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
//package numbersontree;

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

public class numbersontree {
	
	static ArrayList<ArrayList<Integer>> c;
	static int[] nums;
	static boolean isValid;
	
	public static ArrayList<Integer> getAns(int node) {
		//System.out.println(node);
		int midVal = nums[node];
		ArrayList<Integer> ans = new ArrayList<Integer>();
		if(c.get(node).size() == 0) {
			if(midVal != 0) {
				isValid = false;
			}
			ans.add(node);
			return ans;
		}
		else {
			if(midVal == 0) {
				ans.add(node);
			}
			for(int i = 0; i < c.get(node).size(); i++) {
				ArrayList<Integer> nextAns = getAns(c.get(node).get(i));
				for(int j : nextAns) {
					ans.add(j);
					if(ans.size() == midVal) {
						ans.add(node);
					}
				}
			}
			if(midVal > ans.size()) {
				isValid = false;
			}
			return ans;
		}
	}
	
	public static void main(String[] args) throws IOException {
		BufferedReader fin = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(fin.readLine());
		c = new ArrayList<ArrayList<Integer>>();
		for(int i = 0; i < n; i++) {
			c.add(new ArrayList<Integer>());
		}
		int rootIndex = 0;
		nums = new int[n];
		for(int i = 0; i < n; i++) {
			StringTokenizer st = new StringTokenizer(fin.readLine());
			int a = Integer.parseInt(st.nextToken()) - 1;
			int val = Integer.parseInt(st.nextToken());
			if(a != -1) {
				c.get(a).add(i);
			}
			else {
				rootIndex = i;
			}
			nums[i] = val;
		}
		isValid = true;
		ArrayList<Integer> ans = getAns(rootIndex);
		StringBuilder fout = new StringBuilder();
		if(isValid) {
			fout.append("YES\n");
			int[] printAns = new int[n];
			for(int i = 0; i < ans.size(); i++) {
				int next = ans.get(i);
				printAns[next] = i + 1;
			}
			for(int i : printAns) {
				fout.append(i).append(" ");
			}
			fout.append("\n");
		}
		else {
			fout.append("NO\n");
		}
		System.out.println(fout);
	}
}
