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.*;
import java.io.*;
public class Main
{
    static int poss[];
    static ArrayList<Integer> edge[];
    static int ans[],c[];
    public static void dfs(int v,int[] par)
    {
        if(v==0)
        return;
        poss[v]++;
        dfs(par[v],par);
    }
    public static void dfs2(int v,TreeSet<Integer> ts,boolean vis[])
    {
        vis[v]=true;
        int cntr=0;
        for(int i:ts)
        {
            cntr++;
            if(cntr==c[v]+1)
            {
                ans[v]=i;
                break;
            }
        }
        ts.remove(new Integer(ans[v]));
        for(int i=0;i<edge[v].size();i++)
        {
            if(!vis[edge[v].get(i)])
            dfs2(edge[v].get(i),ts,vis);
        }
    }
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(System.out);
        int n=Integer.parseInt(br.readLine());
        int par[]=new int[n+1];
        c=new int[n+1];
        ans=new int[n+1];
        int root=1;
        edge=new ArrayList[n+1];
        for(int i=0;i<=n;i++)
        edge[i]=new ArrayList<>();
        poss=new int[n+1];
        for(int i=1;i<=n;i++)
        {
            String str[]=br.readLine().split(" ");
            par[i]=Integer.parseInt(str[0]);
            c[i]=Integer.parseInt(str[1]);
            edge[par[i]].add(i);
            if(par[i]==0)
            root=i;
        }
        int vert[]=new int[n+1];
        for(int i=1;i<=n;i++)
        dfs(par[i],par);
        boolean possible=true;
        for(int i=1;i<=n;i++)
        {
            if(c[i]>poss[i])
            {
                possible=false;
                break;
            }
        }
        if(!possible)
        pw.println("NO");
        else
        {
            TreeSet<Integer> ts=new TreeSet<>();
            for(int i=1;i<=n;i++)
            ts.add(i);
            dfs2(root,ts,new boolean[n+1]);
            pw.println("YES");
            for(int i=1;i<=n;i++)
            pw.print(ans[i]+" ");
        }
        pw.flush();
        pw.close();
    }
}