}}}0{0110}0{10{0{0}0}}}
{{1{0}}1{{10{{{1}}0}}0}{0{{1}00}10}}
{01110}
{0}
{0{0{0}1{1}}1{1}}
{000}
{100}
{{0}{1{{01}01}{10}}10}
{{0{00}}100}
{1{{{00}{0}0}}1{{{00}{{1}}0}}1}
{1{0111}{1}1}
{{10}1}
{1100}
{{0000}0{0}}
{{{1}{0}0{10}}0{{01}1{0}1}1}
{1{{{1{{{1}}}}{1{0}}}}01}
{1011}
{{0}001}
{{00}01{{{0{1}}0}00}1}
{0{0{{0}}{110}1}{0}{1000}}
{{1}{0{{1}{00}}00}{{1{{{{{{{1}}}}}}}}0}}
{{101}{100{{1}00}}1{0}0}
{{01}}
{{1100}1{0}10}
{00{1{1}}{0}}
{{10{01}0}}
{{11}0}
{11011}
{111}
{{00}{1{010}1}{10}}
{1{01}000}
{{11}0{{1{10}}{1{0}}{{1}0}0}1}
{11111}
{001{0}{0}}
{001}
{{{{{1}}}{00}{{{1}{{{0}}}}}}{{{{1}1}}101}0{1{00}{0{1{{{0}}}}{0}}1}{000}}
{110}
{1001}
{0101{111}}
{1{1}}
{{100}}
{{{{01}11}{101}}{1}110}
{{1}00}
{0000}
{{1}1}
{0{001{01{00}}}101}
{{{1}}10{01{{01}11}}1}
{0011}
{0001}
{0{{{0{1}}}{11}}1{0{{11}}{11}}{00}}
{0{{00{1{0}}}100}11}
{{1}01}
{{01}{{{1}00}11}}
{{1100}101{111{00}}}
{{1{{01}1}}{0}0}
{{1{{1}{1}{0}}}0{1}{{{0}00}}1}
{{011}{01{{0{1}}10}{{00}1}}1{{00}{10{{1}}}11}1}
{1100{{01}11{{{{{1}}}}0}}}
{0{01{{1}1}{{1{0}}}}}
{01}
{{0}1}
{0{00{{{0}}}0}0}
{{0{0}1{{1}11}}{0}1{10}{{10}}}
{10{1{{00}}00}1{{{0{1}}1}{{1}{10}1}1}}
{01{{11}01}}
{1{01{{{{1}}}0}{01}}0{0{10}0{{0{0}}{{1}}0}}0}
{{10}0{0{1{{1}1}{{1}1}}}10}
{00{0}1{0{000}{11}{{{{1}}0}0}}}
{0{{10{{0}0}}1{01{10}}0}{0000}{{{{{0}}1}0{10}}{{0}}}1}
{0{0}{1{111}0}{{10}1{{0}10}}}
{{1}{00}}
{001{1{{10}{{{0}}{1}}}01}}
{0{{100}}0}
{{10{{{1}0}}}11}
{{110}{1}}
{110{11{0{{{{{1}}}}}}}}
{{001}1101}
{{111}111{0{011}1}}
{1110}
{{0{{00}1}}{1}{{00{0}}{1}}1{{{1}}}}
{1{0{{1{1}}10}{{0}00}{{0{0}}}}}
{{00{1{1}{{{1}}}}}{{0{1}}111}10{0}}
{1{{0}{0}00}}
{011}
{{0{{{1}}}{{00}}1}1}
{{{0}001}}
{111{01}}
{{{10}}{0{1}}{110}1}
{0{10}}
{{100}00{11}{0{{0}1}0}}
{0{1{1{{0}{1}}{1}}}{10{{0}1}}11}
{{0{00}}}
{{1{{00}}0}{{1}{001}0}{{0{11}1}1}{10}{0{110}{1}}}
{1{00}01{0}}
{{10}0{00}{00}}
{11}
{10{{1}11}0{1{01}0{1{11}}}}
{{0}{0}{{{{1}{{0}}}0{0{{1}}}}}{11}}
{1101{0}}
{{0011}{010{{10}{11}0}}00{0}}
{00}
{{{{{{0}}}}{0}{{0}{1}0}}}
{00011}
{{010{{00}{1}0}}}
{0{{0{1{{0}}}}01{{{0}}01}}10}
{10{1{{0{0}}01}}1}
{110{0}0}
{0010}
{{1}10}
{{{{11}}{10}{0}{1}}}
{{101}0}
{1{0{00}0}00}
{110{1}0}
{{11}11}
{1{10}}
{10{000}}
{01{{{1}1{0{0}}}111}{1{01}}0}
{{{01}{01}{10{1}}1}{1}01}
{{11{00}0}1}
{01{1}}
{0{{0}}0}
{111{{{10}{0}1}0{1}}0}
{0{001}0}
{00010}
{{{110}}{00{01}{0}}}
{01{01}}
{{0{{1{1}}0}1}}
{1{0{1}{1{1}}}011}
{{{{{1}{{1}}}}0}{111}10}
