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.awt.*;
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.math.RoundingMode;
import java.util.*;

public class Abc {
    static ArrayList<Integer> adj[];
    static int c[];
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int n=sc.nextInt();
        c=new int[n+1];
        adj=new ArrayList[n+1];
        for (int i=0;i<=n;i++)adj[i]=new ArrayList<>();
        for (int i=1;i<=n;i++){
            adj[sc.nextInt()].add(i);
            c[i]=sc.nextInt();
        }
        int ans[]=new int[n+1];
        ArrayList<Integer> ind=dfs(adj[0].get(0));
        for (int i=0;i<n;i++){
            ans[ind.get(i)]=i+1;
        }
        StringBuilder sb=new StringBuilder();
        for (int i=1;i<=n;i++){
            sb.append(ans[i]+" ");
        }
        System.out.println("YES");
        System.out.println(sb);
    }
    static ArrayList<Integer> dfs(int v){
        ArrayList<Integer> res=new ArrayList<>();
        for (int u:adj[v]){
            ArrayList<Integer> a=dfs(u);
            res.addAll(a);
        }
        if (c[v]>res.size()){
            System.out.println("NO");
            System.exit(0);
        }
        res.add(c[v],v);
        return res;
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}