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A histogram is a polygon composed of a sequence of rectangles aligned at a common base line. In this problem all rectangles have a width of unit length. But their heights are distinct. Some permutation of the heights will give the maximum perimeter. Your task is to find the maximum perimeter of the histogram and the number of permutations that give the maximum perimeter.

Input

Input consists of multiple test cases(T). Each test case describes a histogram and starts with an integer N, 2 <= N <= 15, denoting the number of rectangles it is composed of. Next line consists of N space separated positive integers representing the heights of the rectangles. All heights are distinct and less than or equal to 100. N=0 indicates the end of tests.

1<=T<=1000

Output

For each test case output the maximum possible perimeter of the histogram and the number of permutations that give maximum perimeter in a single line, separated by a single space.

Sample Input


4
1 2 3 4
3
2 6 5
0


Sample Output


20 8
24 2


Languages: C,C++,Java

Time Limit: 5 Second(s)
Score: 100 Point(s)
Input File Limit: 50000 Bytes

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