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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import javax.xml.crypto.Data;
import java.io.BufferedInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;

public class Main {

    private final static InputReader inputReader = new InputReader(System.in);
    private final static OutputWriter outputWriter = new OutputWriter(System.out);

    public static void main(String[] args) throws IOException {
        int numberOfTestCases = 1;//inputReader.scanInt();
        for (int testCase = 1; testCase <= numberOfTestCases; ++testCase) {
            final ProblemParameters parameters = new ProblemParameters();
            parameters.numberOfFlowers = inputReader.scanInt();
            parameters.heightOfFlower = inputReader.scanListOfIntegers(parameters.numberOfFlowers);
            parameters.beautyOfFlower = inputReader.scanListOfLongs(parameters.numberOfFlowers);

            final Solver solver = new Solver(parameters);
            solver.solve();
        }

        outputWriter.close();
    }

    static class Solver {

        private final long[] dp;
        private final ProblemParameters parameters;

        public Solver(final ProblemParameters parameters) {
            this.parameters = parameters;
            this.dp = new long[parameters.numberOfFlowers];
        }

        public void solve() {
            outputWriter.println(iterativeDp());
        }

        private long iterativeDp() {
            final SegmentTree segmentTree = new SegmentTree(parameters.numberOfFlowers + 1,
                    new MaxSegmentTreeProperty());
            for (int currentFlower = 0; currentFlower < parameters.numberOfFlowers; ++currentFlower) {
                final int heightOfCurrentFlower = parameters.heightOfFlower.get(currentFlower);
                long maximumBeauty = segmentTree.query(0, heightOfCurrentFlower);
                dp[currentFlower] = maximumBeauty + parameters.beautyOfFlower.get(currentFlower);
                segmentTree.updateForOnePoint(heightOfCurrentFlower, dp[currentFlower]);
            }

            return segmentTree.query(0, parameters.numberOfFlowers);
        }
    }

    static class ProblemParameters {

        int numberOfFlowers;
        List<Integer> heightOfFlower;
        List<Long> beautyOfFlower;
    }

    static class SegmentTree { // Assuming segment will start from 0

        private long[] tree;
        private int expectedNumberOfElements;
        private SegmentTreeProperty property;

        public SegmentTree(final int expectedNumberOfElements, final SegmentTreeProperty property) {
            this.expectedNumberOfElements = expectedNumberOfElements;
            this.tree = new long[4 * expectedNumberOfElements];
            this.property = property;
        }

        public void updateForOnePoint(final int index, final long valueToUpdate) {
            update(1, 0, expectedNumberOfElements - 1, index, index, valueToUpdate);
        }

        private void update(final int treeNode, final int start, final int end, final int updateStart,
                            final int updateEnd, final long value) {
            if (updateStart <= start && updateEnd >= end) {
                final long existingValue = tree[treeNode];
                final long updatedValue = property.combine(existingValue, value);
                tree[treeNode] = updatedValue;
                return;
            }

            if (start > end || start > updateEnd || end < updateStart) {
                return;
            }

            final int leftNode = getLeftNodeFor(treeNode);
            final int endOfLeftNode = getEndForLeftNode(start, end);
            update(leftNode, start, endOfLeftNode, updateStart, updateEnd, value);

            final int rightNode = getRightNodeFor(treeNode);
            final int startOfRightNode = getStartOfRightNode(start, end);
            update(rightNode, startOfRightNode, end, updateStart, updateEnd, value);

            final long leftTreeValue = tree[leftNode];
            final long rightTreeValue = tree[rightNode];
            final long combinedResultOfSubTrees = property.combine(leftTreeValue, rightTreeValue);
            tree[treeNode] = combinedResultOfSubTrees;
        }

        public long query(final int startInSegment, final int endInSegment) {
            return query(1, 0, expectedNumberOfElements - 1, startInSegment, endInSegment);
        }

