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.*;
import static java.lang.Math.*;

public class B {
    static TreeSet<Integer>st;
    static ArrayList<Integer>g[];
    static int c[];
    static int ans[];
    static int size[];
    static int n;
    static void jfs(int v, int p){
        size[v] = 1;
        for(int to : g[v])if(to != p){
            jfs(to,v);
            size[v]+=size[to];
        }
    }
    static void dfs(int v, int p){
        ArrayList<Integer>f = new ArrayList<>();
        for (int i = 0; i <= c[v]; i++) {
            f.add(st.pollFirst());
        }
        ans[v] = f.get(f.size() - 1);
        for (int i = 0; i < f.size() - 1; i++) {
            st.add(f.get(i));
        }
        for(int to : g[v])if(to != p)dfs(to,v);
    }
    public static void main(String[] args) throws IOException {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        n = in.nextInt();
        int rt = -1;
        c = new int[n];
        st = new TreeSet<>();
        g = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            g[i] = new ArrayList<>();
            st.add(i+1);
        }
        size = new int[n];
        ans = new int[n];
        for (int i = 0; i < n; i++) {
            int u = in.nextInt() - 1;
            int cc = in.nextInt();
            c[i] = cc;
            if(u == -1)rt = i;
            else g[u].add(i);
        }
        jfs(rt,-1);
        boolean bad = false;
        for (int i = 0; i < n; i++) {
            bad|=(size[i] - 1 < c[i]);
        }
        if(bad){
            out.println("NO");
            out.close();
            return;
        }
        dfs(rt,-1);
        out.println("YES");
        for (int i = 0; i < n; i++) {
            out.print(ans[i] + " ");
        }
        out.close();
    }
}
