B. Numbers on Treetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputEvlampiy 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_iAfter 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!InputThe 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.OutputIf 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".ExamplesInput
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

3
2 0
0 2
2 0

YES 1 2 1 
['constructive algorithms', 'data structures', 'dfs and similar', 'graphs', 'greedy', 'trees', '*1800']