Evlampiy was gifted a rooted tree. The vertices of the tree are numbered from 1 to n. Each of its vertices also has an integer a_i written on it. For each vertex i, Evlampiy calculated c_i — the number of vertices j in the subtree of vertex i, such that a_j < a_i. 

<image>Illustration for the second example, the first integer is a_i and the integer in parentheses is c_i

After the new year, Evlampiy could not remember what his gift was! He remembers the tree and the values of c_i, but he completely forgot which integers a_i were written on the vertices.

Help him to restore initial integers!

Input

The first line contains an integer n (1 ≤ n ≤ 2000) — the number of vertices in the tree.

The next n lines contain descriptions of vertices: the i-th line contains two integers p_i and c_i (0 ≤ p_i ≤ n; 0 ≤ c_i ≤ n-1), where p_i is the parent of vertex i or 0 if vertex i is root, and c_i is the number of vertices j in the subtree of vertex i, such that a_j < a_i.

It is guaranteed that the values of p_i describe a rooted tree with n vertices.

Output

If a solution exists, in the first line print "YES", and in the second line output n integers a_i (1 ≤ a_i ≤ {10}^{9}). If there are several solutions, output any of them. One can prove that if there is a solution, then there is also a solution in which all a_i are between 1 and 10^9.

If there are no solutions, print "NO".

Examples

Input


3
2 0
0 2
2 0


Output


YES
1 2 1 

Input


5
0 1
1 3
2 1
3 0
2 0


Output


YES
2 3 2 1 2
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        Node[] tree;
        int N;
        boolean flag = true;
        int INF = (int) (1e9) + 5;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            N = in.nextInt();
            tree = new Node[N];
            for (int i = 0; i < N; i++) {
                tree[i] = new Node();
            }
            int rt = 0;
            for (int i = 0; i < N; i++) {
                int pi = in.nextInt() - 1;
                int ci = in.nextInt();
                if (pi == -1) {
                    rt = i;
                } else {
                    tree[pi].ch.add(i);
                }
                tree[i].ci = ci;
            }
            dfs(rt);
            if (!flag) {
                out.println("NO");
            } else {
                int[] res = new int[N];
                out.println("YES");
                for (int i = 0; i < N; i++) {
                    res[tree[rt].nums.arr[i]] = (i + 1);
                }
                for (int j : res) {
                    out.print(j + " ");
                }
            }
        }

        void dfs(int N) {
            for (int ch : tree[N].ch) {
                dfs(ch);
                tree[N].nums.merge(tree[ch].nums);
            }
            if (!tree[N].nums.insert(N)) {
                flag = false;
            }
        }

        class Node {
            int ci;
            ArrayList<Integer> ch = new ArrayList<>();
            Arr nums = new Arr();

            Node(int ci, int N) {
                this.ci = ci;
            }

            Node() {
                Arrays.fill(nums.arr, INF);
            }

        }

        class Arr {
            int[] arr = new int[N];
            int sz = 0;

            Arr() {

            }

            void merge(Arr a) {
                for (int i = sz; i < a.sz + sz; i++) {
                    arr[i] = a.arr[i - sz];
                }
                sz += a.sz;
            }

            boolean insert(int i) {
                if (tree[i].ci > sz || !flag) {
                    return false;
                }
                sz++;
                for (int j = sz - 1; j >= tree[i].ci + 1; j--) {
                    arr[j] = arr[j - 1];
                }
                arr[tree[i].ci] = i;
                return true;
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

