Algorithms and Data Structures

  • Profound Academy

    • Status
      • 1
        Implementation
      • 2
        Bitwise operations
      • 3
        Prefix Sums
      • 4
        Sliding window / Two pointers
      • 5
        Modular Arithmetic
      • 6
        Number Theory
      • 7
        Binary Search
      • 8
        Basic Sorting
      • 9
        Greedy Algorithms
      • 10
        Basic Dynamic Programming
      • 11
        Recursion
      • 12
        Linked LIst
      • 13
        Queue & Stack
      • 14
        Binary tree + BST
      • 15
        Divide & Conquer + Advanced Sorting
      • 16
        Heap
      • 17
        Hashing
      • 18
        Graph Representation

    • Fix the bracket sequence

    Given a string s of opening and closing brackets, you are allowed to change some opening brackets to closing ones and some closing to opening ones. At least how many operations are necessary to obtain a valid sequence of brackets?

    Input

    The only line of the input contains the string s (1 ≤ |s| ≤ ). It’s guaranteed that the length of s is even.

    Output

    The program should print the least amount of modifications needed to make the sequence valid.

    Examples

    Input
    Output
    ()((
    1
    )(
    2
    ()()
    0
    ((()
    1

    Explanation

    1. ()(( → ()() ⇒ 1 modification
    1. )( → () ⇒ 2 modifications
    1. ()() ⇒ no modifications needed
    1. ((() → ()() ⇒ 2 modifications
     

    Constraints

    Time limit: 1 seconds

    Memory limit: 512 MB

    Output limit: 1 MB

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