Write the proof of correctness for an algorithm that finds the maximum element of a unimodal array using modified binary search. Below is the pseudocode of the algorithm:

int findMaximum(int array[], int i, int j) { //i and j= lower and upperbounds of array while (i <= j) { mid = i + (j - i) / 2; // if middle element is the greatest if(array[mid] > array[mid+1] && array[mid] > array[mid-1]) return array[mid]; // moving to right else if (arr[mid] < arr[mid + 1]) i = mid + 1; //moving to left else j = mid - 1; } return array[j]; }