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
#Tuan_Kkura
import sys
sys.setrecursionlimit(10 ** 6)
push = lambda: map(int, input().split())
from collections import defaultdict as Def

DSK = Def(list)

ok = True
n = int(input())
vi = [False]*(n+1); c = [0]*(n+1); NumChild = [0]*(n+1); res = [0]*(n+1)

def DFS(u, pre) :
    global ok
    NumChild[u] = 1
    cnt = 0
    for i in range (1, n+1):
        cnt = cnt + (not vi[i])
        if cnt-1 == c[u]:
            res[u] = i
            vi[i] = True
            break
    for v in DSK[u]:
        if v != pre: 
            DFS(v, u)
            NumChild[u] += NumChild[v]
    if NumChild[u]-1 < c[u]:
        ok = False

for i in range(1, n+1) :
    p, c[i] = push()
    if p != 0 : DSK[p].append(i)
    else : root = i 

DFS(root, 0)
if not ok: print("NO")
else:
    print("YES")
    print(*res[1:])