# Problem C

Tai's formula

Can you, just like Tai, reinvent the wheel and calculate the area under a glucose curve? Instead of publishing a paper, you need to implement the algorithm. You need this algorithm in your new app, that logs your glucose values that comes from a continuous glucose monitor. You have also figured out the trick of the device. It’s not actually continuous, it just samples the glucose value frequently, automatically.

## Input

Input contains several lines of numbers separated by spaces. The first line contains the integer $N$, $2 \leq N \leq 10^4$, the number of glucose samples.

The following $N$ lines describe each glucose sample.

Each line contains two numbers $t_ i$, $v_ i$, where $t_ i$ is the time of the sample, and $v_ i$ is the glucose value at time $t_ i$.

The glucose values $v_ i$ are inside the measurement domain: $2.0 \leq v_ i \leq 23.0$ mmol/L.

Each glucose value is given with exactly one decimal digit.

Since you are working with a computer program, the time of each sample is given as an integer, the number of milliseconds since the first of January $1970$.

The samples are always given in increasing order by time, meaning $0 < t_1 < t_2 < \dots < t_ N < 10^{14}$ ms.

Note that a second is a thousand milliseconds.

## Output

The area under the glucose curve in the unit $\text {mmol/L} \cdot \text {s}$

Answers within a relative or absolute error of $10^{-6}$ will be accepted.

## Sample Explanation

In Sample Input $1$ there are three data points, where the area between the t-axis and the curve is formed by two Trapezoids. The first trapezoid have the area of $\frac{2+12}{2}\cdot (2\, 000-1\, 000) = 7\, 000\, \text {mmol/L} \cdot \text {ms}$, making $7\, \text {mmol/L} \cdot \text {s}$. The second has an area of $17\, \text {mmol/L} \cdot \text {s}$, making the total area $24\, \text {mmol/L} \cdot \text {s}$.

Sample Input 1 | Sample Output 1 |
---|---|

3 1000 2.0 2000 12.0 3000 22.0 |
24 |

Sample Input 2 | Sample Output 2 |
---|---|

3 1000 4.0 2000 8.0 3001 7.3 |
13.65765 |