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 com.sun.javafx.scene.control.skin.IntegerFieldSkin;

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

public class D {
    public static Node[] nodes;
    public static LinkedList<Integer>[] edges;
    public static int root;
    public static void main(String[] args) throws IOException{
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(f.readLine());
        nodes = new Node[n+1];
        edges = new LinkedList[n+1];
        for(int i = 0; i <= n; i++){
            edges[i] = new LinkedList<Integer>();
        }
        root = 0;

        for(int i = 1; i <= n; i++){
            StringTokenizer st = new StringTokenizer(f.readLine());
            int p = Integer.parseInt(st.nextToken());
            int c = Integer.parseInt(st.nextToken());
            if(p == 0) root = i;
            nodes[i] = new Node(i, c, p);
            edges[p].add(i);
        }

        for(int i = 1; i <= n; i++){
            int curr = dfs(i);
            while(!(curr == 0)){
                nodes[curr].val-=1;
                curr = nodes[curr].parent;
            }
        }

        System.out.println("YES");
        StringBuilder ans = new StringBuilder();
        for(int i = 1; i <= n; i++){
            ans.append(nodes[i].number);
            ans.append(" ");
        }
        System.out.println(ans.toString().trim());




    }
    public static int dfs(int i){
        HashSet<Integer> seen = new HashSet<Integer>();
        Stack<Integer> stk = new Stack<Integer>();
        stk.add(root);
        while(!stk.isEmpty()){
            int curr = stk.pop();
            if(seen.contains(curr)) continue;
            seen.add(curr);
            Node currNode = nodes[curr];
            if(currNode.val == 0){
                currNode.number = i;
                return curr;
            }
            for(int temp: edges[curr]){
                stk.add(temp);
            }
        }
        System.out.println("NO");
        System.exit(0);
        return -1;
    }

}
class Node{
    public int id;
    public int val;
    public int parent;
    public int number;

    public Node(int i, int v, int p){
        this.id = i;
        this.val = v;
        this.parent = p;
        this.number = 0;
    }
}
