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
# https://codeforces.com/contest/1287/problem/D

def push(g, u, v):
    if u not in g:
        g[u] = []
    g[u].append(v)    
    
def build():
    S     = [root]
    i     = 0
    order = {}
    
    while i < len(S):
        u = S[i]
        if u in g:
            for v in g[u]:
                S.append(v)
        i+=1            
        
    for u in S[::-1]:
        order[u] = []
        flg=False
        
        if u not in g:
            if cnt[u]==0:
                order[u].append(u)
                flg=True
            else:
                return False, root, order
        else:
            cur = 0
            for v in g[u]:
                for x in order[v]:
                    if cur==cnt[u]:
                        flg=True
                        order[u].append(u)
                        cur+=1    
                    order[u].append(x)    
                    cur+=1
                    
        if flg == False:
            if cnt[u] > len(order[u]):
                return False, root, order
            else:
                order[u].append(u)
            
    return True, root, order

n    = int(input()) 
g    = {} 
cnt  = {}

for i in range(1, n+1):
    p, c     = map(int, input().split())
    cnt[i]   = c   
    
    if p==0:
        root = i
    else:
        push(g, p, i)

flg, root, order = build()
if flg==False:
    print('NO')
else:
    ans = [-1] * n
    for val, u in zip(list(range(n)), order[root]):
        ans[u-1] = val + 1
    print('YES')
    print(' '.join([str(x) for x in ans]))
    
#5
#0 1
#1 3
#2 1
#3 0
#2 0

#3
#2 0
#0 2
#2 0