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 "( )".
//  package CF;
// reference https://www.geeksforgeeks.org/partition-problem-dp-18/
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
public class Q1 {
    public static void main(String[] args) {
        in =new FastReader();
     int n=ni();
        HashMap<Integer,Integer> hm=new HashMap<>();
      ArrayList<Integer> al=new ArrayList<>();
        for (int i=0;i<n;i++){
            String str=n();
            int rank=calculateRank(str);
            boolean bl;
            if (rank>=0){
                bl=checkPositive(str);
            }else{
                bl=checkNegative(str,rank);
            }
            if (bl){

                if (rank>=0&&(!hm.containsKey(rank)))al.add(rank);
                int key=hm.getOrDefault(rank,0);
                hm.put(rank,key+1);

            }
        }
        long ans=0;
        for (int i=0;i<al.size();i++){
            int rank1=al.get(i);

            int key1=hm.getOrDefault(rank1,0);
            if (rank1==0){
                ans+=key1/2;
                continue;
            }
            int key2=hm.getOrDefault(-rank1,0);
            ans+=Math.min(key1,key2);
        }
        System.out.println(ans);
    }
    static boolean checkNegative(String str,int rank){
        int p=0;
        for (int i=0;i<str.length();i++){
            if (str.charAt(i)=='(')p++;
            else p--;
            if (p<(rank))return false;
        }
        return true;
    }
    static boolean checkPositive(String str){
        int p=0;
        for (int i=0;i<str.length();i++){
            if (str.charAt(i)=='(')p++;
            else p--;
            if (p<0)return false;
        }
        return true;
    }
    static int calculateRank(String str){
        int p=0;
        for (int i=0;i<str.length();i++){
            if (str.charAt(i)=='(')p++;
            else p--;
        }
        return p;

    }

    static boolean findPartition (int arr[], int pos,long ls,long rs)
        {
            if (pos==arr.length){
                ls=ls%360;
                rs=rs%360;
                if (ls==rs)return true;
                return false;
            }
            boolean bl=findPartition(arr,pos+1,ls+arr[pos],rs);
            if (bl)return bl;
            bl=findPartition(arr,pos+1,ls,rs+arr[pos]);
            return bl;
    }
    // SIEVE  http://codeforces.com/blog/entry/3519
//    private static final int LIMIT = 200;
//     private static final boolean[] isPrime = new boolean[LIMIT + 1];
//     private static ArrayList<Integer> primes = new ArrayList<Integer>();
//     static {
//         Arrays.fill( isPrime, true ); // first we assume all numbers are primes if not shown otherwise
//         isPrime[ 0 ] = false; // zero is not prime - it'is not greater than 1
//         isPrime[ 1 ] = false; // one is not prime - it'is not greater than 1
//         isPrime[ 2 ] = true; // only one even prime
//         primes.add( 2 );
//         for ( int i = 4; i <= LIMIT; i += 2 ) {
//             isPrime[ i ] = false;
//         }
//         for ( int p = 3; p <= LIMIT; p += 2 ) {
//             if ( isPrime[ p ] ) {
//                 primes.add( p );
//                 for ( int m = 3; m * p < LIMIT; m += 2 ) {
//                     isPrime[ m * p ] = false;
//                 }
//             }
//         }
//     }
    public static long binarySearch(long low, long high) {
        while (high - low > 1) {
            long mid = (high - low)/2 + low;
            //System.out.println(mid);
            if (works(mid)) {
                high = mid;
            } else {
                low = mid;
            }
        }
        return (works(low) ? low : high);
    }
    private static String toString(List<Integer> list) {
        StringBuilder result = new StringBuilder();
        for(int x : list) {
            result.append(x + " ");
        }
        return result.toString();
    }
    //     static long ncr(int n,int r)
//     {
//         if(n<0 || r<0 || n<r)
//             return 0;
//         return nCr[n][r];
//     }
    public static void sortbyColumn(int arr[][], int col)
    {
        //this method is taken from geeks for geeks
        // Using built-in sort function Arrays.sort
        Arrays.sort(arr, new Comparator<int[]>() {

            @Override
            // Compare values according to columns
            public int compare(final int[] entry1,
                               final int[] entry2) {

                // To sort in descending order revert
                // the '>' Operator
                if (entry1[col] > entry2[col])
                    return 1;
                else
                    return -1;
            }
        });  // End of function call sort().
    }

    private static Set<Integer> getPrime(int value) {

        Set<Integer> set = new HashSet<>();
        for (int i = 2;i * i <= value;i ++) {
            if (value % i == 0) {
                while (value % i == 0) {
                    value /= i;
                }
                set.add(i);
            }
        }
        if (value > 1) {
            set.add(value);
        }
        return set;

