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class Solution {
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  public boolean isValid(String s) {
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    Stack<Character> stack = new Stack<Character>(); // create an empty stack
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    for (char c : s.toCharArray()) { // loop through each character in the string
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      if (c == '(') // if the character is an opening parenthesis
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      stack.push(')'); // push the corresponding closing parenthesis onto the stack
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      else if (c == '{') // if the character is an opening brace
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      stack.push('}'); // push the corresponding closing brace onto the stack
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      else if (c == '[') // if the character is an opening bracket
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      stack.push(']'); // push the corresponding closing bracket onto the stack
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      else if (stack.isEmpty() || stack.pop() != c) // if the character is a closing bracket
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        // if the stack is empty (i.e., there is no matching opening bracket) or the top of the
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        // stack
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        // does not match the closing bracket, the string is not valid, so return false
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        return false;
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    }
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    // if the stack is empty, all opening brackets have been matched with their corresponding
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    // closing brackets,
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    // so the string is valid, otherwise, there are unmatched opening brackets, so return false
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    return stack.isEmpty();
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  }
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}