On an island, there is this strange pattern - boys always lie while girls always tell the truth. Now you encounter six children.

The oldest one says, "The number of girls among us is a perfect square."

The second one says, "The number of girls among us is a prime number."

The third one says, "The number of girls among us is odd."

The fourth one says, "The number of girls among us is even."

The fifth one says, "There are exactly 3 girls among us."

The youngest one says, "There are exactly 3 boys among us."

Let 1 denote boys and 0 girls. In order of birth, identify the gender of each child and convert it into a number accordingly. Submit your answer as a string of 6 ones and/or zeroes. For example, if all six are boys, then your answer is 111111.

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