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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class B_Numbers_On_Trees {
	
	static ArrayList<ArrayList<Integer>> sortedPos;
	static ArrayList<ArrayList<Integer>> children;
	static int[] parents;
	static int[] greaterCount;
	
	public static void main(String[] args) {
		MyScanner sc = new MyScanner();
	    PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	    int n = sc.nextInt();
	    
	    sortedPos = new ArrayList<>();
	    children = new ArrayList<>();
	    parents = new int[n + 1];
	    greaterCount = new int[n + 1];
	    
	    for(int i = 0; i <= n; i++) {
	    	children.add(new ArrayList<Integer>());
	    	sortedPos.add(new ArrayList<Integer>());
	    }
	    
	    for(int node = 1; node <= n; node++) {
	    	int parent = sc.nextInt();
	    	greaterCount[node] = sc.nextInt();
	    	
	    	parents[node] = parent;
	    	children.get(parent).add(node);
	    }
	    
	    int root = 1;
	    while(root <= n && parents[root] != 0)
	    	root++;
	    assert parents[root] == 0;
	    
	    // check fail condition (are there any nodes with c_i > subtree.size()?
	    // run buildVectors alg
	    if(buildVectors(root)) {
	    	out.println("YES");

		    // populate values to our root vector in strictly increasing order
		    int[] ans = new int[n + 1];
		    for(int i = 0; i < sortedPos.get(root).size(); i++) {
		    	int node = sortedPos.get(root).get(i);
		    	ans[node] = i + 1;
		    }
		    
		    // print ans
		    for(int i = 1; i <= n; i++) {
		    	out.print(ans[i] + " ");
		    }
		    out.println();
	    }else {
	    	out.println("NO");
	    }
	  
	    out.close();
	}
	
	// recursively build vectors for each node starting at the root
	public static boolean buildVectors(int curr_node) {
		boolean possible = true;
		for(int i = 0; possible && i < children.get(curr_node).size(); i++) {
			possible = buildVectors(children.get(curr_node).get(i));
		}
		
		if(possible) {
			ArrayList<Integer> vals = new ArrayList<>();
			for(int child : children.get(curr_node)) {
				for(int val : sortedPos.get(child)) {
					vals.add(val);
				}
			}
			
			//c_i must be <= # of elems that we can possibly place before it
			possible = greaterCount[curr_node] <= vals.size();
			
			if(possible) {
				// combine vectors and insert curr_node in the right place
				int vals_ptr = 0;
				int vector_ptr = 0;
				ArrayList<Integer> curr_vector = sortedPos.get(curr_node);
				while(vector_ptr < vals.size() + 1) {
					if(vector_ptr == greaterCount[curr_node]) {
						curr_vector.add(curr_node);
					}else {
						curr_vector.add(vals.get(vals_ptr));
						vals_ptr++;
					}
					
					vector_ptr++;
				}
			}
		}
		
		return possible;
	}

	
	private static class MyScanner {
		BufferedReader br;
	    StringTokenizer st;
	 
	    public MyScanner() {
	       br = new BufferedReader(new InputStreamReader(System.in));
	    }
	 
	    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());
	   }
	 
	   double nextDouble() {
		   return Double.parseDouble(next());
	   }
	 
	   String nextLine(){
		   String str = "";
		   try {
			   str = br.readLine();
		   } catch (IOException e) {
			   e.printStackTrace();
		   }
		   return str;
	   }
	}
}