Challenge 4 - Help Pythagoras Junior

Pythagoras Junior is not a great mathematician like his great great great grandfather. When he gets a list of numbers, he finds it hard to match 3 numbers and create a triangle out of them.

You need to help Pythagoras Junior to identify which is the smallest possible triangle given a list of side lengths. We define the smallest triangle as the one with the minimum perimeter.

Input

The first line will contain an integer C, the number of cases for our problem.
Each case consists of a line starting with an integer N, the number of sides, followed by N integers, each indicating the length of a side. All the integers are separated by spaces.

Output

For each case, a line starting with "Case #x: " followed by the perimeter of the smallest triangle or, if it's not possible to form a valid triangle, "IMPOSSIBLE". Every line is followed by a new line character.

Examples

Case 1:

6 13 9 1 13 17 6

Case 2:

7 110 40 10 1 20 60 3

In Case 1, the answer is 27, as the triangle with the smallest perimeter is (13, 13, 1).
In Case 2, the answer is IMPOSSIBLE. You cannot create a valid triangle from any three of the given numbers.

Limits

• 3 ≤ N ≤ 10⁵
• 1 ≤ Lengths ≤ 2³²

Sample Input

2
6 13 9 1 13 17 6
7 110 40 10 1 20 60 3

Sample Output

Case #1: 27
Case #2: IMPOSSIBLE