import java.io.*;
import java.util.*;

class BracketMatch {

  static int bracketMatch(String text) {
    if (text == null || text.isEmpty()) {
        throw new IllegalArgumentException("Provide a text");
    }
    if (!text.replaceAll("[()]", "").isEmpty()) {
      throw new IllegalArgumentException("Found invalid character");
    }

    int count = 0;
    int orphanCloseBracket = 0;
    for (int idx = 0; idx < text.length(); idx++) {
      if (text.charAt(idx) == '(') {
        count++;
      } else {
        if (count == 0) {
          orphanCloseBracket++;
        } else if (count > 0 ) {
          count--;
        }
      }
    }
    return count+orphanCloseBracket;
  }

  public static void main(String[] args) {

    System.out.println(bracketMatch("(()"));   // 1
    System.out.println(bracketMatch("(())"));  // 0
    System.out.println(bracketMatch("())("));  // 2
  }
}
/*

    text = "())("
    n=0
    ---------+
            (| push
    ---------+
    n=1
    ---------+
             | pop
    ---------+
    n=2
    ---------+
             | orphanCloseBracket : 1
    ---------+
    n=3
    ---------+
            )| push
    ---------+
    openBracketSize: 1

    text = "(())"
    n=0
    ---------+
            (| push
    ---------+
    n=1
    ---------+
           ((| push
    ---------+
    n=2
    ---------+
            (| pop
    ---------+
    n=3
    ---------+
             | pop
    ---------+
    openBracketSize: 0

*/