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 main;
import java.io.*;
import java.util.*;
import java.lang.*;
import java.math.*;
public class Submission {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter (System.out);
        //BufferedReader reader = new BufferedReader(new InputStreamReader(new FileInputStream("input.txt")));
        int n = Integer.parseInt(reader.readLine());
        int[] parent = new int[n];
        int bigpoppa=0;
        HashMap<Integer,List<Integer>> order = new HashMap<>();
        HashMap<Integer,List<Integer>> kids = new HashMap<>();
        int[] kidCount = new int[n];
        for (int i=0;i<n;i++) kids.put(i, new ArrayList<>());
        int[] c = new int[n];
        for (int i=0;i<n;i++) {
        	StringTokenizer st = new StringTokenizer(reader.readLine()," ");
        	int p = Integer.parseInt(st.nextToken())-1;
        	c[i]=Integer.parseInt(st.nextToken());
        	if (p>=0) {
        		kids.get(p).add(i);
        		kidCount[p]++;
        	}
        	else bigpoppa=i;
        	parent[i]=p;
        }
        List<Integer> childless = new ArrayList<>();
        for (int i=0;i<n;i++) {
        	if (kids.get(i).size()==0) childless.add(i);
        }
        int fail=0;
        while (!childless.isEmpty()) {
        	int me = childless.get(0);
        	childless.remove(childless.indexOf(me));
        	if (parent[me]>=0) {
        		kidCount[parent[me]]--;
        		if (kidCount[parent[me]]==0) childless.add(parent[me]);
        	}
        	order.put(me,new ArrayList());
        	for (int i : kids.get(me)) {
        		order.get(me).addAll(order.get(i));
        	}
        	if (c[me]<=order.get(me).size()) order.get(me).add(c[me],me);
        	else {
        		//out.println(order.get(me).size());
        		fail=1;
        		break;
        	}
        }
        if (fail==1) out.println("NO");
        else {
        	out.println("YES");
        	int[] answers = new int[n];
        	for (int i=0;i<n;i++) answers[order.get(bigpoppa).get(i)]=i+1;
        	for (int i=0;i<n;i++) {
        		out.print(answers[i]);
        		if (i<n-1) out.print(" ");
        	}
        	out.println();
        }
        reader.close();
        out.close();
    }
}