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
# x = int(input())
# m, n = map(int, input().split())
# nums = list(map(int, input().split()))
N=2010
idx=0;n=0;root=0;p=0;head=[-1]*N
sz=[0]*N;vis=[0]*N;c=[0]*N;num=[0]*N
class node(object):
    def __init__(self):
        self.to=0
        self.next=0
edge=[node() for i in range(1,N+1)]
def add(u,v):
    global idx,head,edge
    edge[idx].to=v
    edge[idx].next=head[u]
    head[u]=idx
    idx+=1
def dfs_in(x):
    global sz,head,edge
    sz[x]=1
    i=head[x]
    while i!=-1:
        y=edge[i].to
        dfs_in(y)
        sz[x]+=sz[y]
        i=edge[i].next

def dfs(x):
    global head,vis,num,c,edge,n
    cnt=0
    for i in range(1,n+1):
        if vis[i]==0:
            cnt+=1
        if c[x]+1==cnt:
            num[x]=i
            vis[i]=1
            break;
    i=head[x]
    while i!=-1:
        y=edge[i].to
        dfs(y)
        i=edge[i].next

n=int(input())
for i in range(1,n+1):
    p,c[i]=map(int,input().split())
    if p==0:
        root=i
    else:
        add(p,i)
dfs_in(root)
for i in range(1,n+1):
    if c[i]+1>sz[i]:
        print('NO')
        exit(0)
dfs(root)
print('YES')
for i in range(1,n+1):
    print(num[i],end=' ')
  						 	   	    	 	 			