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.util.*;
import java.io.*;

public class Main {
	public static void main(String args[]) {new Main().run();}

	FastReader in = new FastReader();
	PrintWriter out = new PrintWriter(System.out);
	void run(){
		work();
		out.flush();
	}
	long mod=1000000007;
	int[] B;
	ArrayList<Integer>[] graph;
	int[] ret;
	boolean f=true;
	void work() {
		int n=in.nextInt();
		graph=(ArrayList<Integer>[])new ArrayList[n];
		for(int i=0;i<n;i++)graph[i]=new ArrayList<>();
		B=new int[n];
		ret=new int[n];
		int root=0;
		for(int i=0;i<n;i++) {
			int s=in.nextInt()-1;
			if(s==-1) {
				root=i;
			}else {
				graph[i].add(s);
				graph[s].add(i);
			}
			int e=in.nextInt();
			B[i]=e;
		}
		ArrayList<Integer> l=dfs(root,new boolean[n]);
		if(!f) {
			out.println("NO");
			return;
		}
		out.println("YES");
		for(int i=0;i<n;i++) {
			ret[l.get(i)]=i+1;
		}
		for(int i=0;i<n;i++) {
			out.print(ret[i]+" ");
		}
	}
	private ArrayList<Integer> dfs(int node, boolean[] vis) {
		vis[node]=true;
		ArrayList<Integer> list=new ArrayList<>();
		for(int nn:graph[node]) {
			if(!vis[nn]) {
				ArrayList<Integer> l=dfs(nn,vis);
				if(!f)return null;
				for(int i=0;i<l.size();) {
					if(list.size()==B[node]) {
						list.add(node);
					}else {
						list.add(l.get(i++));
					}
				}
			}
		}
		if(list.size()==B[node]) {
			list.add(node);
		}else if(list.size()<B[node]) {
			f=false;
			return null;
		}
		return list;
	}
}	



class FastReader
{
	BufferedReader br;
	StringTokenizer st;

	public FastReader()
	{
		br=new BufferedReader(new InputStreamReader(System.in));
	}
	
	
	public String next() 
	{
		if(st==null || !st.hasMoreElements())
		{
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}

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

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