OpenKattis
University of Chicago

# Antiarithmetic?

A sequence $a_{1}, a_{2}, a_{3}, \ldots$ is an arithmetic progression if there exists a constant $c$ such that $a_{i} - a_{i+1} = c$ for $i = 1, 2, 3, \ldots$.

A permutation of $n$ is a bijective function of the initial $n$ natural numbers: $0, 1, \ldots n-1$. A permutation $p$ is called antiarithmetic if there is no subsequence of it forming an arithmetic progression of length greater than $2$, i.e., there are no three indices $0 \le i < j < k < n$ such that $(p_{i} , p_{j} , p_{k})$ forms an arithmetic progression.

For example, the sequence $(2, 0, 1, 4, 3)$ is an antiarithmetic permutation of $5$. The sequence $(0, 5, 4, 3, 1, 2)$ is not an antiarithmetic permutation as its first, fifth and sixth term $(0, 1, 2)$ form an arithmetic progression; and so do its second, forth and fifth term $(5, 3, 1)$.

Your task is to check whether a given permutation of $n$ is antiarithmetic.

## Input

There are several test cases (at most $5$), followed by a line containing $0$. Each test case is a line of the input file containing a natural number $3 \le n \le 10\, 000$ followed by a colon and then followed by $n$ distinct numbers separated by whitespace. All $n$ numbers are nonnegative integers smaller than $n$.

## Output

For each test case output one line with yes or no stating whether the permutation is antiarithmetic or not.

Sample Input 1 Sample Output 1
3: 0 2 1
5: 2 0 1 3 4
6: 2 4 3 5 0 1
0

yes
no
yes