Problem F
The N Days of Christmas
Consider the first three verses of the classic Christmas carol, The Twelve Days of Christmas:
On the first day of Christmas my true love gave to me
A partridge in a pear tree.On the second day of Christmas my true love gave to me
Two turtle doves,
And a partridge in a pear tree.On the third day of Christmas my true love gave to me
Three French hens,
Two turtle doves,
And a partridge in a pear tree.
The carol continues this pattern for a total of $12$ days. On the $d^\textrm {th}$ day, you receive $d$ copies of a new kind of gift, along with $(d-1)$ copies of the gift introduced on the previous day, $(d-2)$ copies of the gift introduced the day before that, and so on. This raises some interesting questions:
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How many gifts do you receive on the $12^{\textrm{th}}$ day?
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What is the total number of gifts you have received by the end of the $12^{\textrm{th}}$ day?
But why should the Christmas season be limited to $12$ days? If your goal is to get as many gifts as possible (clearly a noble aspiration), then it is advantageous to generalize $12$ to an integer $N,$ where $N$ can be as large as the number of days in a year $(366$ for a leap year).
Given $N$, what are the answers to the generalized versions of the two questions above?
Input
The input consists of a single integer, $N$, the number of days of Christmas $(1 \leq N \leq 366).$
Output
Output two lines, the first of which contains the number of gifts you receive on the $N^{\textrm{th}}$ day, and the second of which contains the total number of gifts you have received by the end of the $N^{\textrm{th}}$ day.
| Sample Input 1 | Sample Output 1 |
|---|---|
2 |
3 4 |
| Sample Input 2 | Sample Output 2 |
|---|---|
12 |
78 364 |
