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.*;
public class HelloWorld{
    public static int tmp;
    public static class Node implements Comparable<Node>{
        int x;
        int num;
        public Node(int a,int b)
        {
            x=a;
            num=b;
        }
        public int compareTo(Node b)
        {
            return this.num-b.num;
        }
    }
    public static ArrayList<Integer>[] adj;
    public static int[] val;
     public static void main(String []args){
       Scanner sc=new Scanner(System.in);
       int n=sc.nextInt();
        val=new int[n];
        adj=new ArrayList[n];
        for(int i=0;i<n;i++)
        adj[i]=new ArrayList();
        int root=-1;
        for(int i=0;i<n;i++)
        {
            int x=sc.nextInt()-1;
            int y=sc.nextInt();
            if(x==-1)
                root=i;
            else
                adj[x].add(i);
            val[i]=y;
        }
        ArrayList<Node> list=dfs(root);
        if(list==null)
        System.out.println("NO");
        else{
        Collections.sort(list,(p,q) -> (p.x-q.x));
        System.out.println("YES");
        for(int i=0;i<n;i++)
        System.out.print(list.get(i).num+" ");
        }
     }
     public static ArrayList<Node> dfs(int x)
     {
         ArrayList<Node>list=new ArrayList();
         for(int v:adj[x])
         {
             ArrayList<Node> ll=dfs(v);
             if(ll==null)
             return null;
             list.addAll(ll);
         }
         int l=list.size();
         if(l<val[x])
         return null;
         if(l==0)
         list.add(new Node(x,++tmp));
         else{
             Collections.sort(list);
             int p=0;
             if(val[x]==0)
             p=list.get(val[x]).num;
             else
              p=list.get(val[x]-1).num+1;
             list.add(val[x],new Node(x,p));
             tmp++;
         }
         l++;
         for(int i=val[x]+1;i<l;i++)
         list.get(i).num++;
         return list;
     }
}