Give pseudocode for the following problem: given an array A[1...n] containing the numbers 1, 2, . . . , n and representing a permutation, modify A to represent the next lexicographic permutation. Analyze running time (which should not exceed O(n)) and argue correctness (why the output is lexicographically bigger than the input? why other permutations lexicographically bigger than the input are bigger than the output?).