    }
    static class Graph{
        ArrayList<Integer> al_array[];
        int nodes;
        Graph(int no){
            this.nodes=no;
            this.al_array=new ArrayList[no];
            for (int i=0;i<no;i++){
                al_array[i]=new ArrayList<>();
            }
        }
        void addDir(int i,int j){
            this.al_array[i].add(j);
        }
        void addUndir(int i,int j){
            this.al_array[i].add(j);
            this.al_array[j].add(i);
        }
        Graph compliment(){
            Graph com=new Graph(this.nodes);
            for (int i=0;i<this.nodes;i++){
                ArrayList<Integer> al=this.al_array[i];
                for (int j=0;j<al.size();j++){
                    int node=al.get(j);
                    com.addDir(node,i);
                }
            }
            return com;
        }

    }
    static void  printLN2DArray(int[][] arr){
        StringBuilder sb=new StringBuilder();
        for (int i=0;i<arr.length;i++){
            for (int j=0;j<arr[i].length;j++){
                sb.append(arr[i][j]).append(" ");
            }
            sb.append("\n");
        }
        System.out.println(sb.toString());
    }
    static long fast_exp_with_mod(long base, long exp) {
        long MOD=1000000000+7;
        long res=1;
        while(exp>0) {
            if(exp%2==1) res=(res*base)%MOD;
            base=(base*base)%MOD;
            exp/=2;
        }
        return res%MOD;
    }
    public static long gcd(long a, long b)
    {
        if (a == 0)
            return b;
        return gcd(b%a, a);
    }
    static class my_no{
        long num;
        long denom;

        @Override
        public String toString() {
            if (denom<0){
                this.num=-this.num;
                this.denom=-this.denom;
            }
            if (num==0)return "0";
            return (num+"/"+denom);
        }

        my_no(int no){
            this.num=no;
            this.denom=1;
        }
        my_no(long num,long denom){
            this.num=num;
            this.denom=denom;
        }

        my_no multiply(my_no obj){
            long num1=obj.num;
            long denom1=obj.denom;
            long n=num1*num;
            long d=denom1*denom;
            long gcd=gcd(n,d);
            n/=gcd;
            d/=gcd;
            return new my_no(n,d);

        }
//        my_no multiply(my_no obj){
//            long num1=obj.num;
//            long denom1=obj.denom;
//            long num2=this.num;
//            long denom2=this.denom;
//
//        }

        my_no multiply(int no){
            long n=num*no;
            long d=denom;
            long gcd=gcd(n,d);
            n/=gcd;
            d/=gcd;
            return new my_no(n,d);

        }
    }

    static void memset(int[][] arr,int val){
        for (int i=0;i<arr.length;i++){
            for (int j=0;j<arr[i].length;j++){
                arr[i][j]=val;
            }
        }
    }
    static void memset(int[] arr,int val){
        for (int i=0;i<arr.length;i++){
            arr[i]=val;
        }
    }


    static void memset(long[][] arr,long val){
        for (int i=0;i<arr.length;i++){
            for (int j=0;j<arr[i].length;j++){
                arr[i][j]=val;
            }
        }
    }
    static void memset(long[] arr,long val){
        for (int i=0;i<arr.length;i++){
            arr[i]=val;
        }
    }
    static private boolean works(long test){
        return true;
    }


    static void reverse(char[] arr ,int i,int j){
        if (i==j)
            return;
        while (i<j){
            char temp=arr[i];
            arr[i]=arr[j];
            arr[j]=temp;
            ++i;
            --j;
        }
    }
    static int[]  takeIntegerArrayInput(int no){
        int[] arr=new int[no];
        for (int i=0;i<no;++i){
            arr[i]=ni();
        }
        return arr;
    }
    static long fast_Multiply(long no , long pow){
        long result=1;
        while (pow>0){
            if ((pow&1)==1){
                result=result*no;
            }
            no=no*no;
            pow>>=1;
        }
        return result;
    }

    static long[]  takeLongArrayInput(int no){
        long[] arr=new long[no];
        for (int i=0;i<no;++i){
            arr[i]=ni();
        }
        return arr;
    }
    static final long MOD = (long)20011;
    static FastReader in;


    static void p(Object o){
        System.out.print(o);
    }

    static void pn(Object o){
        System.out.println(o);
    }

    static String n(){
        return in.next();
    }

    static String nln(){
        return in.nextLine();
    }

    static int ni(){
        return Integer.parseInt(in.next());
    }

    static int[] ia(int N){
        int[] a = new int[N];
        for(int i = 0; i<N; i++)a[i] = ni();
        return a;
    }

    static long[] la(int N){
        long[] a = new long[N];
        for(int i = 0; i<N; i++)a[i] = nl();
        return a;
    }

    static long nl(){
        return Long.parseLong(in.next());
    }

    static double nd(){
        return Double.parseDouble(in.next());
    }

    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();
        }

        String nextLine(){
            String str = "";
            try{
                str = br.readLine();
            }catch (IOException e){
                e.printStackTrace();
            }
            return str;
        }
    }
    static void println(String[] arr){
        for (int i=0;i<arr.length;++i){
            System.out.println(arr[i]);
        }
    }

}
