For some starting configurations, it is not always possible to obtain the goal of strictly increasing order.

Input Specification

The input will contain some number of test cases. A test case consists of two lines. The first line will contain a positive integer \(n\) ( \(n < 8\) ), which is the number of coins. We assume that the coins are labeled \(1, 2, 3, \dots, n\) . The second line will contain a list of numbers \(1\) to \(n\) in an arbitrary order, which represents the initial coin configuration. For the above example, the input test case would be:

3
3 2 1

The end of test cases is indicated by \(0\) on a line by itself.

Output Specification

For each test case, output one line, which will either contain the minimal number of moves in which Jo can achieve the goal coin line-up, or, if it is not possible to achieve the goal coin line-up, IMPOSSIBLE .

Sample Input

3
3 2 1
2
2 1
0

Output for Sample Input

20
IMPOSSIBLE