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 com.company;
import java.util.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class EF4 {
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    public static void main(String[] Args)throws Exception{
        FastReader scan=new FastReader(System.in);
        int t=1;
//        t=scan.nextInt();
        while(t-->0){
            int n=scan.nextInt();
            Node[] gr=new Node[n];
            for(int i=0;i<n;i++){
                gr[i]=new Node();
            }
            int root=-1;
            for(int i=0;i<n;i++){
                int pi=scan.nextInt();
                int ci=scan.nextInt();
                if(pi!=0){
                    gr[pi-1].ns.add(i);
                }else{
                    root=i;
                }
                gr[i].ci=ci;
            }
            dfs(gr,root);
            boolean pos=true;
            for(int i=0;i<n;i++){
                if(!gr[i].pos){
                    pos=false;
                }
            }
            if(pos){
                out.println("YES");
                for(int i=0;i<n;i++){
                    out.print(gr[i].ai+" ");
                }
                out.println();
            }else{
                out.println("NO");
            }
        }
        out.flush();
        out.close();
    }
    static int dfs(Node[] gr,int u){
        if(gr[u].ns.size()==0){
            if(gr[u].ci>0){
                gr[u].pos=false;
            }
            return 1;
        }
        int c=0;
        for(Integer v:gr[u].ns){
            c+=dfs(gr,v);
        }
        if(gr[u].ci>c){
            gr[u].pos=false;
        }else{
            Queue<Integer> q=new LinkedList<>();
            for(Integer v:gr[u].ns){
                ((LinkedList<Integer>) q).add(v);
            }
            ArrayList<pair> sort=new ArrayList<>();
            while(!q.isEmpty()){
                int cur=q.remove();
                sort.add(new pair(cur,gr[cur].ai));
                for(Integer nxt:gr[cur].ns){
                    ((LinkedList<Integer>) q).add(nxt);
                }
            }
            Collections.sort(sort);
            if(gr[u].ci==0){
                gr[u].ai=1;
            }else {
                gr[u].ai = sort.get(gr[u].ci - 1).val + 1;
            }
            for(int i=gr[u].ci;i<sort.size();i++){
                pair cur=sort.get(i);
                gr[cur.id].ai+=2;
            }
        }
        return c+1;
    }
    static class pair implements Comparable<pair>{
        int id;
        int val;
        pair(int id,int val){
            this.id=id;
            this.val=val;
        }

        @Override
        public int compareTo(pair o) {
            return this.val-o.val;
        }
    }
    static class Node{
        ArrayList<Integer> ns;
        int ci;
        int ai;
        boolean pos;
        Node(){
            ai=1;
            pos=true;
            ns=new ArrayList<>();
        }
    }
    static class FastReader {

        byte[] buf = new byte[2048];
        int index, total;
        InputStream in;

        FastReader(InputStream is) {
            in = is;
        }

        int scan() throws IOException {
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0) {
                    return -1;
                }
            }
            return buf[index++];
        }

        String next() throws IOException {
            int c;
            for (c = scan(); c <= 32; c = scan()) ;
            StringBuilder sb = new StringBuilder();
            for (; c > 32; c = scan()) {
                sb.append((char) c);
            }
            return sb.toString();
        }

        int nextInt() throws IOException {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
        long nextLong() throws IOException {
            int c;
            long val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
    }
}
