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 {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().run(in, out);
        out.close();
    }

    int N;
    int[] c;
    List<Integer>[] adj;
    int root = -1;
    void run(FastScanner in, PrintWriter out) {
        N = in.nextInt();
        c = new int[N+1];
        adj = new List[N+1];
        stIndex = new int[N+1];
        for (int i = 1; i <= N; i++) adj[i] = new ArrayList<>();

        for (int i = 1; i <= N; i++) {
            int parent = in.nextInt();
            if (parent == 0) root = i;
            else adj[parent].add(i);
            c[i] = in.nextInt();
        }

        if (!dfs(root)) {
            out.println("NO");
            return;
        }
        out.println("YES");
        int[] ans = new int[N+1];
        int curr = 1;
        for (int num : l) ans[num] = curr++;
        for (int i = 1; i <= N; i++) {
            out.print(ans[i] + " ");
        }
        out.println();

        // List<Integer> l = dfs(root);
        // if (l.isEmpty()) {
        //     out.println("NO");
        // } else {
        //     out.println("YES");
        //     int[] ans = new int[N+1];
        //     int curr = 1;
        //     for (int num : l) ans[num] = curr++;
        //     for (int i = 1; i <= N; i++) {
        //         out.print(ans[i] + " ");
        //     }
        //     out.println();
        // }
    }

    int[] stIndex;
    int currStIndex = 0;
    LinkedList<Integer> l = new LinkedList<>();

    // returns number of children
    boolean dfs(int u) {
        int startIndex = currStIndex;
        if (adj[u].isEmpty()) {
            if (c[u] != 0) return false;
            l.add(u);
            currStIndex++;
            return true;
        }

        for (int v : adj[u]) {
            if (!dfs(v)) return false;
        }

        if (c[u] > currStIndex-startIndex) return false;
        l.add(startIndex+c[u], u);
        currStIndex++;
        return true;
    }

    // List<Integer> dfs(int u) {

    //     if (adj[u].isEmpty()) {
    //         if (c[u] != 0) return Collections.emptyList();
    //         return Arrays.asList(u);
    //     }

    //     LinkedList<Integer> myList = new LinkedList<>();

    //     for (int v : adj[u]) {
    //         List<Integer> childList = dfs(v);
    //         if (childList.isEmpty()) return childList;
    //         myList.addAll(childList);
    //     }

    //     if (c[u] > myList.size()) return Collections.emptyList();
    //     myList.add(c[u], u);
    //     return myList;
    // }


    static class FastScanner {

        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}
