1287_D. 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

# inf = open('input.txt', 'r')
# reader = (line.rstrip() for line in inf)
reader = (line.rstrip() for line in sys.stdin)
input = reader.__next__

n = int(input())
cs = [0] * (n + 1)
ps = [0] * (n + 1)
children = [[] for _ in range(n+1)]
for i in range(1, n+1):
    p, c = map(int, input().split())
    ps[i] = p
    children[p].append(i)
    cs[i] = c

def sortDescendants(v):
    result = []
    pos = cs[v]
    for child in children[v]:
        result += sortDescendants(child)
    if len(result) < pos:
        print('NO')
        sys.exit()
    result.insert(pos, v)
    return result

root = children[0][0]
order = sortDescendants(root)
a = [0] * n
for i, v in enumerate(order):
    a[v - 1] = i + 1
print('YES')
print(*a)

# inf.close()

```