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Check if a Parentheses String Can Be Valid

A parentheses string is a non-empty string consisting only of '(' and ')'.

A parentheses string is a non-empty string consisting only of '(' and ')'. It is valid if any of the following conditions is true:

You are given a parentheses string s and a string locked, both of length n. locked is a binary string consisting only of '0's and '1's. For each index i of locked,

Return true if you can make s a valid parentheses string. Otherwise, return false.

Example 1

Input: s = "))()))", locked = "010100"

Output: true

Explanation: locked[1] == '1' and locked[3] == '1', so we cannot change s[1] or s[3]. We change s[0] and s[4] to '(' while leaving s[2] and s[5] unchanged to make s valid.

Example 2

Input: s = "()()", locked = "0000"

Output: true

Explanation: We do not need to make any changes because s is already valid.

Example 3

Input: s = ")", locked = "0"

Output: false

Explanation: locked permits us to change s[0]. Changing s[0] to either '(' or ')' will not make s valid.

Example 4

Input: s = "(((())(((())", locked = "111111010111"

Output: true

Explanation: locked permits us to change s[6] and s[8]. We change s[6] and s[8] to ')' to make s valid.

Constraints

  • n == s.length == locked.length
  • 1 <= n <= 10^5
  • s[i] is either '(' or ')'.
  • locked[i] is either '0' or '1'.

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