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.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.StringTokenizer;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author xylenox
 */     
public class b {
    static ArrayList<Integer>[] child;
    static int[] res;
    static int[] c;
    static int[] size;
    public static void main(String[] args) {
        FS in = new FS(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = in.nextInt();
        child = new ArrayList[n];
        for(int i = 0; i < n; i++) {
            child[i] = new ArrayList<>();
        }
        c = new int[n];
        res = new int[n];
        size = new int[n];
        int root = 0;
        for(int i = 0; i < n; i++) {
            int par = in.nextInt()-1;
            if(par != -1) child[par].add(i);
            else root = i;
            c[i] = in.nextInt();
        }
        size(root);
        for(int i = 0; i < n; i++) {
            if(c[i] >= size[i]) {
                System.out.println("NO");
                return;
            }
        }
        ArrayDeque<Integer> tmp = new ArrayDeque<>();
        for(int i = 1; i <= n; i++) tmp.add(i);
        out.println("YES");
        dfs(root, tmp);
        for(int i = 0; i < n; i++) out.print(res[i] + " ");
        out.println();
        out.close();
    }
    
    static int size(int node) {
        size[node] = 1;
        for(int i : child[node]) size[node] += size(i);
        return size[node];
    }
    
    static void dfs(int node, ArrayDeque<Integer> nums) {
        int num = c[node];
        for(int i : child[node]) {
            ArrayDeque<Integer> tmp = new ArrayDeque<>();
            int j;
            for(j = 0; j < size[i] && num > 0; j++, num--) {
                tmp.add(nums.poll());
            }
            if(res[node] == 0 && num == 0) res[node] = nums.poll();
            for(; j < size[i]; j++) tmp.add(nums.poll());
            dfs(i, tmp);
        }
        if(res[node] == 0) res[node] = nums.poll();
    }
    
    static class FS {
        BufferedReader in;
        StringTokenizer token;
        
        public FS(InputStream st) {
            in = new BufferedReader(new InputStreamReader(st));
        }
        
        public String next() {
            if(token == null || !token.hasMoreElements()) {
                try {
                    token = new StringTokenizer(in.readLine());
                } catch(Exception e) {}
                return next();
            }
            return token.nextToken();
        }
        
        public int nextInt() {
            return Integer.parseInt(next());
        }
    }
}
