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
input = sys.stdin.readline

n=int(input())

C=[(0,0)]+[tuple(map(int,input().split())) for i in range(n)]

V=n+1
EDGEIN=[0]*V# その点に入るEDGEの個数
EDGEOUT=[-1]*V# EDGEの行き先

for i in range(1,n+1):
    p,x=C[i]

    if p!=0:
        EDGEIN[p]+=1
        EDGEOUT[i]=p

from collections import deque
QUE = deque()

ANS=[0]*V
USE=[[] for i in range(V)]

for i in range(1,V):
    if EDGEIN[i]==0:
        QUE.append(i)# 行き先のない点をQUEに入れる
        ANS[i]=i
        if C[i][1]!=0:
            print("NO")
            sys.exit()
        USE[i].append(i)



TOP_SORT=[]
while QUE:
    x=QUE.pop()
    TOP_SORT.append(x)# 行き先がない点を答えに入れる

    to=EDGEOUT[x]

    EDGEIN[to]-=1# 行き先がない点を削除し,そこから一歩先の点のEDGEINを一つ減らす.
    if EDGEIN[to]==0:
        QUE.appendleft(to)


for po in TOP_SORT:
    #print(po)
    to=EDGEOUT[po]

    if ANS[po]!=0:
        USE[to].extend(USE[po])
        USE[po]=[]

    else:
        x=C[po][1]
        USE[po].sort()

        if len(USE[po])<x:
            print("NO")
            sys.exit()

        elif len(USE[po])==x:
            #print(po,USE[po])
            ANS[po]=max(ANS)+1
            USE[to].append(ANS[po])
            USE[to].extend(USE[po])
            USE[po]=[]

        else:
            #print(po,x,USE[po])

            if x!=0:
                AP=USE[po][x]

            else:
                AP=1

            for i in range(1,n+1):
                if ANS[i]>=AP:
                    ANS[i]+=1
                    
            for i in range(1,n+1):
                for j in range(len(USE[i])):
                    if USE[i][j]>=AP:
                        USE[i][j]+=1
                    
            ANS[po]=AP

            USE[to].append(ANS[po])
            USE[to].extend(USE[po])
            USE[po]=[]

    #print(ANS)
    #print(USE)
    #print()
      
compression_dict={a: ind for ind, a in enumerate(sorted(set(ANS)))}
ANS=[compression_dict[a] for a in ANS]
    

print("YES")
print(*ANS[1:])
