Problem:
Score : 600 points

Problem Statement

We have a tree with N vertices, whose i-th edge connects Vertex u_i and Vertex v_i.
Vertex i has an integer a_i written on it.
For every integer k from 1 through N, solve the following problem:

We will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex 1 to Vertex k, in the order they appear. Find the length of the longest increasing subsequence of this sequence.

Here, the longest increasing subsequence of a sequence A of length L is the subsequence A_{i_1} , A_{i_2} , ... , A_{i_M} with the greatest possible value of M such that 1 \leq i_1 < i_2 < ... < i_M \leq L and A_{i_1} < A_{i_2} < ... < A_{i_M}.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq a_i \leq 10^9

1 \leq u_i , v_i \leq N

u_i \neq v_i

The given graph is a tree.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N
u_1 v_1
u_2 v_2
:
u_{N-1} v_{N-1}

Output

Print N lines. The k-th line, print the length of the longest increasing subsequence of the sequence obtained from the shortest path from Vertex 1 to Vertex k.

Sample Input 1

10
1 2 5 3 4 6 7 3 2 4
1 2
2 3
3 4
4 5
3 6
6 7
1 8
8 9
9 10

Sample Output 1

1
2
3
3
4
4
5
2
2
3

For example, the sequence A obtained from the shortest path from Vertex 1 to Vertex 5 is 1,2,5,3,4. Its longest increasing subsequence is A_1, A_2, A_4, A_5, with the length of 4.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)


import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

class Node {
    int index;
    int changedDpIndex;
    int changedValue;
    public Node() {
        this.index = -1;
        this.changedValue = -1;
        this.changedDpIndex = -1;
    }
    public void setChangedDpIndex(int changedDpIndex) {
        this.changedDpIndex = changedDpIndex;
    }
    public void setChangedValue(int changedValue) {
        this.changedValue = changedValue;
    }
}
public class Main {
    public static void main(String [] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int[] value = new int[n + 1];
        for (int i = 1; i <= n; ++i) {
            value[i] = scanner.nextInt();
        }
        int[] nodeSons = new int[n + 1];
        int[][] tree = new int[n + 1][n + 1];
        for (int i = 1; i < n; ++i) {
            int u = scanner.nextInt();
            int v = scanner.nextInt();
            tree[u][nodeSons[u]] = v;
            tree[v][nodeSons[v]] = u;
            nodeSons[u]++;
            nodeSons[v]++;
        }
        int [] ans = new int[n + 1];
        ans[1] = 1;
        int[] dpValue = new int[n];
        for (int i = 0; i < n; ++i) {
            dpValue[i] = Integer.MAX_VALUE;
        }
        Node[] nodes = new Node[n + 1];
        for (int i = 1; i <= n; ++i) {
            nodes[i] = new Node();
        }
        dfs(tree, nodes, dpValue, ans, 1, value, -1, nodeSons);
        for (int k = 1; k <= n; ++k) {
            System.out.println(ans[k]);
        }
    }
    public static void dfs(
            int[][] tree,
            Node[] nodes,
            int[] dpValue,
            int[] ans,
            int currentIndex,
            int[] value,
            int father,
            int[] nodeSons
    ) {
        int binarySearchIndex = Arrays.binarySearch(dpValue, value[currentIndex]);
        int length;
        if (binarySearchIndex >= 0 && binarySearchIndex < dpValue.length) {
          // nodes[currentIndex] = new Node(currentIndex, -1, -1);
            length = ans[father];
        } else {
            int insertPos = -1 - binarySearchIndex;
            nodes[currentIndex].setChangedDpIndex(insertPos);
            nodes[currentIndex].setChangedValue(dpValue[insertPos]);
            if (dpValue[insertPos] == Integer.MAX_VALUE) {
                length = insertPos + 1;
            } else {
                length = ans[father];
            }
            dpValue[insertPos] = value[currentIndex];
        }
      //  length = -Arrays.binarySearch(dpValue, Integer.MAX_VALUE - 1) - 1;
        ans[currentIndex] = length;

        // visit sons
        for (int i = 0; i < nodeSons[currentIndex]; ++i) {
            int son = tree[currentIndex][i];
            if (son == father) {
                continue;
            }
            dfs(tree, nodes, dpValue, ans, son, value, currentIndex, nodeSons);
        }

        if (nodes[currentIndex].changedDpIndex != -1) {
            // this node replaced some node before, recover it
            dpValue[nodes[currentIndex].changedDpIndex] = nodes[currentIndex].changedValue;
        //    nodes[currentIndex] = new Node(currentIndex, -1, -1);
        }

    }
}