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 R612D2D{
 
	public static void main(String[] args) throws Exception{
		int num = 998244353;
		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 	
 		int n = Integer.parseInt(bf.readLine());
 		ArrayList<Integer> numbers = new ArrayList<Integer>();
 		int[] numsubtree = new int[n+1];
 		
 		
 		int[] c = new int[n+1];
 		int[] parent = new int[n+1];
 		int[] answers = new int[n+1];
 		Map<Integer, List<Integer>> graph = new HashMap<Integer,List<Integer>>();
 		int root = -1;
 		for(int i = 1;i<=n;i++){
 			numbers.add(i);
 			StringTokenizer st= new StringTokenizer (bf.readLine());
 			int a = Integer.parseInt(st.nextToken());
 			int b = Integer.parseInt(st.nextToken());
 			if (a == 0)
 				root = i;
 			parent[i] = a;
 			c[i] = b;
 			if (a != 0){
	 			if (graph.containsKey(a)){
	 				graph.get(a).add(i);
	 			}
	 			else{
	 				ArrayList<Integer> newa = new ArrayList<Integer>();
	 				newa.add(i);
	 				graph.put(a,  newa);
	 			}
 			}
 		}
		
 		boolean found = true;
 		int[] temp = new int[n+1];
 		int[] newarray = childrensubtree(graph, root, temp);
 		
 		for(int i = 1;i<newarray.length;i++){
 			if (c[i] >= newarray[i]){
 				found = false;
 				break;
 			}
 		}
 		
 		
 
 		Stack<Integer> dfs = new Stack<Integer>();
 		dfs.push(root);
 		while(!dfs.isEmpty()){
 			int cf = dfs.pop();
 			
 			if (c[cf] < numbers.size()){
 				answers[cf] = numbers.get(c[cf]);
 				numbers.remove(c[cf]);
 			}
 			else{
 				found = false; 
 				break;
 			}
 			if (graph.containsKey(cf)){
 			for(int k:graph.get(cf)){
 				dfs.push(k);
 			}
 			}
 			
 		}
 		if (found == false){
 			out.println("NO");
 		}
 		else{
 		out.println("YES");
 		for(int i = 1;i<=n;i++){
 			out.print(answers[i] + " ");
 		}
 		
 		out.println();
 		}
 		out.close();
 		
 		
 		
	}
	
	public static int[] childrensubtree(Map<Integer, List<Integer>> graph, int vertex, int[] array){
		if (!graph.containsKey(vertex)){
			array[vertex] = 1;
			return array;
		}
		else{
			int sum = 0;
			for (int i : graph.get(vertex)){
				sum+= childrensubtree(graph, i, array)[i];
			}
			sum+=1;
			array[vertex] = sum;
			return array;
		}
	}
 
}