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 < 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".