Warning: This question strictly requires the use of C/C++ language for answering, and Python is prohibited from use. The numbers and output results that appear during the calculation process of this question may not be represented by long long int or unsigned long int because they can be too large, but it can be guaranteed that all results can be represented as an integer of no more than $2000$ decimal bits.

Background

Mr. Sha from ShanghaiTech University felt that his life was too boring, so he established a paradise in an unknown place in the universe and built a track connecting the university and the paradise. On the track, there was a commuter train from the university to the paradise. After multiple track repairs, trains departed from the university one after another, carrying classmates who thought similarly to Mr. Sha, heading towards the paradise filled with eternal hope and happiness.

The $1$st train departs in the $0$th minute. $2$ minutes later, the $2$nd train departed. Another $5$ minutes passed, and the $3$rd train departed. After another $7$ minutes, the $4$th train departed. Starting from the $4$th train, the interval between the $n$-th train and the $(n-1)$-th train is the same as the interval between the $(n-1)$-th train and the $(n-3)$-th train. Mr. Sha wants to know the departure time of the $k$-th train to ensure that he can arrive at the station on time for boarding.

Description

Input a positive integer $k$, output the interval between the $k$-th train and the $1$st train.

Format

Input

A positive integer $k$.

Output

Another positive integer $t$, satisfying that the interval between the $k$-th train and the $1$st train is $t$ minutes.

Samples

5

26

The $5$th train departs at the $26$th minutes after the $1$st train departs, because $0+2+5+7+12=26$.

Limitation

1s, 1024KiB for each test case.