        private long query(final int treeNode, final int start, final int end, final int queryStart,
                               final int queryEnd) { // This is not accepted signature, but in CP world we don't care about best practices. :P
            if (queryStart <= start && queryEnd >= end) {
                return tree[treeNode];
            }

            if (start > end || start > queryEnd || end < queryStart) {
                return property.getValueForOutOfBound();
            }

            final int leftNode = getLeftNodeFor(treeNode);
            final int endOfLeftNode = getEndForLeftNode(start, end);
            final long leftPartOfTree = query(leftNode, start, endOfLeftNode, queryStart, queryEnd);

            final int rightNode = getRightNodeFor(treeNode);
            final int startOfRightNode = getStartOfRightNode(start, end);
            final long rightPartOfTree = query(rightNode, startOfRightNode, end, queryStart, queryEnd);

            return property.combine(leftPartOfTree, rightPartOfTree);
        }

        private int getLeftNodeFor(final int currentNode) {
            return (currentNode << 1);
        }

        private int getRightNodeFor(final int currentNode) {
            return getLeftNodeFor(currentNode) + 1;
        }

        private int getEndForLeftNode(final int start, final int end) {
            return (start + end) >> 1;
        }

        private int getStartOfRightNode(final int start, final int end) {
            return getEndForLeftNode(start, end) + 1;
        }
    }

    interface SegmentTreeProperty {

        long getValueForOutOfBound();
        long combine(final long leftPart, final long rightPart);
    }

    static class MaxSegmentTreeProperty implements SegmentTreeProperty {

        public long getValueForOutOfBound() {
            return 0L;
        }

        public long combine(final long leftPart, final long rightPart) {
            return Math.max(leftPart, rightPart);
        }
    }

    static class Pair<F, S> {

        F first;
        S second;

        public Pair(final F first, final S second) {
            this.first = first;
            this.second = second;
        }
    }

    static class MatrixLib {

        private final long modulo;

        private MatrixLib(final long mod) {
            this.modulo = mod;
        }

        public Matrix pow(final Matrix matrix, long exponent) {
            Matrix resultantMatrix = Matrix.getIdentityMatrix(matrix.rowSize, matrix.colSize);
            Matrix copyOfSourceMatrix = new Matrix(matrix.rowSize, matrix.colSize);
            copyOfSourceMatrix.copyFrom(matrix);

            while (exponent > 0) {
                if ((exponent & 1) != 0) {
                    resultantMatrix = multiply(resultantMatrix, copyOfSourceMatrix);
                }

                exponent >>= 1;
                copyOfSourceMatrix = multiply(copyOfSourceMatrix, copyOfSourceMatrix);
            }

            return resultantMatrix;
        }

        private Matrix multiply(final Matrix firstMatrix, final Matrix secondMatrix) {
            assert firstMatrix.colSize == secondMatrix.rowSize;
            final Matrix resultantMatrix = new Matrix(firstMatrix.rowSize, secondMatrix.colSize);
            for (int row = 0; row < firstMatrix.rowSize; ++row) {
                for (int col = 0; col < secondMatrix.colSize; ++col) {
                    for (int inter = 0; inter < secondMatrix.rowSize; ++inter) {
                        long currentValue = resultantMatrix.getValueAt(row, col);
                        long multiplyValue = firstMatrix.getValueAt(row, inter) * secondMatrix.getValueAt(inter, col);
                        long updatedValue = adjustWithMod(adjustWithMod(currentValue) + adjustWithMod(multiplyValue));
                        resultantMatrix.setValueAt(row, col, updatedValue);
                    }
                }
            }

            return resultantMatrix;
        }

        private long adjustWithMod(final long value) {
            return value >= modulo
                    ? value % modulo
                    : (value < 0)
                    ? (value + modulo) % modulo
                    : value;
        }
    }

    static class Matrix {

        int rowSize;
        int colSize;
        long[][] matrix;

        public Matrix(final int rowSize, final int colSize) {
            this.rowSize = rowSize;
            this.colSize = colSize;
            this.matrix = new long[rowSize + 1][colSize + 1];
        }

