Given an array of strings called products and a word to search, design a system that, when each character of the searched word is typed, suggests at most three product names from products. Suggested products should share a common prefix with the searched word. If more than three products exist with a common prefix, return the three product names that appear first in lexicographical order.

Return the suggested products, which will be a list of lists after each character of searched word is typed.

Constraints:

• $1 \leq$ products.length $\leq 1000$
• $1 \leq$ products[i].length $\leq 3000$
• $1 \leq$ sum(products[i].length) $\leq 2 \times 10^3$
• All the strings of products are unique.
• products[i] consists of lowercase English letters.
• $1 \leq$ searched word.length $\leq 1000$
• The searched word consists of lowercase English letters.

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