You are provided a weighted tree that consists of \(n\) nodes. For each edge of the tree, print the number of diameters that is a part of an edge. Note:

• Diameter is the longest path in the tree.
• The edges are numbered in the same order as they are mentioned in the sample input.

Input format

The first line of the input consists of an integer \(n\) that is followed by \(n-1\) lines. Each line consists of three space-separated integers, \(a\), \(b\), and \(c\). These space-separated integers denote an edge between nodes \(a\) and \(b\) that weighs \(c\).

Output format

For each edge of the tree (in the order they are mentioned in the sample input), print the total number of diameters that is a part of an edge.

Constraints

\(1\leq n\leq 10^5\)

\(1\leq a,b\leq n\)

\(a\neq b\)

\(0\leq c\leq 10^9\)