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


n = int(input())
sons = [[]for i in range(n+1)]
fa = [0]*(1+n)
cs = [0]*(1+n)
for i in range(n):
   p,c = map(int,raw_input().split(" "))
   sons[p].append(i+1)
   cs[i+1]= c
   fa[i+1] = p
   if p ==0:
    root = i+1


vals = range(1,n+1)
q = [root]
s = []
ans = [0]*(1+n)
cnt = 0
l1 = n
flag = True
seq = [root]

while q:
    node = q.pop()
    for son in sons[node]:
        q.append(son)
        seq.append(son)

subtree = [1]*(1+n)
for node in seq[::-1]:
    for son in sons[node]:
        subtree[node] += subtree[son]
for i in range(n+1):
    subtree[i] -= 1
q = [root]
while q:
    node = q.pop()
    pos = cs[node]
    # print node,pos,subtree[node]
    if pos > subtree[node]:
        flag = False
        break
    if pos < l1:
        ans[node] = vals.pop(pos)
    else:
        flag = False
        break
    l1 -= 1
    for son in sons[node]:
        q.append(son)

if flag:
    print "YES"
    print " ".join(map(str,ans[1:]))
else:
    print "NO"


