1286_B. Numbers on Tree
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
```python
import sys
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
import collections
from collections import defaultdict
n=int(input())
c,root=[],0
graph=defaultdict(list)
for i in range(n):
    a,b=map(int,input().split())
    if a!=0:
        graph[i+1].append(a)
        graph[a].append(i+1)
    else:
        root=i+1
    c.append(b)
ans=[0]*(n+1)
store=[[] for _ in range(n+1)]
OBSERVE = 0
CHECK = 1
stack = [(OBSERVE, root, 0)]
if n==1 and c[0]==0:
    sys.stdout.write('YES'+'\n')
    sys.stdout.write('1'+'\n')
else:
    while len(stack):
        state, vertex, parent = stack.pop()
        if state == OBSERVE:
            stack.append((CHECK, vertex, parent))
            for child in graph[vertex]:
                if child != parent:
                    stack.append((OBSERVE, child, vertex))
        else:
            i=0
            while i<(len(graph[vertex])):
                if graph[vertex][i] != parent:
                    if len(graph[graph[vertex][i]])==1 and graph[vertex][i]!=root:
                        store[graph[vertex][i]].append([i+1,graph[vertex][i]])
                    store[vertex]+=store[graph[vertex][i]]
                i+=1
            store[vertex].sort()
            ok=True
            if c[vertex-1]>len(store[vertex]):
                ok=False
                break
            else:
                if len(store[vertex])>0:
                    if c[vertex-1]!=0:
                        store[vertex].insert(c[vertex-1],[store[vertex][c[vertex-1]-1][0]+1,vertex])
                    else:
                       store[vertex].insert(c[vertex-1],[store[vertex][c[vertex-1]][0],vertex])
                for ijk in range(len(store[vertex])):
                    store[vertex][ijk][0]=ijk+1
    if ok==True:
        for ij in store[root]:
            ans[ij[1]]=ij[0]
        sys.stdout.write('YES'+'\n')
        ans=' '.join(map(str,ans[1:]))
        sys.stdout.write(ans+'\n')
    else:
        sys.stdout.write('NO'+'\n')

```