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 sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__

from collections import deque

n = int(input())
c = [0]*n
p = [0]*n
cnt = [0]*n
for i in range(n):
    pi ,ci  = map(int, input().split())
    if pi:
        cnt[pi-1] += 1
    p[i] = pi-1
    c[i] = ci

que = deque()

for i in range(n):
    if cnt[i] == 0:
        que.append(i)

done = [0]*n
ans = None
rem = [[] for i in range(n)]
while que:
    i = que.pop()
    if done[i] or cnt[i]:
        continue
    done[i] = 1
    if len(rem[i]) < c[i]:
        print("NO")
        exit()
    new = rem[i][:c[i]] + [i] + rem[i][c[i]:]
    if p[i] != -1:
        rem[p[i]].extend(new)
        que.appendleft(p[i])
        cnt[p[i]] -= 1
    else:
        ans = new
ret = [0]*n
for i in range(n):
    ret[ans[i]] = i+1
print("YES")
print(*ret)