        public void setValueAt(final int row, final int col, final long value) {
            this.matrix[row][col] = value;
        }

        public long getValueAt(final int row, final int col) {
            return this.matrix[row][col];
        }

        public void copyFrom(final Matrix sourceMatrix) {
            assert sourceMatrix.rowSize == rowSize && sourceMatrix.colSize == colSize;
            for (int row = 0; row < rowSize; ++row) {
                for (int col = 0; col < colSize; ++col) {
                    setValueAt(row, col, sourceMatrix.getValueAt(row, col));
                }
            }
        }

        public static Matrix getIdentityMatrix(final int rows, final int cols) {
            assert rows == cols : "Asked matrix is not square matrix can not provide identity matrix.";
            final Matrix resultantMatrix = new Matrix(rows, cols);
            for (int row = 0; row < rows; ++row) {
                resultantMatrix.setValueAt(row, row, 1);
            }

            return resultantMatrix;
        }

        @Override
        public String toString() {
            StringBuffer stringBuffer = new StringBuffer();
            stringBuffer.append("rowSize -> " + rowSize + " colSize -> " + colSize + "\n");
            for (int i = 0; i < rowSize; ++i) {
                for (int j = 0; j < colSize; ++j) {
                    stringBuffer.append(matrix[i][j] + " ");
                }
                stringBuffer.append("\n");
            }

            return stringBuffer.toString();
        }
    }

    static class NumberTheoryLib {

        public List<Integer> getMobiousFunctionValuesTill(final int maximumValue) {
            final List<Integer> mobiousFunctionValues = new ArrayList<>();
            mobiousFunctionValues.add(0); // For 0 dummy value
            mobiousFunctionValues.add(1); // For 1

            final int[] lowestPrimeDivisor = new int[maximumValue + 2];
            for (int currentNumber = 2; currentNumber <= maximumValue; ++currentNumber) {
                if (lowestPrimeDivisor[currentNumber] == 0) {
                    for (int multipleOfCurrentNumber = currentNumber; multipleOfCurrentNumber <= maximumValue;
                         multipleOfCurrentNumber += currentNumber) {
                        lowestPrimeDivisor[multipleOfCurrentNumber] = currentNumber;
                    }
                }

                boolean isNumberSqureFree = true;
                int numberOfDistinctPrimeDivisors = 0;
                int tempValueOfCurrentNumber = currentNumber;
                while (tempValueOfCurrentNumber > 1) {
                    int divisor = lowestPrimeDivisor[tempValueOfCurrentNumber];
                    if (tempValueOfCurrentNumber % divisor == 0) {
                        tempValueOfCurrentNumber /= divisor;
                        if (tempValueOfCurrentNumber % divisor == 0) { // Not a squareFree
                            isNumberSqureFree = false;
                            break;
                        }

                        numberOfDistinctPrimeDivisors++;
                    }
                }

                if (isNumberSqureFree) {
                    mobiousFunctionValues.add((numberOfDistinctPrimeDivisors & 1) != 0 ? -1 : 1);
                } else {
                    mobiousFunctionValues.add(0);
                }
            }

            return mobiousFunctionValues;
        }
    }

    // We can use abstract method or loaner pattern to create different classes for different dataTypes and
    // keep repeated code in with generic class. But can't follow OOPS in CP :( because of TLE or MLE.
    // So try to use less object creation in CP.
    static class InputReader {

        private final BufferedInputStream bufferedInputStream;

        private final static char NEGATIVE_CHAR = '-';
        private final static char SPACE_CHAR = ' ';
        private final static char TAB_CHAR = '\t';
        private final static char NEW_LINE_WITH_N = '\n';
        private final static char NEW_LINE_WITH_R = '\r';
        private final static int END_OF_INPUT_STREAM = -1;

        public InputReader(final InputStream inputStream) {
            bufferedInputStream = new BufferedInputStream(inputStream);
        }

