package main import ( "bufio" "fmt" "os" "sort" "strconv" ) var sc = bufio.NewScanner(os.Stdin) var wr = bufio.NewWriter(os.Stdout) func out(x ...interface{}) { fmt.Fprintln(wr, x...) } func getI() int { sc.Scan() i, e := strconv.Atoi(sc.Text()) if e != nil { panic(e) } return i } func getF() float64 { sc.Scan() i, e := strconv.ParseFloat(sc.Text(), 64) if e != nil { panic(e) } return i } func getInts(N int) []int { ret := make([]int, N) for i := 0; i < N; i++ { ret[i] = getI() } return ret } func getS() string { sc.Scan() return sc.Text() } // min, max, asub, absなど基本関数 func max(a, b int) int { if a > b { return a } return b } func min(a, b int) int { if a < b { return a } return b } func asub(a, b int) int { if a > b { return a - b } return b - a } func abs(a int) int { if a >= 0 { return a } return -a } func lowerBound(a []int, x int) int { idx := sort.Search(len(a), func(i int) bool { return a[i] >= x }) return idx } func upperBound(a []int, x int) int { idx := sort.Search(len(a), func(i int) bool { return a[i] > x }) return idx } // NextPermutation generates the next permutation of the // sortable collection x in lexical order. It returns false // if the permutations are exhausted. // // Knuth, Donald (2011), "Section 7.2.1.2: Generating All Permutations", // The Art of Computer Programming, volume 4A. // ※NextPermutationは辞書順で次を返す func NextPermutation(x sort.Interface) bool { n := x.Len() - 1 if n < 1 { return false } j := n - 1 for ; !x.Less(j, j+1); j-- { if j == 0 { return false } } l := n for !x.Less(j, l) { l-- } x.Swap(j, l) for k, l := j+1, n; k < l; { x.Swap(k, l) k++ l-- } return true } type dat struct { l, r, n int } var N int var d []dat func main() { defer wr.Flush() sc.Split(bufio.ScanWords) sc.Buffer([]byte{}, 1000000) // this template is new version. // use getI(), getS(), getInts(), getF() N = getI() s := getS() d = make([]dat, N) l, r := 0, 0 n := 0 tot := 0 for i := 0; i < N; i++ { if s[i] == '(' { l++ } else { if l > 0 { l-- n++ } else { r++ } } d[i] = dat{l, r, n} tot += n } // sort.Slice(d, func(i, j int) bool { // if d[i].l == d[j].l { // return d[i].r < d[j].r // } // return d[i].l > d[j].l // }) dp := make([]map[int]int, N+1) for i := 0; i <= N; i++ { dp[i] = make(map[int]int) } dp[0][0] = 0 for i := 0; i < N; i++ { for e, n := range dp[i] { if e < 0 { dp[i+1][e+d[i].l] = max(dp[i+1][e+d[i].l], n+min(d[i].l, -e)) dp[i+1][e-d[i].r] = max(dp[i+1][e-d[i].r], n) } else { dp[i+1][e+d[i].l] = max(dp[i+1][e+d[i].l], n) dp[i+1][e-d[i].r] = max(dp[i+1][e-d[i].r], n+min(e, d[i].r)) } } } // for i := 0; i <= N; i++ { // out(dp[i]) // } maxV := 0 for _, e := range dp[N] { maxV = max(maxV, e) } out((maxV + tot) * 2) }