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
from sys import stdin, stdout

valid = True

def getnumberfromtree(node, dic, slist):
    rst = []
    leftCnt = slist[node]
    global valid

    for next in dic[node]:
        subRst = getnumberfromtree(next, dic, slist)
        if subRst is None:
            return None
        rst.extend(subRst)

    #print(leftCnt)
    #print(rst)
    if leftCnt > len(rst):
        valid = False
        return None

    rst.insert(leftCnt, node)

    return rst

if __name__ == '__main__':
    n = int(stdin.readline())

    dic = [[] for i in range(n)]
    root = 0
    slist = [0]*n
    for i in range(n):
        pc = list(map(int, stdin.readline().split()))
        slist[i] = pc[1]
        if pc[0] == 0:
            root = i
        else:
            dic[pc[0]-1].append(i)

    #print(root)
    #print(dic)
    res = getnumberfromtree(root, dic, slist)
    #print(valid)

    if valid:
        stdout.write('YES' + '\n')
        for i in range(len(res)):
            stdout.write(str(res.index(i) + 1) + ' ')
    else:
        stdout.write('NO')