Descr iption



n个元素{1,2,..., n }有n!个不同的排列。将这n!个排列按字典序排列，并编号为0，1，…，n!-1。每个排列的编号为其字典序值。例如，当n=3时，6 个不同排列的字典序值如下：





任务：给定n 以及n 个元素{1,2,..., n }的一个排列，计算出这个排列的字典序值，以及按字典序排列的下一个排列。





Input



第1 行是元素个数n(n < 15)。接下来的1 行是n个元素{1,2,..., n }的一个排列。



Output



第一行是字典序值，第2行是按字典序排列的下一个排列。



Sample Input





8

2 6 4 5 8 1 7 3



Sample Output





8227

2 6 4 5 8 3 1 7

-Descr iption n elements (1,2 ,..., n) there are n! Different order. This n! Were arranged according to lexicographic order, and numbered 0,1, ..., n!-1. With the numbering of each sequence value for the dictionary. For example, when n = 3 when six different lexicographic order of value are as follows: Missions: given n and n elements (1,2 ,..., n) an array to calculate the lexicographic order of value , as well as lexicographic order with the next. Input Line 1 is the number of elements n (n <15). The next one line is n elements (1,2 ,..., n) of an array. Output the first line is the lexicographic value, line 2 is arranged according to lexicographic order of the next. Sample Input 82 6 4 5 8 1 7 3Sample Output 82272 6 4 5 8 3 1 7