        public int scanInt() throws IOException {
            int currentByte = findFirstUsefulByte();
            boolean isNegative = false;
            if (currentByte == NEGATIVE_CHAR) {
                isNegative = true;
                currentByte = bufferedInputStream.read();
            }

            int number = 0;
            while (isUsefulByte(currentByte)) {
                number = (number * 10) + (currentByte - '0');
                currentByte = bufferedInputStream.read();
            }

            return isNegative ? -number : number;
        }

        public long scanLong() throws IOException {
            int currentByte = findFirstUsefulByte();
            boolean isNegative = false;
            if (currentByte == NEGATIVE_CHAR) {
                isNegative = true;
                currentByte = bufferedInputStream.read();
            }

            long number = 0;
            while (isUsefulByte(currentByte)) {
                number = (number * 10) + (currentByte - '0');
                currentByte = bufferedInputStream.read();
            }

            return isNegative ? -number : number;
        }

        public String scanString() throws IOException {
            int currentByte = findFirstUsefulByte();
            final StringBuilder stringBuilder = new StringBuilder();
            while (isUsefulByte(currentByte)) {
                stringBuilder.append((char) currentByte);
                currentByte = bufferedInputStream.read();
            }

            return stringBuilder.toString();
        }

        public double scanDouble() throws IOException { //Reason to use java's parser is because we had to write a lot of cases to handle floating point problems.
            return Double.parseDouble(scanString());
        }

        public List<Integer> scanListOfIntegers(int numbersCount) throws IOException {
            final List<Integer> numberList = new ArrayList<>();
            while (numbersCount-- > 0) {
                numberList.add(scanInt());
            }

            return numberList;
        }

        public List<Long> scanListOfLongs(int numbersCount) throws IOException {
            final List<Long> numberList = new ArrayList<>();
            while (numbersCount-- > 0) {
                numberList.add(scanLong());
            }

            return numberList;
        }

        public List<String> scanListOfStrings(int numbersCount) throws IOException {
            final List<String> stringList = new ArrayList<>();
            while (numbersCount-- > 0) {
                stringList.add(scanString());
            }

            return stringList;
        }

        public List<Double> scanListOfDoubles(int numbersCount) throws IOException {
            final List<Double> doubleList = new ArrayList<>();
            while (numbersCount-- > 0) {
                doubleList.add(scanDouble());
            }

            return doubleList;
        }

        private int findFirstUsefulByte() throws IOException {
            int currentByte = bufferedInputStream.read();
            while (!isUsefulByte(currentByte)) {
                currentByte = bufferedInputStream.read();
            }

            return currentByte;
        }

        private boolean isUsefulByte(final int currentByte) {
            if (currentByte == SPACE_CHAR || NEW_LINE_WITH_N == currentByte || NEW_LINE_WITH_R == currentByte
                    || currentByte == TAB_CHAR || currentByte == END_OF_INPUT_STREAM) {
                return false;
            } else {
                return true;
            }
        }
    }

    // Try to use it in tr-resource block.
    // To avoid close call manually.
    static class OutputWriter implements AutoCloseable {

        private final static boolean IS_AUTO_FLUSH_FOR_NEW_LINE = true;
        private final PrintWriter printWriter;

        public OutputWriter(final OutputStream outputStream) {
            this.printWriter = new PrintWriter(outputStream, IS_AUTO_FLUSH_FOR_NEW_LINE);
        }

        public void print(Object... objects) {
            for (int objectIndex = 0; objectIndex < objects.length; ++objectIndex) {
                if (objectIndex != 0) {
                    printWriter.print(' ');
                }
                printWriter.print(objects[objectIndex]);
            }
        }

        public void println(Object... objects) {
            print(objects);
            printWriter.println();
        }

        public void flush() { //Force flush if require after printing each element on one line
            printWriter.flush();
        }

        public void close() {
            printWriter.close();
        }
    }
}