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.List;
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;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        List<Integer>[] adj;
        int[] a;
        int[] c;

        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            a = new int[n];
            c = new int[n];
            adj = new List[n];
            for (int i = 0; i < n; i++) {
                adj[i] = new ArrayList<>();
            }

            int root = -1;
            for (int i = 0; i < n; i++) {
                int p = in.nextInt() - 1;
                c[i] = in.nextInt();
                if (p < 0) {
                    root = i;
                } else {
                    adj[i].add(p);
                    adj[p].add(i);
                }
            }

            List<Integer> order = dfs(root, -1);
            if (order == null) {
                out.println("NO");
                return;
            }
            for (int i = 0; i < order.size(); i++) {
                a[order.get(i)] = i + 1;
            }

            out.println("YES");
            for (int i = 0; i < n; i++) {
                if (i > 0) {
                    out.print(" ");
                }
                out.print(a[i]);
            }
            out.println();
        }

        private List<Integer> dfs(int v, int p) {
            List<Integer> all = new ArrayList<>();
            for (int u : adj[v]) {
                if (u == p) {
                    continue;
                }
                List<Integer> ch = dfs(u, v);
                if (ch == null) {
                    return null;
                }
                all.addAll(ch);
            }
            if (c[v] > all.size()) {
                return null;
            }
            all.add(c[v], v);
            return all;
        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

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

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

    }
}

