Problem:
Score : 100 points

Problem Statement

There are N flowers arranged in a row.
For each i (1 \leq i \leq N), the height and the beauty of the i-th flower from the left is h_i and a_i, respectively.
Here, h_1, h_2, \ldots, h_N are all distinct.

Taro is pulling out some flowers so that the following condition is met:

The heights of the remaining flowers are monotonically increasing from left to right.

Find the maximum possible sum of the beauties of the remaining flowers.

Constraints

All values in input are integers.

1 \leq N \leq 2 × 10^5

1 \leq h_i \leq N

h_1, h_2, \ldots, h_N are all distinct.

1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
h_1 h_2 \ldots h_N
a_1 a_2 \ldots a_N

Output

Print the maximum possible sum of the beauties of the remaining flowers.

Sample Input 1

4
3 1 4 2
10 20 30 40

Sample Output 1

60

We should keep the second and fourth flowers from the left.
Then, the heights would be 1, 2 from left to right, which is monotonically increasing, and the sum of the beauties would be 20 + 40 = 60.

Sample Input 2

1
1
10

Sample Output 2

10

The condition is met already at the beginning.

Sample Input 3

5
1 2 3 4 5
1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 4

9
4 2 5 8 3 6 1 7 9
6 8 8 4 6 3 5 7 5

Sample Output 4

31

We should keep the second, third, sixth, eighth and ninth flowers from the left.

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var (
	N    int
	h, a [212345]int
)

func readVariables() {
	N = nextInt()
	for i := 0; i < N; i++ {
		h[i] = nextInt()
	}
	for i := 0; i < N; i++ {
		a[i] = nextInt()
	}
}

func main() {
	readVariables()
	bit := NewBIT(N)
	answer := 0
	for i := 0; i < N; i++ {
		v := a[i] + bit.Accumulate(h[i]-1)
		bit.Add(h[i], v)
		// fmt.Println(bit.Nodes)
		answer = MaxInt(v, answer)
	}
	fmt.Println(answer)
}

/* 以下、テンプレート*/

var scanner *bufio.Scanner

func init() {
	Max := 1001001
	scanner = bufio.NewScanner(os.Stdin)
	scanner.Buffer(make([]byte, 0, Max), Max)
	scanner.Split(bufio.ScanWords)
}

//nextInt converts next token from stdin and returns integer value.
//nextInt panics when conversion into an integer fails.
func nextInt() int {
	if !scanner.Scan() {
		panic("No more token.")
	}
	num, err := strconv.Atoi(scanner.Text())
	if err != nil {
		panic("nextInt(): cannot convert to int: " + scanner.Text())
	}
	return num
}

func nextStr() string {
	if !scanner.Scan() {
		panic("No more token.")
	}
	return scanner.Text()
}

// MinInt は、2つの整数を受け取り、最小値を返します。
func MinInt(x, y int) int {
	if x < y {
		return x
	} else {
		return y
	}
}

//MaxInt は、2つの整数を受け取り、最大値を返します。
func MaxInt(x, y int) int {
	if x < y {
		return y
	} else {
		return x
	}
}

//AbsInt は、整数の絶対値を返します。
func AbsInt(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

//ModPow は整数の累乗関数で、剰余もサポートします。
//base^exponentの値をmoduleで割った余りを返します。
//moduloが1以下の場合には、剰余演算をしません。
//baseが負の値である場合には、返す値が負になることがあります。
func ModPow(base, exponent, modulo int) (result int) {
	result = 1
	for exponent > 0 {
		if exponent%2 == 1 {
			result *= base
			if modulo > 1 {
				result %= modulo
			}
		}
		base *= base
		if modulo > 1 {
			base %= modulo
		}
		exponent /= 2
	}
	return
}

//Gcd は、引数の整数全ての最大公約数を返します。
func Gcd(vals ...int) (result int) {
	if len(vals) == 0 {
		return
	}
	result = vals[0]
	for i := 1; i < len(vals); i++ {
		result = gcd(result, vals[i])
	}
	return
}

func gcd(x, y int) int {
	x, y = AbsInt(x), AbsInt(y)
	for y > 0 {
		x, y = y, x%y
	}
	return x
}

//Lcm は、与えられた整数の最小公倍数を返します。
func Lcm(vals ...int) (result int) {
	if len(vals) == 0 {
		return
	}
	result = vals[0]
	for i := 1; i < len(vals); i++ {
		result = lcm(result, vals[i])
	}
	return
}

func lcm(x, y int) int {
	return x * y / gcd(x, y)
}

type BIT struct {
	Nodes []int
	Size  int
}

func NewBIT(size int) *BIT {
	bit := new(BIT)
	bit.Size = size
	bit.Nodes = make([]int, size+1)
	return bit
}

func (bit *BIT) Add(location, value int) {
	for i := location + 1; i <= bit.Size; i += (i & -i) {
		bit.Nodes[i] = MaxInt(bit.Nodes[i], value)
	}
}

func (bit *BIT) Sum(start, end int) int {
	return bit.Accumulate(end) - bit.Accumulate(start-1)
}

func (bit *BIT) Accumulate(end int) (result int) {
	result = -1234567890
	if end >= bit.Size {
		end = bit.Size - 1
	}
	for i := end + 1; i > 0; i -= i & -i {
		result = MaxInt(bit.Nodes[i], result)
	}
	return
}