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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"sort"
	"strconv"
	"strings"
)

var sc = bufio.NewScanner(os.Stdin)

type kakko struct {
	str string
	min int
	max int
}

func main() {
	N := getStdinInt()
	F := make([]kakko, 0, N)
	L := make([]kakko, 0, N)
	for i := 0; i < N; i++ {
		s := getStdin()
		min, max := minmaxKakko(s)
		if min >= 0 {
			F = append(F, kakko{s, min, max})
		} else {
			L = append(L, kakko{s, min, max})
		}
	}
	sort.Slice(F, func(i, j int) bool { return F[i].max-F[i].min < F[j].max-F[j].min })
	sort.Slice(L, func(i, j int) bool { return L[i].max > L[j].max })

	K := make([]kakko, N)
	for i := 0; i < len(F); i++ {
		K[i] = F[i]
	}
	for i := 0; i < len(L); i++ {
		K[i+len(F)] = L[i]
	}

	first := -1
	last := -1
	for i := 0; i < len(K); i++ {
		if K[i].str[0] == '(' {
			first = i
			break
		}
	}
	for i := len(K) - 1; i >= 0; i-- {
		if first != i && K[i].str[len(K[i].str)-1] == ')' {
			last = i
			break
		}
	}

	if first == -1 || last == -1 {
		fmt.Printf("No\n")
		return
	}

	stack := 0
	stack = okKakko(K[first].str, stack)
	if stack < 0 {
		fmt.Printf("No\n")
		return
	}
	for i := 0; i < len(K); i++ {
		if first == i || last == i {
			continue
		}
		stack = okKakko(K[i].str, stack)
		if stack < 0 {
			fmt.Printf("No\n")
			return
		}
	}
	stack = okKakko(K[last].str, stack)
	if stack < 0 {
		fmt.Printf("No\n")
		return
	}

	if stack == 0 {
		fmt.Printf("Yes\n")
	} else {
		fmt.Printf("No\n")
	}
}

func minmaxKakko(s string) (int, int) {
	stack := 0
	max := math.MinInt32
	min := math.MaxInt32
	for i := 0; i < len(s); i++ {
		if s[i] == '(' {
			stack++
			if stack > max {
				max = stack
			}
		}
		if s[i] == ')' {
			stack--
			if stack < min {
				min = stack
			}
		}
	}
	return min, max
}

func okKakko(s string, stack int) int {
	for i := 0; i < len(s); i++ {
		if s[i] == '(' {
			stack++
		}
		if s[i] == ')' {
			stack--
		}
		if stack < 0 {
			return -1
		}
	}
	return stack
}

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
}