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 "( )".
import java.util.*;
import java.math.*;
import java.io.*; 
 public class A{
 
static FastReader scan=new FastReader();
 public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
  static LinkedList<Integer>edges[];
 // static LinkedList<Pair>edges[];
  static boolean stdin = true;
    static String filein = "input";
    static String fileout = "output";
static int dx[] = { -1, 0, 1, 0 };
static int dy[] = { 0, 1, 0, -1 };
int dx_8[]={1,1,1,0,0,-1,-1,-1};
int dy_8[]={-1,0,1,-1,1,-1,0,1};
static char sts[]={'U','R','D','L'};
static boolean prime[];
static long LCM(long a,long b){
    return (Math.abs(a*b))/gcd(a,b);
   }
    public static int upperBound(long[] array, int length, long value) {
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = low+(high-low) / 2;
            if ( array[mid]>value) {
                high = mid ;
            } else {
                low = mid+1;
            }
        }
        return low;
    }
   static long gcd(long a, long b) {
    if(a!=0&&b!=0)
        while((a%=b)!=0&&(b%=a)!=0);
    return a^b;
}
static int countSetBits(int n) 
    { 
        int count = 0; 
        while (n > 0) { 
            if((n&1)!=1)
                count++;
            //count += n & 1; 
            n >>= 1; 
        } 
        return count; 
    } 
 static void sieve(long n) 
    { 
        
        prime = new boolean[(int)n+1]; 
        for(int i=0;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) 
        { 
           
            if(prime[p] == true) 
            { 
                
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
    }  
  
 
 
           static boolean isprime(long x)
           {
            for(long i=2;i*i<=x;i++)
                if(x%i==0)
                    return false;
                return true;
           }
           static int perm=0,FOR=0;
           
     
 
static boolean flag=false;
static int len=100000000;
 
static ArrayList<Pair>inters=new ArrayList<Pair>();
 
  
static class comp1 implements  Comparator<Pair>{  
public int compare(Pair o1,Pair o2){
return  Integer.compare((int)o2.x,(int)o1.x);
}
  }
  public static class comp2 implements Comparator<Pair>{  
public int compare(Pair o1,Pair o2){
return Integer.compare((int)o2.x,(int)o1.x); 
}
  }
  static StringBuilder a,b;
 
    static boolean isPowerOfTwo(int n)
{
    if(n==0)
    return false;
 
return (int)(Math.ceil((Math.log(n) / Math.log(2)))) == 
       (int)(Math.floor(((Math.log(n) / Math.log(2)))));
}
static ArrayList<Integer>v;
static ArrayList<Integer>pows;
static void block(long x) 
{ 
   v = new ArrayList<Integer>(); 
      
    pows=new ArrayList<Integer>();
   
    while (x > 0)  
    { 
        v.add((int)x % 2); 
        x = x / 2; 
    } 
  
    // Displaying the output when 
    // the bit is '1' in binary 
    // equivalent of number. 
    for (int i = 0; i < v.size(); i++)  
    { 
        if (v.get(i)==1)  
        { 
      pows.add(i); 
        } 
    } 
 
} 
 
 
   static long ceil(long a,long b)
   {
    if(a%b==0)
        return a/b;
    return a/b+1;
   }
   static int n,m;
   static int arr[];
   static long ans=0;
   static boolean vis[]=new boolean[21];
   static int c[]=new int[21];
   static ArrayList<Integer>comps[];
static   int idx=0;
   static void add(int x)
   {
    vis[x]=true;
    comps[idx].add(x);
    for(int v:edges[x])
        if(!vis[v])
            add(v);
   }
static int k;
static boolean can=false;
 static void dfs(int x,int y,int res)
 {
    if(x==n&&y==m)
    {
  //     out.println(res);
        if(res==k){
            can=true;
            return;
        }
        return;
    }
    if(x>n||y>m){
        //System.out.println("FUCK");
        return;
    }
   // out.println(x);
    dfs(x+1,y,res+y);
   // out.println(x);
    dfs(x,y+1,res+x);

    
    
 }
public static void main(String[] args)  throws Exception 
{
//SUCK IT UP AND DO IT ALRIGHT
//scan=new FastReader("hps.in");
//out = new PrintWriter("hps.out");
   //System.out.println( 1005899102^431072812);
    //int elem[]={1,2,3,4,5};
//System.out.println("avjsmlfpb".compareTo("avjsmbpfl"));
int tt=1;

/*for(int i=0;i<=100;i++)
    if(prime[i])
        arr.add(i);
    System.out.println(arr.size());*/
   // check(new StringBuilder("05:11"));
   // System.out.println(26010000000000L%150);
 
