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
/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
If I'm the sun, you're the moon
Because when I go up, you go down
*******************************
*/
import java.util.*;
import java.io.*;

   public class x1287D
   {
      public static void main(String args[]) throws Exception
      {
         //omkar is my dad
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         LinkedList<Integer>[] edges = new LinkedList[N+1];
         for(int i=0; i <= N; i++)
            edges[i] = new LinkedList<Integer>();
         int[] arr = new int[N+1];
         int[] parent = new int[N+1];
         int root = 0;
         for(int i=1; i <= N; i++)
         {
            st = new StringTokenizer(infile.readLine());
            int p = Integer.parseInt(st.nextToken());
            int c = Integer.parseInt(st.nextToken());
            if(p == 0)
               root = i;
            edges[p].add(i);
            parent[i] = p;
            arr[i] = c;
         }
         //assign
         int[] res = new int[N+1];
         for(int i=1; i <= N; i++)
         {
            int id = -1;
            Queue<Integer> q = new LinkedList<Integer>();
            q.add(root);
            outer:while(q.size() > 0)
            {
               int curr = q.poll();
               if(arr[curr] == 0)
               {
                  id = curr;
                  break outer;
               }
               for(int next: edges[curr])
                  q.add(next);
            }
            if(id == -1)
            {
               System.out.println("NO");
               return;
            }
            //go up
            res[id] = i;
            arr[id]--; //set as visited
            id = parent[id];
            while(id != 0)
            {
               arr[id]--;
               id = parent[id];
            }
         }
         StringBuilder sb = new StringBuilder("YES\n");
         for(int i=1; i <= N; i++)
            sb.append(res[i]+" ");
         System.out.println(sb);
      }
   }