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 ai written on it. For each vertex i, Evlampiy calculated ci — the number of vertices j in the subtree of vertex i, such that aj<ai.

Illustration for the second example, the first integer is ai and the integer in parentheses is ci

After the new year, Evlampiy could not remember what his gift was! He remembers the tree and the values of ci, but he completely forgot which integers ai were written on the vertices.

Help him to restore initial integers!

The first line contains an integer n (1≤n≤2000) — the number of vertices in the tree.

The next n lines contain descriptions of vertices: the i-th line contains two integers pi and ci (0≤pi≤n; 0≤ci≤n−1), where pi is the parent of vertex i or 0 if vertex i is root, and ci is the number of vertices j in the subtree of vertex i, such that aj<ai.

It is guaranteed that the values of pi 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 ai (1≤ai≤109). 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 ai are between 1 and 109.

If there are no solutions, print "NO".

3
2 0
0 2
2 0

YES
1 2 1

5
0 1
1 3
2 1
3 0
2 0

YES
2 3 2 1 2