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 io
import os
import sys


from collections import Counter, defaultdict, deque

sys.setrecursionlimit(10 ** 5)


def solve(N, PC):
    children = [[] for i in range(N)]
    cost = [None for i in range(N)]
    root = None
    for i, (p, c) in enumerate(PC):
        cost[i] = c
        p -= 1
        if p != -1:
            children[p].append(i)
        else:
            root = i

    def getOrder(node):
        ret = []
        for child in children[node]:
            ret.extend(getOrder(child))
        i = cost[node]
        if not (0 <= i <= len(ret)):
            print("NO")
            exit()
        return ret[:i] + [node] + ret[i:]

    order = getOrder(root)

    nodeToVal = {}
    for v, node in enumerate(order):
        nodeToVal[node] = str(v + 1)

    return "YES\n" + " ".join(nodeToVal[i] for i in range(N))


if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    (N,) = [int(x) for x in input().split()]
    PC = [[int(x) for x in input().split()] for i in range(N)]
    ans = solve(N, PC)
    print(ans)
