Ildar is the algorithm teacher of William and Harris. Today, Ildar is teaching Cartesian Tree. However, Harris is sick, so Ildar is only teaching William.

A cartesian tree is a rooted tree, that can be constructed from a sequence of distinct integers. We build the cartesian tree as follows:

1. If the sequence is empty, return an empty tree;
2. Let the position of the maximum element be $x$;
3. Remove element on the position $x$ from the sequence and break it into the left part and the right part (which might be empty) (not actually removing it, just taking it away temporarily);
4. Build cartesian tree for each part;
5. Create a new vertex for the element, that was on the position $x$ which will serve as the root of the new tree. Then, for the root of the left part and right part, if exists, will become the children for this vertex;
6. Return the tree we have gotten.

For example, this is the cartesian tree for the sequence $4, 2, 7, 3, 5, 6, 1$:

After teaching what the cartesian tree is, Ildar has assigned homework. He starts with an empty sequence $a$.

In the $i$-th round, he inserts an element with value $i$ somewhere in $a$. Then, he asks a question: what is the sum of the sizes of the subtrees for every node in the cartesian tree for the current sequence $a$?

Node $v$ is in the node $u$ subtree if and only if $v = u$ or $v$ is in the subtree of one of the vertex $u$ children. The size of the subtree of node $u$ is the number of nodes $v$ such that $v$ is in the subtree of $u$.

Ildar will do $n$ rounds in total. The homework is the sequence of answers to the $n$ questions.

The next day, Ildar told Harris that he has to complete the homework as well. Harris obtained the final state of the sequence $a$ from William. However, he has no idea how to find the answers to the $n$ questions. Help Harris!