The coronation of King Berl XXII is soon! The whole royal family, including 𝑛 daughters of Berl XXII, will be present.
The King has ordered his jeweler to assemble 𝑛 beautiful necklaces, so each of the princesses could wear exactly one necklace during the ceremony — and now these necklaces are finished. Each necklace consists of 𝑚 gems attached to a gold chain. There are two types of gems used in the necklaces — emeralds and sapphires. So, each necklace can be represented by a sequence of 𝑚 gems (listed from left to right), and each gem is either an emerald or a sapphire. Formally, the 𝑖-th necklace can be represented by a binary string 𝑠𝑖 of length 𝑚; if the 𝑗-th character of 𝑠𝑖 is 0, then the 𝑗-th gem in the 𝑖-th necklace is an emerald; otherwise, this gem is a sapphire.