# Practice on Toph

Participate in exhilarating programming contests, solve unique algorithm and data structure challenges and be a part of an awesome community.

## Sofdor Ali and Histogram

The Great Sofdor Ali is now interested in competitive programming. Seeing this, his friend and also a renowned scientist Anik Lumba gave him a problem. The problem statement is simple. You have a non-decreasing histogram. You have to find the area of largest rectangle contained within the histogram. For example, in the histogram below, where the **6** bars have heights **1 2 2 4 5 7**, the area colored in red is the largest rectangle contained by the histogram. The area of this rectangle is **12**.

But unfortunately for our great scientist Sofdor Ali, he could not write the solution for this problem. So he asked you to solve the problem.

### Input

First line contains an integer **T (0 < T ≤ 10)** representing number of test case. Each case starts with an integer **N (0 < N ≤ 10 ^{5})**. Next there are

**N**integers in non-decreasing order representing the heights of columns in the histogram. Height of any column is positive and less than or equal to

**10**.

^{8}For **20** percent of the cases, we have **0 < N ≤ 100** and **0 < height ≤ 100**.

For **50** percent of the cases, we have **0 < N ≤ 1000** and **0 < height ≤ 10000**.

### Output

For each case print the case number and the maximum area of rectangle contained by the histogram.

### Samples

Input | Output |
---|---|

2 5 1 2 3 4 5 8 4 7 22 26 48 78 87 95 | Case 1: 9 Case 2: 234 |

Login to submit