human
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. 

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
assistant
#Here is Python program to print "YES", and in the second line output n integers a_i (1 ≤ a_i ≤ {10}^{9}).

from sys import stdin
from collections import *
from copy import copy
from bisect import *

class graph:
    # initialize graph
    def __init__(self, gdict=None):
        self.gdict = defaultdict(list)

    # add edge
    def addEdge(self, node1, node2, w=None):
        self.gdict[node1].append(node2)
        self.gdict[node2].append(node1)

    def subtree(self, v):
        queue, visit, ans, order = deque([v]), [0] * (n + 1), [], [[] for _ in range(n + 1)]
        visit[v], self.nodes = 1, [0] * (n + 1)

        while queue:
            s = queue.popleft()

            for i in self.gdict[s]:
                if not visit[i]:
                    queue.append(i)
                    visit[i] = 1
                    ans.append([i, s])

        for i, j in ans[::-1]:
            self.nodes[j] += self.nodes[i] + 1

        while ans:
            cur, par = ans.pop()
            visit[cur] = 0
            if c[cur] > self.nodes[cur]:
                print('NO')
                exit()

            for i in self.gdict[cur]:
                if not visit[i]:
                    order[cur].extend(order[i])

            order[cur].sort()
            order[cur].insert(c[cur], [c[cur] + 1, cur])

            for i in range(c[cur] + 1, len(order[cur])):
                order[cur][i][0] = i + 1

        order[self.gdict[0][0]].sort(key=lambda x: x[1])
        # print(order[self.gdict[0][0]])
        print('YES')
        print(' '.join(map(str, [x for x, y in order[self.gdict[0][0]]])))

rints = lambda: [int(x) for x in stdin.readline().split()]
n = int(input())
g, c = graph(), [0]

for i in range(1, n + 1):
    x, y = rints()
    c.append(y)
    g.addEdge(i, x)

g.subtree(0)