tests

assert eggs('0000000000') == ('0000000000', 1)
assert eggs('0000110000') == ('0000000011', 0)
assert eggs('1111111111') == ('1111111111', 0)
assert eggs('0000000111 0101010000') == ('0000000000 0000111111', 1)
assert eggs('1110000111 0101010011') == ('0000000001 1111111111', 0)
assert eggs('0000000000 0000000000 0000000000') == ('0000000000 0000000000 0000000000', 3)
assert eggs('1111111111 1111111111 1111111111') == ('1111111111 1111111111 1111111111', 0)
assert eggs('1000000000 0000000000 0000000000') == ('0000000000 0000000000 0000000001', 2)
assert eggs('0000000000 0000000000 0000000001') == ('0000000000 0000000000 0000000001', 2)
assert eggs('0101010101 1010101010 0101010101') == ('0000000000 0000011111 1111111111', 1)
assert eggs('1000000000 0000100000 0000000001') == ('0000000000 0000000000 0000000111', 2)
assert eggs('0000000001 1000000001 1000000000') == ('0000000000 0000000000 0000001111', 2)
assert eggs('1101101101 1011011011 0110110011') == ('0000000000 1111111111 1111111111', 1)
assert eggs('1101101111 1011011011 0110110010') == ('0000000000 1111111111 1111111111', 1)
assert eggs('1101101111 1011011011 0110110011') == ('0000000001 1111111111 1111111111', 0)
assert eggs('1111111111 1111100000 0000000000') == ('0000000000 0000011111 1111111111', 1)
assert eggs('1101101101 1011011011 0110110011 0101010100') == ('0000000000 0000001111 1111111111 1111111111', 1)