Example

Input

3
()(()((
))()()(()
)())(())


Output

Yes
#include <stdio.h>
#include <cmath>
#include <algorithm>
#include <cfloat>
#include <stack>
#include <queue>
#include <vector>
#include <string>
#include <iostream>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;

bool FLG;

int N,calc_N,value,PLUS,MINUS;
char table[100][101];
int minimum[100],add[100],rev_minimum[100],rev_add[100];

void recursive_PLUS(vector<int> V,int used_num,int diff){

    if(FLG)return;

    if(used_num == calc_N){
         FLG = true;
         PLUS = diff;
        return;
    }

    for(int i = 0; i < V.size(); i++){

        if(diff+minimum[V[i]] >= 0){

            vector<int> next_V;
            for(int k = 0; k < V.size(); k++){
                if(k != i)next_V.push_back(V[k]);
            }
            recursive_PLUS(next_V,used_num+1,diff+add[V[i]]);
        }
    }
}

void recursive_MINUS(vector<int> V,int used_num,int diff){

    if(FLG)return;

    if(used_num == calc_N){
         FLG = true;
         MINUS = diff;
        return;
    }

    for(int i = 0; i < V.size(); i++){

        if(diff+rev_minimum[V[i]] >= 0){

            vector<int> next_V;
            for(int k = 0; k < V.size(); k++){
                if(k != i)next_V.push_back(V[k]);
            }
            recursive_MINUS(next_V,used_num+1,diff+rev_add[V[i]]);
        }
    }
}


int main(){

    FLG = false;

    scanf("%d",&N);

    int open_num = 0,close_num = 0;

    for(int i = 0; i < N; i++){
        scanf("%s",table[i]);
        for(int k = 0; table[i][k] != '\0';k++){
            if(table[i][k] == '(')open_num++;
            else{
                close_num++;
            }
        }
    }

    if(open_num != close_num){
        printf("No\n");
        return 0;
    }

    for(int k = 0; k < N; k++){
        minimum[k] = 0;
        rev_minimum[k] = 0;
    }

    int tmp,length;

    for(int i = 0; i < N; i++){
        tmp = 0;
        length = 0;
        for(int k = 0; table[i][k] != '\0'; k++){
        	length++;
            if(table[i][k] == '(')tmp++;
            else{
                tmp--;
                minimum[i] = min(minimum[i],tmp);
            }
        }
        add[i] = tmp;
        if(add[i] < 0){
        	tmp = 0;
        	for(int k = length-1; k >= 0; k--){
        		if(table[i][k] == ')')tmp++;
        		else{
        			tmp--;
        			rev_minimum[i] = min(rev_minimum[i],tmp);
        		}
        	}
        	rev_add[i] = tmp;
        }
    }

    vector<int> V;
    tmp = N;
    calc_N = N;
    PLUS = 0;
    for(int i = 0; i < tmp; i++){
        if(minimum[i] == 0 && add[i] == 0){
            calc_N--;
        }else if(add[i] < 0){
            calc_N--;
        }else if(minimum[i] == 0){
            PLUS += add[i];
            calc_N--;
        }else{
        	V.push_back(i);
        }
    }

    if(calc_N > 0){
    	recursive_PLUS(V,0,PLUS);
    }else{
    	FLG = true;
    }

    if(!FLG){
        printf("No\n");
        return 0;
    }

    FLG = false;

    V.clear();
    tmp = N;
    calc_N = N;
    MINUS = 0;
    for(int i = 0; i < tmp; i++){
        if(minimum[i] == 0 && add[i] == 0){
            calc_N--;
        }else if(add[i] >= 0){
            calc_N--;
        }else if(rev_minimum[i] == 0){
        	MINUS += rev_add[i];
        	calc_N--;
        }else{
            V.push_back(i);
        }
    }
    if(MINUS < 0){
        printf("No\n");
        return 0;
    }

    recursive_MINUS(V,0,MINUS);

    if(FLG == true && PLUS == MINUS){
        printf("Yes\n");
    }else{
        printf("No\n");
    }

    return 0;
}