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 Solution {
    static ArrayList<Integer> tree[];
    static int c[];
    public static void main(String[] args) {

        Scanner input=new Scanner(System.in);
        int n=input.nextInt();
        c=new int[n+1];
        tree=new ArrayList[n+1];
        for (int i = 0; i <=n ; i++) {
            tree[i]=new ArrayList<>(); }
        for (int i = 1; i <=n ; i++) {
            int x=input.nextInt();
            tree[x].add(i);
            c[i]=input.nextInt();
        }
        ArrayList<Integer> res=dfs(tree[0].get(0));
        if (!flag) {
            int a[] = new int[n + 1];
            for (int i = 0; i < n; i++) {
                a[res.get(i)] = i + 1;

            }
            System.out.println("YES");
            for (int i = 1; i <= n; i++) {
                System.out.print(a[i] + " ");
            }
        }else {
            System.out.println("NO");
        }
    }

    static boolean flag=false;
    private static ArrayList<Integer> dfs(Integer root) {
        ArrayList<Integer> res=new ArrayList<>();
        for (Integer a:tree[root]) {
            res.addAll(dfs(a));
            if (flag){
                return new ArrayList<>();
            }
        }
        if (c[root]>res.size()){
           flag=true;
           return new ArrayList<>();
        }
        res.add(c[root],root);
        return res;
    }

}