//tt=scan.nextInt();
  //  System.out.println(2^6^4);
    //StringBuilder o=new StringBuilder("GBGBGG");
    //o.insert(2,"L");
 int T=tt;
//System.out.println(gcd(99970002,99980000));
 
outer:while(tt-->0)
{
int n=scan.nextInt();
int neg[]=new int[(int)5e5+5];
int pos[]=new int[(int)5e5+5];
for(int i=0;i<n;i++)
{
    int cur=0,cur2=0;
    String s=scan.next();
    int min=0;
    for(int j=0;j<s.length();j++)
    {
        if(s.charAt(j)=='('){
            cur2++;
            cur++;
        }
        else 
            {
                cur--;
                cur2--;
            }
        min=Math.min(cur,min);
    }
    if(cur>=0&&min<0)
        continue;
//if(-cur==3||cur==3)
          //  out.println(min+" "+cur);
    if(cur!=min&&min!=0&&cur<0)
        continue;
  
    if(cur<0){

        neg[-cur]++;
    }
    else pos[cur]++;
    
}

int res=pos[0]/2;
//out.println(res);
for(int i=1;i<=(int)5e5;i++){
   // if(neg[i]>0&&pos[i]>0)
     //   out.println(i+" "+neg[i]+" "+pos[i]);
    res+=Math.min(neg[i],pos[i]);
}
out.println(res);
}

out.close();
 
//SEE UP 
 
}
static class special implements Comparable<special>{
    int x,y;
    String s;
    special(int x,String s,int y)
    {
        this.x=x;
        this.s=s;
        this.y=y;
    }
 
 @Override
        public boolean equals(Object o){
            if (o == this) return true;
            if (o.getClass() != getClass()) return false;
            special t = (special)o;
            return t.x == x && t.y == y&&t.s.equals(s);
        }
 
public int compareTo(special o)
{
    return Integer.compare(x,o.x);
}
}
static long binexp(long a,long n)
{
    if(n==0)
        return 1;
    long res=binexp(a,n/2);
    if(n%2==1)
        return res*res*a;
    else 
        return res*res;
}
 
static long powMod(long base, long exp, long mod) {
       if (base == 0 || base == 1) return base;
       if (exp == 0) return 1;
       if (exp == 1) return (base % mod+mod)%mod;
       long R = (powMod(base, exp/2, mod) % mod+mod)%mod;
       R *= R;
       R %= mod;
       if ((exp & 1) == 1) {
           return (base * R % mod+mod)%mod;
       }
       else return (R %mod+mod)%mod;
   }
static double dis(double x1,double y1,double x2,double y2)
{
    return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
static long mod(long x,long y)
    {
        if(x<0)
            x=x+(-x/y+1)*y;
        return x%y;
    }
 public static  long pow(long b, long e) {
            long r = 1;
            while (e > 0) {
                if (e % 2 == 1) r = r * b ;
                b = b * b;
                e >>= 1;
            }
            return r;
        }
private static void sort(int[] arr) {
        List<Integer> list = new ArrayList<>();
        for (int object : arr) list.add(object);
        Collections.sort(list);
    //Collections.reverse(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }
private static void sort2(int[] arr) {
        List<Integer> list = new ArrayList<>();
        for (int object : arr) list.add(object);
        Collections.sort(list);
    Collections.reverse(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }
 public static class FastReader {
        BufferedReader br;
        StringTokenizer root;
        
 
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        FastReader(String filename)throws Exception
        {
 
            br=new BufferedReader(new FileReader(filename));
        }
 
        boolean hasNext(){
            String line;
            while(root.hasMoreTokens())
                return true;
            return false;
        }
 
        String next() {
            while (root == null || !root.hasMoreTokens()) {
                try {
                    root = new StringTokenizer(br.readLine());
                } catch (Exception addd) {
                    addd.printStackTrace();
                }
            }
            return root.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
 
        long nextLong() {
            return Long.parseLong(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (Exception addd) {
                addd.printStackTrace();
            }
            return str;
        }
         public int[] nextIntArray(int arraySize) {
            int array[] = new int[arraySize];
 
            for (int i = 0; i < arraySize; i++) {
                array[i] = nextInt();
            }
 
            return array;
        }
}
 static class Pair implements Comparable<Pair>{
        public long x, y;
        public Pair(long x1, long y1) {
            x=x1;
            y=y1;
        }
        @Override
        public int hashCode() {
            return (int)(x + 31 * y);
        }
        public String toString() {
            return x + " " + y;
        }
        @Override
        public boolean equals(Object o){
            if (o == this) return true;
            if (o.getClass() != getClass()) return false;
            Pair t = (Pair)o;
            return t.x == x && t.y == y;
        }
public int compareTo(Pair o)
{
    return (int)(o.x-x);
 
    }
 
}
 static class tuple{
        int x,y,z;
        tuple(int a,int b,int c){
            x=a;
            y=b;
            z=c;
        }
    }
    static class Edge{
        int d,w;
        Edge(int d,int w)
        {
            this.d=d;
            this.w=w;
        }
    }
}
 
 