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
#!/usr/bin/python3
# -*- coding: utf-8 -*-
"""
 @file Codeforces/612/div1_b.py
 @author SHawnHardy
 @date 2020-01-08
 @copyright MIT License
"""

n = int(input())
graph = [[] for _ in range(n + 1)]
ci = [0]


def solve(x):
    rst = []
    if graph[x]:
        for s in graph[x]:
            rst.extend(solve(s))

    if len(rst) < ci[x]:
        raise ValueError

    rst.insert(ci[x], x)
    return rst


for i in range(1, n + 1):
    p, c = map(int, input().split())
    graph[p].append(i)
    ci.append(c)

try:
    ans = solve(graph[0][0])
except ValueError:
    print("NO")
else:
    print("YES")
    for i in range(1, n + 1):
        print(ans.index(i) + 1, end=' ')
