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.*;
import java.text.*;

public class D1287 {

	static ArrayList<Integer>[] adjList;
	static int[] c;

	public static ArrayList<Integer> solve(int node) {
		ArrayList<Integer> a = new ArrayList<Integer>();
		for (int x : adjList[node]) {
			ArrayList<Integer> temp = solve(x);
			if (temp == null)
				return null;
			for (int y : temp)
				a.add(y);
		}
		if (c[node] <= a.size()) {
			a.add(c[node], node);
			return a;
		} else
			return null;
	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		c = new int[n];
		adjList = new ArrayList[n];
		for (int i = 0; i < c.length; i++) {
			adjList[i] = new ArrayList<Integer>();
		}
		int root = -1;
		for (int i = 0; i < n; i++) {
			int p = sc.nextInt() - 1;
			c[i] = sc.nextInt();
			if (p == -1)
				root = i;
			else
				adjList[p].add(i);
		}
		ArrayList<Integer> ans = solve(root);
		if (ans == null) {
			pw.println("NO");
			pw.close();
			return;
		}
//		pw.println(ans);
		pw.println("YES");
		int[] p = new int[n];
		for (int i = 0; i < ans.size(); i++) {
			p[ans.get(i)] = i + 1;
		}
		for (int i = 0; i < p.length; i++) {
			pw.print(p[i] + " ");
		}
		pw.println();
		pw.close();
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}
}
