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.io.*;
import java.util.*;
public final class code
// class code
// public class Solution
{
    static int n,c[],a[],subcount[];
    static ArrayList<ArrayList<Integer>> list;
    static ArrayList<Integer> clist;
    static void solve()throws IOException
    {
        n=nextInt();
        list=new ArrayList<ArrayList<Integer>>();
        for(int i=0;i<=n;i++)
            list.add(new ArrayList<Integer>());
        c=new int[n+1];
        a=new int[n+1];
        clist=new ArrayList<Integer>();
        for(int i=1;i<=n;i++)
            clist.add(i);
        int root=0;
        for(int i=1;i<=n;i++)
        {
            int p=nextInt();
            if(p==0)
                root=i;
            else
                list.get(p).add(i);
            c[i]=nextInt();
        }
        subcount=new int[n+1];
        dfs1(root);
        // debug(subcount);
        if(dfs(root))
        {
            out.println("YES");
            for(int i=1;i<=n;i++)
                out.print(a[i]+" ");
        }
        else
            out.println("NO");
    }
    static boolean dfs(int v)
    {
        if(c[v]>=clist.size() || c[v]>=subcount[v])
            return false;
        a[v]=clist.get(c[v]);
        clist.remove(c[v]);
        boolean ret=true;
        for(int i:list.get(v))
            ret=ret && dfs(i);
        return ret;
    }
    static int dfs1(int v)
    {
        subcount[v]=1;
        for(int vv:list.get(v))
            subcount[v]+=dfs1(vv);
        return subcount[v];
    }


    
     
    ///////////////////////////////////////////////////////////
    public static void main(String args[])throws IOException
    {
        br=new BufferedReader(new InputStreamReader(System.in));
        out=new PrintWriter(new BufferedOutputStream(System.out));
        random=new Random();
         
        solve();
         
        // int t=nextInt();
        // for(int i=1;i<=t;i++)
        // {
        //     // out.print("Case #"+i+": ");
        //     solve();
        // }
         
        out.close();
    }
     
    static final long mod=(int)(1e9+7);
    static final int inf=(int)(1e9+1);
    // static final long inf=(long)(1e18);
     
    static class Pair implements Comparable<Pair>
    {
        int first,second;
        Pair(int a,int b)
        {
            first=a;
            second=b;
        }
        public int compareTo(Pair p)
        {
            return first-p.first;
        }
        public String toString()
        {
            return first+" "+second;
        }
    }
    static class Triplet
    {
        int first,second,third;
        Triplet(int a,int b,int c)
        {
            first=a;
            second=b;
            third=c;
        }
    }
    
    static long modinv(long x)
    {
        return modpow(x,mod-2);
    }
    static long modpow(long a,long b)
    {
        if(b==0)
            return 1;
        long x=modpow(a,b/2);
        x=(x*x)%mod;
        if(b%2==1)
            return (x*a)%mod;
        return x;
    } 
    static int max(int ... a)
    {
    int ret=a[0];
    for(int i=1;i<a.length;i++)
    ret=Math.max(ret,a[i]);
    return ret;
    }
    static int min(int ... a)
    {
    int ret=a[0];
    for(int i=1;i<a.length;i++)
    ret=Math.min(ret,a[i]);
    return ret;
    }
    static void debug(Object ... a)
    {
    System.out.print("> ");
    for(int i=0;i<a.length;i++)
    System.out.print(a[i]+" ");
    System.out.println();
    }
    static void debug(int a[]){debuga(Arrays.stream(a).boxed().toArray());}
    static void debug(long a[]){debuga(Arrays.stream(a).boxed().toArray());}
    static void debuga(Object a[])
    {
    System.out.print("> ");
    for(int i=0;i<a.length;i++)
    System.out.print(a[i]+" ");
    System.out.println();
    }
    static Random random;
    static BufferedReader br;
    static StringTokenizer st;
    static PrintWriter out;
    static String nextToken()throws IOException
    {
    while(st==null || !st.hasMoreTokens())
    st=new StringTokenizer(br.readLine());
    return st.nextToken();
    }
    static String nextLine()throws IOException
    {
    return br.readLine();
    }
    static int nextInt()throws IOException
    {
    return Integer.parseInt(nextToken());
    }
    static long nextLong()throws IOException
    {
    return Long.parseLong(nextToken());
    }
    static double nextDouble()throws IOException
    {
    return Double.parseDouble(nextToken());
    }
}