A13260 | 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 $a_j < a_i$ .

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!

The first line contains an integer $n$ $(1 \leq n \leq 2000)$ — 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 $c_i$ ( $0 \leq p_i \leq n$ ; $0 \leq c_i \leq n-1$ ), 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.

If a solution exists, in the first line print "YES", and in the second line output $n$ integers $a_i$ $(1 \leq a_i \leq {10}^{9})$ . 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".