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.ArrayList;
import java.util.Scanner;

public class numbersonatree {
	static ArrayList<Integer> set ;
	static ArrayList<Integer>[] tree;
	static int n;
	static int [] c, ret;
	static int [] subsize = new int[n];
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		 n = sc.nextInt();
		tree =new ArrayList[n];
		for(int i=0;i<n;i++) {
			tree[i] = new ArrayList<Integer>();
		}
		int root = -1;
		c = new int[n];
		for(int i=0;i<n;i++) {
			int a = sc.nextInt()-1;
			int b = sc.nextInt();
			c[i] = b;
			if(a==-1) {
				root = i;
			}
			else {
				tree[a].add(i);
				tree[i].add(a);
			}
			
		}
		set =new ArrayList<Integer>();
		for(int i=1;i<=n;i++) {
			set.add(i);
		}
		ret = new int[n];
		subsize = new int[n];
		subsize(root,-1);
		
		for(int i=0;i<n;i++) {

			if(c[i]>=subsize[i]) {
				fail = true;
			}
		}
		if(fail) {
			System.out.println("NO");
			return;
		}
		dfs(root,-1);
		StringBuilder sb = new StringBuilder();
		for(int i=0;i<n;i++) {
			sb.append(ret[i] + " ");
		}
		System.out.println("YES");
		System.out.println(sb.toString());
	}
	static boolean fail;
	static void subsize(int curr,int parent) {
		subsize[curr] = 1;
		for(int next : tree[curr]) {
			if(next!=parent) {
				subsize(next,curr);
			}
		}
		for(int next : tree[curr]) {
			if(next!=parent) {
				subsize[curr]+=subsize[next];
			}
		}
	}
	static void dfs(int curr,int parent) {
//		System.out.println(curr + "  " + parent + " " + c[curr]);
		int add = c[curr];
//		if(c[curr]>=set.size()) {
//			System.out.println("NO");
//			fail = true;
//			return;
//		}
		ret[curr] = set.get(add);
		set.remove(add);
		for(int next : tree[curr]) {
			if(next!=parent) {
				dfs(next,curr);
			}
		}
	}
}
