One day, Yuhao came across a problem about checking if some bracket sequences are correct bracket sequences.

A bracket sequence is any non-empty sequence of opening and closing parentheses. A bracket sequence is called a correct bracket sequence if it's possible to obtain a correct arithmetic expression by inserting characters "+" and "1" into this sequence. For example, the sequences "(())()", "()" and "(()(()))" are correct, while the bracket sequences ")(", "(()" and "(()))(" are not correct.

Yuhao found this problem too simple for him so he decided to make the problem harder. You are given many (not necessarily correct) bracket sequences. The task is to connect some of them into ordered pairs so that each bracket sequence occurs in at most one pair and the concatenation of the bracket sequences in each pair is a correct bracket sequence. The goal is to create as many pairs as possible.

This problem unfortunately turned out to be too difficult for Yuhao. Can you help him and solve it?

Input

The first line contains one integer n (1 ≤ n ≤ 10^5) — the number of bracket sequences.

Each of the following n lines contains one bracket sequence — a non-empty string which consists only of characters "(" and ")".

The sum of lengths of all bracket sequences in the input is at most 5 ⋅ 10^5.

Note that a bracket sequence may appear in the input multiple times. In this case, you can use each copy of the sequence separately. Also note that the order in which strings appear in the input doesn't matter.

Output

Print a single integer — the maximum number of pairs which can be made, adhering to the conditions in the statement.

Examples

Input


7
)())
)
((
((
(
)
)


Output


2


Input


4
(
((
(((
(())


Output


0


Input


2
(())
()


Output


1

Note

In the first example, it's optimal to construct two pairs: "(( )())" and "( )".
//    A Computer is Like a mischievous genie.
//    It will give you exactly what you ask for,
//    but not always what you want
//    A code by Rahul Verma


import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.Spliterator.OfPrimitive;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;



public class Main {



  public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

  static class FastReader {

    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
      br = new BufferedReader(new
          InputStreamReader(System.in));
    }

    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }

    int nextInt() {
      return Integer.parseInt(next());
    }

    long nextLong() {
      return Long.parseLong(next());
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    String[] nextSArray() {
      String sr[] = null;
      try {
        sr = br.readLine().trim().split(" ");
      } catch (IOException e) {
        e.printStackTrace();
      }
      return sr;
    }

    String nextLine() {
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }

      return str;
    }
  }


  static long powmodulo(long a, long p) {
    if (p == 0)
      return 1 % mod;
    if (p == 1)
      return a % mod;
    long ans = 1;
    while (p > 0) {
      if ((p & 1) > 0) {
        ans = (ans * a) % mod;
      }
      a = (a * a) % mod;
      p = p >> 1;
    }
    return ans % mod;
  }




  static long mod = 1000000007;

  static long gcd(long a,long b)
  {
    if(a==0)
      return b;
    return  gcd(b%a,a);
  }

  static long fast_powerNumbers(long a,long n)
  {
    if(n==1)
      return a;
    long ans=fast_powerNumbers(a,n/2);
    if(n%2==0)
      return (ans*ans);
    else
      return ((ans*ans)*(a));
  }



  static void dfs_helper(int [][] arr,int i,int j,int team,int n,int m)
  {
    arr[i][j]=team;
    if(i-1>=0 && arr[i-1][j]==1)
      dfs(arr,i-1,j,team,n,m);
    if(j-1>=0 && arr[i][j-1]==1)
      dfs(arr,i,j-1,team,n,m);
    if(i+1< n && arr[i+1][j]==1)
      dfs(arr,i+1,j,team,n,m);
    if(j+1<m && arr[i][j+1]==1)
      dfs(arr,i,j+1,team,n,m);

  }

  static void dfs(int [][] arr,int i,int j,int team,int n,int m)
  {
        dfs_helper(arr,i,j,team,n,m);

  }



  public static void merge(int arr1[], int arr2[], int n, int m) {
    // code here

    int last = arr1[n-1];
    int b=m-1;
    while(b>0 && arr2[b]>last)
    {
      --b;

