P1202 [USACO1.1] Friday the Thirteenth

Is Friday the 13th really an unusual event? That is, does the 13th of the month land on a Friday less often than on any other day of the week? To answer this question, write a program that will compute the frequency that the 13th of each month lands on Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday, and Friday over a given period of $N$ years. The time period to test will be from January 1, 1900 to December 31, $1900+N-1$ for a given number of years, $N$. $N$ is positive and will not exceed $400$. **Note that the start year is nineteen hundred, not nineteen ninety.** There are a few facts you need to know before you can solve this problem: - January 1, 1900 was on a Monday. - Thirty days has September, April, June, and November, all the rest have $31$ except for February which has $28$ except in leap years when it has $29$. - Every year evenly divisible by $4$ is a leap year. - The rule above does not hold for century years. Century years divisible by $400$ are leap years, all others are not. Thus, the century years $1700$, $1800$, $1900$ and $2100$ are not leap years, but $2000$ is a leap year. Do not use any built-in date functions in your computer language. Do not just precompute the answers.

One line with the integer $N$.

Seven space separated integers on one line. These integers represent the number of times the $13$th falls on Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday, and Friday.

USACO Training Section $1.1$.