human
Can you provide a Python code to print "YES", and in the second line output n integers a_i (1 ≤ a_i ≤ {10}^{9}) given the following:
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
#!usr
assistant
#Here is Python code to print "YES", and in the second line output n integers a_i (1 ≤ a_i ≤ {10}^{9}).
/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
from itertools import permutations
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
    res = list(sys.stdin.readline())
    if res[-1] == "\n":
        return res[:-1]
    return res
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

def solve():
    def dfs(x):
        size[x] = 1
        for y in v[x]:
            size[x] += dfs(y)
        return size[x]
    def dfs2(x):
        cx = c[x]
        ans[x] = f[cx]
        f.pop(cx)
        for y in v[x]:
            dfs2(y)
    n = I()
    v = [[] for i in range(n)]
    c = [0]*n
    f = [[0,i] for i in range(n)]
    r = None
    for i in range(n):
        a,b = LI()
        a -= 1
        if a >= 0:
            f[a][0] += 1
            v[a].append(i)
        else:
            r = i
        c[i] = b
    size = [0]*n
    dfs(r)
    f = [i+1 for i in range(n)]
    for i in range(n):
        if c[i] >= size[i]:
            print("NO")
            return
    ans = [0]*n
    dfs2(r)
    print("YES")
    print(*ans)
    return

#Solve
if __name__ == "__main__":
    solve()