Problem:
Score : 600 points

Problem Statement

A bracket sequence is a string that is one of the following:

An empty string;

The concatenation of (, A, and ) in this order, for some bracket sequence A ;

The concatenation of A and B in this order, for some non-empty bracket sequences A and B /

Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

Constraints

1 \leq N \leq 10^6

The total length of the strings S_i is at most 10^6.

S_i is a non-empty string consisting of ( and ).

Input

Input is given from Standard Input in the following format:

N
S_1
:
S_N

Output

If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.

Sample Input 1

2
)
(()

Sample Output 1

Yes

Concatenating (() and ) in this order forms a bracket sequence.

Sample Input 2

2
)(
()

Sample Output 2

No

Sample Input 3

4
((()))
((((((
))))))
()()()

Sample Output 3

Yes

Sample Input 4

3
(((
)
)

Sample Output 4

No

Solution in Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"math/rand"
	"os"
	"strconv"
	"strings"
)

var sc = bufio.NewScanner(os.Stdin)

func main() {
	N := getStdinInt()
	S := make([]string, N)
	str := ""
	for i := 0; i < N; i++ {
		S[i] = getStdin()
		str += S[i]
	}

	S_flag := make([]bool, N)
	for i := 0; i < N; i++ {
		S_flag[i] = false
	}
	max := N * N * N
	if max < 10000 {
		max = 10000
	}
	tmp := ""
	for cnt := 0; cnt < max; cnt++ {
		tmp = ""
		for i := 0; i < N; i++ {
			S_flag[i] = false
		}

		for i := 0; i < N; {
			n := rand.Intn(N)
			if S_flag[n] {
				continue
			}

			tmp += S[n]

			i++
		}

		if okKakko(tmp) {
			fmt.Printf("Yes\n")
			return
		}
	}

	fmt.Printf("No\n")
}

func openStackNum(str string) int {
	stack := 0
	for i := 0; i < len(str); i++ {
		if str[i] == '(' {
			stack++
		}
	}
	return stack
}

func closeStackNum(str string) int {
	stack := 0
	for i := 0; i < len(str); i++ {
		if str[i] == ')' {
			stack++
		}
	}
	return stack
}

func okKakko(str string) bool {
	if str[0] == ')' || str[len(str)-1] == '(' {
		return false
	}

	stack := 0
	for i := 0; i < len(str); i++ {
		if str[i] == '(' {
			stack++
		}
		if str[i] == ')' {
			stack--
		}
		if stack < -1 || stack > len(str)/2 {
			return false
		}
	}

	return true
}

func getStdin() string {
	sc.Scan()
	return sc.Text()
}
func getStdinInt() int {
	str := getStdin()
	rtn, _ := strconv.Atoi(str)
	return rtn
}
func getStdinIntArr() []int {
	str := getStdin()
	list := strings.Split(str, " ")
	rtn := make([]int, len(list))
	for idx, val := range list {
		rtn[idx], _ = strconv.Atoi(val)
	}
	return rtn
}