Balanced Brackets

You are given a string s consisting of various characters including open and close brackets: ( ), { }, and [ ]. Your task is to determine whether the brackets in the string are balanced. A string is considered balanced if:

• Every opening bracket has a corresponding closing bracket.
• Brackets are closed in the correct order.

For instance, the string "{[()()]}" is balanced, while "(]" is not.

Note: Other characters in the string should be ignored.

Mathematical Description:

Let \( S = s_1 s_2 \ldots s_n \) be a string of characters. Define a mapping for closing to opening brackets as \( f(\text{')'}) = ( \), \( f(\text{'}'}) = { \), \( f(\text{']'}) = [ \). The string is balanced if for each closing bracket \( s_j \), there exists an earlier index \( i \) such that \( s_i = f(s_j) \) and the substring between them is also balanced.

inputFormat

The input consists of a single line containing the string s which may include letters, digits, spaces, and bracket characters.

outputFormat

Output a single line: True if the brackets are balanced, otherwise False.

## sample

()

True