B'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 . 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 <= q n <= q 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 <= q p_i <= q n ; 0 <= q c_i <= q 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 <= q a_i <= q {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". '...