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

n = int(input())
adj_list = [[] for i in range(n + 1)]
c = [None]
for i in range(1, n + 1):
	p_i, c_i = map(int, input().split())
	c.append(c_i)
	adj_list[p_i].append(i)

sizes = [None for i in range(n + 1)]
values = [None for i in range(n + 1)]
def size(v):
	sizes[v] = 1
	for i in adj_list[v]:
		size(i)
		sizes[v] += sizes[i]

size(adj_list[0][0])
#print(adj_list)
def get_ans(v):
	if len(adj_list[v]) == 0:
		if c[v] != 0:
			return None
		return [[1, v]]
	insert_at = c[v]
	merged_list = []
	current_size = 0
	for child in adj_list[v]:
		ans = get_ans(child)
		if ans == None:
			return None
		merged_list += [[x[0] + current_size, x[1]] for x in ans]
		current_size += sizes[child]
	#print(merged_list)
	if insert_at > len(merged_list) or insert_at < 0:
		return None
	new_list = merged_list[:insert_at]
	new_list.append([insert_at + 1, v])
	new_list += [[x[0] + 1, x[1]] for x in merged_list[insert_at:]]
	#print(new_list)
	return new_list

x = get_ans(adj_list[0][0])
if x == None:
	print("NO")
else:
	print("YES")
	#print(x)
	x.sort(key = lambda i: i[1])
	x = [str(a[0]) for a in x]
	print(" ".join(x))