Pyramids

Time limit1sMemory limit128 MB

Summary

For each positive base size n until a terminating 0, print the total number of blocks in a pyramid whose layers count down from n to 1.

Level: Easy1 of 10
Topics: Math, Implementation, Brute force, Array
Solved: No attempts yet

Problem

A pyramid of blocks is built by first laying a base layer of $n$ blocks, then placing $n-1$ blocks on the layer above it. Each successive layer uses one fewer block than the layer below, and this continues until the top layer holds a single block.

Given the size of the base layer, determine the total number of blocks needed to complete the pyramid. For example, a pyramid whose base has size $4$ needs $10$ blocks in total.

Input

The input is a sequence of integers, one per line. The end of the input is marked by the integer $0$ , which is not the base of any pyramid. Every integer except the final $0$ is positive.

Output

For each positive integer, print the total number of blocks needed to build the pyramid whose base has that size, one result per line.

Examples1

Example 1
Input
```
4
6
0
```
Expected output
```
10
21
```