    }
    for(int i=b;i>=0;--i)
    {
      last=arr1[n-1];
      int j=n-2;
      for(;j>=0;--j)
      {
        if(arr2[i]<arr1[j])
        {
          arr1[j+1]=arr1[j];
        }
        else
          break;
      }
      if(j==-1)
        arr1[0]=arr2[i];
      else
        arr1[j+1]=arr2[i];
      arr2[i]=last;

      //System.out.println(Arrays.toString(arr1));
      //System.out.println(Arrays.toString(arr2));
    }



  }



    public static void main(String[] args) throws Exception {
    FastReader sc = new FastReader();

//    int t1=sc.nextInt();
//      for (int t = 0; t < t1 ; t++) {
//
//      }out.close();


      int n=sc.nextInt();
      ArrayList<Integer>al=new ArrayList<>();

      for (int i = 0; i < n; i++) {
        String s=sc.nextLine();
        int nn=s.length();

        boolean valid=true;
        Stack<Character>st=new Stack<>();
        for (int j = 0; j <nn ; j++) {

          if(s.charAt(j)==')')
          {
            if(st.isEmpty()||st.peek()==')')
              st.push(')');
            else
              st.pop();
          }
          else
          {
              st.push('(');
          }
        }
        boolean open=false,close=false;
        for (Character ch:st
        ) {
          if(open&&close)
            break;
          if(ch=='(')
            open=true;
          else
            close=true;
        }


        if(!(open&&close))
        {
          if(open)
            al.add(st.size());
          if(close)
            al.add(0 -st.size());
        }
        if(st.size()==0)
          al.add(0);

      }
      Collections.sort(al);
      //System.out.println(al);

      int a=0,b=al.size()-1;
      int pair=0;
      int ele=0;
      while(a<b)
      {

        ele=al.get(a)+al.get(b);
        if(ele==0)
        {++pair;++a;--b;}
        else if(ele>0)
        --b;
        else
          ++a;
      }
      System.out.println(pair);



}}


class DSU
{
  int parent[],rank[];
  DSU(int n)
  {
    parent=new int[n];
    rank=new int[n];
    for (int i = 0; i <n ; i++) {
      parent[i]=-1;
      rank[i]=1;
    }
  }

  int find(int s1)
  {
    if(parent[s1]==-1)
      return s1;

    parent[s1]=find(parent[s1]);
    return parent[s1];
  }

  void unite(int s1,int s2)
  {

    int p1 = find(s1);
    int p2=find(s2);
    if(rank[s1]>rank[s2])
    {
      parent[p2]=find(p1);
      rank[p1]+=rank[p2];
    }else
    {
      parent[p1]=p2;
      rank[p2]+=rank[p1];
    }
  }

}

class Pair
{
  int a; int b;
  Pair(int a,int b)
  {
    this.a=a;
    this.b=b;
  }
}


class Graph
{
  HashMap<Integer,ArrayList<Integer>>hm;
  Graph()
  {
    hm=new HashMap<>();
  }
  Graph(int n){

    hm=new HashMap<>();
    for (int i = 0; i <n ; i++) {
      hm.put(i,new ArrayList<Integer>());
    }
  }
  // function for adding an edge.................................................
  public void addEdge(int a,int b,boolean isDir)
  {
    if(isDir)
    {
      if(hm.containsKey(a))
      {
        hm.get(a).add(b);
      }
      else
      {
        hm.put(a,new ArrayList<>(Arrays.asList(b)));
      }
    }
    else
    {
      if(hm.containsKey(a))
      {
        hm.get(a).add(b);
      }
      else if(!hm.containsKey(a))
      {
        hm.put(a,new ArrayList<>(Arrays.asList(b)));
      }

      if(hm.containsKey(b))
      {
        hm.get(b).add(a);
      }
      else if(!hm.containsKey(b))
      {
        hm.put(b,new ArrayList<>(Arrays.asList(a)));
      }
    }
  }



}

// out.println(al.toString().replaceAll("[\\[|\\]|,]",""));

