CF1286B.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 $a_j \lt a_i$.

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!

埃夫拉姆皮收到了一棵有根树作为礼物。树的顶点编号从 $1$ 到 $n$。每个顶点上还写有一个整数 $a_i$。对于每个顶点 $i$，埃夫拉姆皮计算了 $c_i$ —— 即顶点 $i$ 的子树中满足 $a_j \lt a_i$ 的顶点 $j$ 的个数。

第二个样例的示意图，其中第一个整数为 $a_i$，括号内的整数为 $c_i$

新年过后，埃夫拉姆皮完全记不起自己的礼物是什么了！他只记得这棵树以及所有 $c_i$ 的值，却彻底忘记了各个顶点上写的整数 $a_i$ 是什么。

请帮助他恢复原始的整数序列！

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 $a_j \lt a_i$.

It is guaranteed that the values of $p_i$ describe a rooted tree with $n$ vertices.

第一行包含一个整数 $n$（$1 \leq n \leq 2000$）——树中顶点的数量。

接下来的 $n$ 行描述各个顶点：第 $i$ 行包含两个整数 $p_i$ 和 $c_i$（$0 \leq p_i \leq n$；$0 \leq c_i \leq n-1$），其中 $p_i$ 表示顶点 $i$ 的父节点，若顶点 $i$ 为根节点，则 $p_i = 0$；$c_i$ 表示顶点 $i$ 的子树中满足 $a_j \lt a_i$ 的顶点 $j$ 的数量。

保证 $p_i$ 的取值构成一棵含 $n$ 个顶点的有根树。

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".

如果存在解，在第一行输出 "YES"，在第二行输出 $n$ 个整数 $a_i$（$1 \leq a_i \leq {10}^{9}$）。若存在多个解，输出任意一个即可。可以证明：若存在解，则必存在一个所有 $a_i$ 均在 $1$ 到 $10^9$ 范围内的解。

若不存在解，输出 "NO"。