{010{1}}
{{{00}0{11}{{0}}}01{0}}
{110{0{0}{{{1}0}}}}
{{1{{01}0}{10}{011}}{0}{10{{1}{11}}1}{10{1{{0}1}1}{100}}1}
{1101{1}}
{{010}10}
{1011{0}}
{0{0{1{00}}0{1}}000}
{{010}1{{0{{{0}}{0}}}{{11}{{0}0}{0{0}}}}01}
{{1{011}{10}}}
{0{1{{0}11}}0{1{0}1}}
{11000}
{0{{0}01}}
{00{11{0}0}1}
{{0}1{010}}
{0{1}1}
{{01{{00}}}}
{101}
{{{10{10}}101}1}
{0110}
{{{00{{{0}}0}}}}
{11{0{1{1}}1}{1}{0{{1}}1{{{{0}}}{1}0}}}
{{10}}
{0{100}0}
{1{0}11}
{{10{10}0}{{{{1}{{1}}}{{0}}}11}{01}01}
{{1}{{1}{0}1{0}}{0}}
{{10}0{{0}}10}
{{111}01}
{00{{11}}}
{001{0011}0}
{10{1{1}}{1001}}
{1{01}}
{{11}}
{1{{0}}0}
{0{10}0}
{{101}{111}11}
{{{00{{1}0}}}1{11}0}
{{0010}{{100}0}1{1{1{{0}}}}0}
{1{0{0}1{10}}}
{0{{11}}1{0{010}{00}0}}
{{{00}}}
{{010}1010}
{11{0{{00}{10}}0}}
{1{001}}
{01101}
{10{{{1{0}}0}1}}
{{{1}{{1}0}0}0{1{{1}}11}}
{{11{{{1}}0}}01{{{1}1}{1}{101}}}
{{111}110}
{1{0{{01}0{0{{1}}}}}}
{{{1}{1{1{1}}}1}0{1{{{{{0}}}}1}11}}
{00{1}{11{0}1}}
{1111{{{00}0}{0{1{{{1}}}}1}}}
{0{{1}}1}
{11{100{1}}{00}}
{101{1}}
{1{100}0{{0}{{0}0{1}}}}
{110{{0}1{10}}1}
{{{{1}}0}1{{1{00}0}1}00}
{1101}
{0{11}00}
{{{{0}}}01}
{{1110}{0000}1{1111}0}
{00{0}0}
{0{1}}
{110{00}1}
{1{11{10}1}{0}11}
{0{{{01}11}{1}}{{1{{0}1}1}}10}
{1{{011}}0{00}{110{{{{1}}}}}}
{{0100}}
{00{11}}
{0{1{0{{{{{1}}}}0}{1}}1}0{01}1}
{{0{110}0}000}
{00110}
{010}
{{10{{10}{0}1}}{{{1{0}}{0}}}0}
{1{0{{01}}1{00}}}
{{01}{{{00}1}}00{{{{1}0}{10}}11}}
{01{{{{1}}1}1}{{{11}{{1}}}{0}}1}
{01{1{1{{1}1}{11}}}}
{0{{{{{1}}}}0{{11}10}}}
{010{0{001}0}1}
{1{{{{0}{0}}{0}}{{{0}}}}010}
{{010}1}
{00100}
{{{{{0}1}}}{1}0{{0}}}
{00{01{1}0}1}
{{{01}01{{01}}}1{11{00}{01}}}
{1{101}1}
{{0}1{00}{01{1}1}}
{00{1}1}
{{000}110}
{{111}}
{11{{01}{0{0}{1}}0}{1{010}1}}
{0{111}01}
{0{0{1{{1}}{00}}}1{1{{{1}}1}{010}}{00}}
{{{1}1}}
{01{{{{1}1}{0}{1}}01}}
{{1{{10}1}{{0}}{0}}}
{{01{111}1}}
{0{11}{{101}0}{0}0}
{1{0{{0}{{0}}0}{{{{{0}}}{{1}}}11}}1}
{1{10}000}
{{00}01{001}1}
{{1100}0{10{1{0}}{0}}}
{0{0{{10}}{1}}}
{0{01}1}
{0{{100}0}110}
{01{0001}1}
{{011}}
{1{110}{{111}11}{{10}}{1}}
{01{{{{{0}}{0}}}100}01}
{{1{{0{{1}}}00}}01{0{011}}}
{11{0{{{{1}}1}0}0}{1{0}0}}
{{{10{{{1}}}}{110}0}0}
{0{111{{{1}}01}}{11}}
{1{{0{{{0}}{1}}}}}
{{{1}1{11}1}111}
{11{111}}
{100{{{{{0}}}}}1}
{{{0}}{0}}
{1111}
{0{{{11}0}}}
{{{0}10}}
{{{10{1}}110}{{0}{011}1}}
{1{0{{{{1}}}{1}}{1}}100}
{0{0{101}}10{{0}0{{1}{0{{0}}}0}}}
{1{000}01}
{1{{01}{1}{00}0}{1}0}
{1{0{1}0}111}
{{{{00}}1{1{{{0}}1}0}}}
