polski
Task Counting-Out Rhyme (wyl)
Counting-Out Rhyme
Memory limit: 32 MB
Children have gathered in a circle and are playing with a counting-out rhyme.
The children are numbered 
to 
so that (for 
) the child number 
stands to the
left of the child number 
, and the child number 
stands to the left of the child number 
. The child who is counted
out in the rhyme leaves the circle. The counting out is repeated until there is
no one left in the circle. The rules of the play are as follows:
- The first counting is started by the child number
. Each
successive counting is started by the child standing to the left of the child
who was last counted out. - Every time the rhyme consists of
syllables. The child who
starts the counting out says the first syllable of the rhyme; the child standing
to the left of him or her says the second syllable, the next child says the
third one, and so on. The child who says the last syllable of the rhyme is
counted out and leaves the circle.
We observe the children playing counting out and we notice the order in which they leave the circle. Basing on this information we try to guess how many syllables the counting-out rhyme consists of.
Task
Write a program which:
- reads from the standard input the description of the order the children left the circle,
- determines the smallest positive number
, for which the
children playing with a 
-syllable counting-out rhyme would leave the
circle in the given order, or states that such a number 
does not
exist, - writes to the standard output the determined number
or the
word NIE ("no") if such a number 
does not
exist.
Input
In the first line of the standard input there is one positive integer
, 
. In the second line there are
integers separated by single spaces. The 
-th number
tells at which turn of the counting out the child of number 
left
the circle.
Output
Your program should write in the first and only line of the standard output
either one integer: the smallest number 
of syllables that the
counting-out rhyme can consist of, or one word NIE, if such a number
does not exist.
Example
For the input data:
4 1 4 2 3
the correct result is:
5
Task author: Jakub Pawlewicz.