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/env python3

import sys

sys.setrecursionlimit(2500)

from collections import defaultdict

children = defaultdict(set)
num_bigger = dict()
ans = dict()

n = int(input())

root = None

for me in range(1, n+1):
    parent, b = input().split(' ')
    parent, b = int(parent), int(b)
    num_bigger[me] = b
    if parent == 0:
        root = me
    else:
        children[parent].add(me)

assert(root)

def sorted_of(elem):
    ret = []
    for child in children[elem]:
        ret += sorted_of(child)
    if num_bigger[elem] <= len(ret):
        ret.insert(num_bigger[elem], elem)
    else:
        print("NO")
        sys.exit()
    return ret

try:
    s = sorted_of(root)
except Exception as e:
    print("exception", str(e))
    sys.exit()
    
for i in range(n):
    ans[s[i]] = i+1

print("YES")
print(' '.join(str(ans[i]) for i in range(1, n+1)))
