HIST2  Histogram
In statistics, a histogram is a graphical display of tabulated frequencies, shown as bars. It shows what proportion of cases fall into each of several categories. It 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.
In the image Figure (a) shows a histogram with heights {1,2,3,4} (1st sample testcase) and has a perimeter of 16 units. Figure (b) shows one of the permutations {3,1,2,4} having the maximum perimeter of 20 units.
Input
Input consists of multiple test cases. 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. There are atmost 50 test cases.
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.
Example
Input: 4 1 2 3 4 3 2 6 5 0 Output: 20 8 24 2
hide comments
debarghya4469:
20210424 14:19:38
dp[20][(1<<20)] gives TLE while dp[19][1<<20] passes. Had hard time debugging. 

vkgainz:
20201108 19:55:46
dubs


scolar_fuad:
20200105 16:03:47
nice bitmask+dp


mac1309:
20190717 20:57:15
solving by bitmasking requires patience and implementation skill. 

sultania23:
20181223 15:33:03
Good One for learning BitMasking..


amulyagaur:
20180615 10:44:24
1000th solver! 

amrit_saini:
20170926 20:42:13
Can be done wthout dp or bitmasking using logic of factorial. 

sucide:
20170613 20:35:46
Ac in one go ,,,


yashrocks22:
20170305 23:27:15
nice problem,just requires simple math dont go for dp+bitmasking, otherwise it would be very complex... Last edit: 20170305 23:27:57 

prasoonbatham:
20170113 12:36:58
Good Problem. Hint: Try to find a pattern in the number of permutations ;) 
Added by:  Swarnaprakash 
Date:  20081129 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 
Resource:  Kurukshetra 09 OPC 