Drawing

This semester too many students signed up for Drawing, and the professor in charge can no longer handle them. So each student completes a drawing assignment, scans it, and submits it. Large pictures take too long to grade, so color information is recognized using only brightness, approximated as a natural number between 0 and 255.

The first class was simply about filling a sketchbook by drawing lines, and every student whose brightness exceeded 200 passed.

The second class practices brightness gradation. The assignment is to divide the sketchbook into $n$ cells and draw lines so that the brightness forms an arithmetic progression. Because the scan approximates it, the passing condition is that for some real number $a$ and positive real number $b$, the brightness of the $k$-th cell satisfies $\lfloor a+bk\rfloor$. Here $\lfloor\bullet\rfloor$ means rounding down. You must write the grading program.

That is, given the brightness of $n$ cells, write a program that decides whether there exist a real number $a$ and a positive real number $b$ such that for every natural number $k$ between $1$ and $n$, the brightness of the $k$-th cell satisfies $\lfloor a+bk\rfloor$.

The first line gives the number of cells $n$. $n$ satisfies $3\leq n\leq 100$.

The second line gives the $n$ brightness values $\beta_1,\cdots,\beta_n$, separated by spaces. Each brightness satisfies $0\leq\beta_i\leq 255$.

If the condition holds, print "pass"; otherwise print "fail", without the quotation marks.