{{{1}00{110}}10}
{0{{00{{1}}}10}{{1}{0}}}
{{0}{1{{1{{{1}}}}0}}00}
{1{{0{0}}010}{{011}{{{{0}}{0}}0{0{0}}}}}
{1{{000}{{{0}}0}1}}
{{10}0}
{{{01{0}}{1}{0}{{11}0}}00{11{10}}}
{{{1}0}0{0{{01}00}{1}0}1{{{{{{0}}}}1{{{{1}}}}}}}
{{1{{0}0}0{{{{1}}}}}0{10{111}}}
{{{{0}}{0}1}}
{10{0000}}
{0101}
{00{00}0}
{0{{{00}10}0}}
{00000}
{000{10{{1{{1}}}10}}1}
{{1{{{1}{1}}1}10}}
{{{1}{1{{0}1}}0}}
{{11{1}}0{010}}
{{{1{0{1}}}}10}
{{11}11{00}}
{{{01{{1}}}}{{10}0{010}}}
{11{0101}}
{{{{1}{0}1}0{101}}10{1111}}
{0111}
{10110}
{0{{11{{1}}}1}}
{{0{1}}}
{01{01{{0}}{0}}0}
{1000}
{{100}11}
{0{{{1}1}{1{{1}}}{11}{1}}{0000}11}
{0{0{101}}{1101}0}
{10{{0{0}{11}}}{1{{0}{10}}1}0}
{0{1{1}{10{{1}}}{{{0}}10}}1{10}}
{0{0}10}
{11{1000}0}
{0{011{00}}{1110}{10{{11}00}}0}
{{0{{{1}{0}}1{1}}}0}
{10000}
{00{100}}
{{{{1{{1}}}}{01}0{1{{{{{0}}}}1}0}}}
{{{01}010}}
{00{1{101}}}
{{1{{01}}0{{{0}}{1}}}}
{{1}1{111}}
{{1{1{0}1}{1{1}{0}}}0010}
{1{1{1}1}011}
{0{00{00}}}
{{011}1}
{{{11}{{{1}}00}{0}{0}}{{10}101}{0{01}0}}
{0{1010}{0}01}
{{1}0}
{{0{0}}0{0{{1}0}1{1{0}{{0}0}}}10}
{{1}11{1}1}
{{11{101}1}101}
{{{001}}{110}11}
{{00{11}1}1}
{0{{11}}100}
{11{101{010}}0}
{0{{11}0}}
{{000}001}
{{00}{11}0}
{{1{{01}1{0}}10}1}
{0010{1{{{0}}{{0}{0}}{0}}1{{{0}}}}}
{{1{{0{1}}01}}{0}1}
{110{{11}1}}
{{{00}}1}
{11100}
{{{{1}}}1}
{0{{0}}01}
{{010}}
{010{1101}{1001}}
{{{0{{{1}}0}0}}1}
{1{0}0{{{10}}0}}
{00{{{01}10}}10}
{{{11}1{1}0}{{1{{1}}}0{1}1}}
{0{010}0}
{{{{1{1}}00}}}
{11{0011}}
{{0{1}0{1}}}
{{1{{{1}}11}{11}}0}
{{{111}}01}
{1{011{000}}00}
{{{1}}{000{{1}}}}
{10{0}{0}{0}}
{{000}100}
{{010{{10}}}001}
{1{{1{01}{00}}1}0}
{{00{{0}0}0}}
{11{{1{1{0}}1}01}}
{1{{1}{0}{110}}}
{1{100}}
{0{{1}11}{{{10}{0{0}}{{1}}}}}
{0{{{11}{{0}{0}}{0{1}}}00{{01}0}}{{1{{{0}}{0}}0}1}{1}}
{{0}000}
{111{00}}
{11{11}0}
{{{{{0}1}}{{1{1}}}}}
{{10}00}
{{{11}000}00}
{{11{{1{{1}}}0}}}
{{1{{1}}}10}
{{{0}{0}}1{0{0{1}1}}}
{{110}}
{{{11{0{1}}}}{11}1{001}}
{{11{101}{00}}0{00}}
{{111}{01}{01}00}
{0{1111}1}
{11{0}1}
{{{1}{{0{0}}00}1}{010}}
{{10{10}0}0}
{{{{0{{{1}}}}{00}}}}
{01{{0}{00}{00}0}00}
{{1{1}}{{110}{{11}11}}1}
{0{1}{01}}
{11{{01}{0}}}
{0{{1}1}010}
{1{00{0}1}01{0{000}{{1}}{101}}}
{1{{0{0}}}{10{0}0}10}
{{{{11}0}}{0}0{{10}1}1}
{00001}
{01{0}{{10}}{1{01{0}}}}
{0{1{{{{{1}}}}{1}}}}
{{0111}}
{1{1}1}
{{{{10}{1{1}}0}{0}}1}

Sample output:

1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1

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