// idea: keep the array sorted
// whenever we execute the subtraction, place the result in the correct position

/**
 * Inserts the value in a sorted array to keep it sorted.
 * The sort direction is assumed to be ascending.
 * @param arr The sorted array
 * @param value The value to insert
 */
const sortInsert = (arr: number[], value: number): void => {
  let i = 0;
  while (i < arr.length && arr[i] < value) {
    i++;
  }

  arr.splice(i, 0, value);
}

/**
 * Does a single operation on the given array.
 * Keeps the array sorted.
 * @returns True if the array is all the same, false otherwise.
 */
const operate = (arr: number[]): boolean => {
  // last element is the largest
  // find the first element that is not the largest
  let i = arr.length - 1;
  while (i >= 0 && arr[i] === arr[arr.length - 1]) {
    i--;
  }

  if (i < 0) {
    // all elements are the same
    return true;
  }

  // subtract
  const value = arr[arr.length - 1] - arr[i];

  // remove the last element
  arr.pop();

  // insert the value in the correct position
  sortInsert(arr, value);

  return false;
}

export function solution(numbers: number[]): number {
  numbers.sort((a, b) => a - b);
  let done = false;
  while (!done) {
    done = operate(numbers);
  }

  // sum the numbers
  return numbers.reduce((acc, num) => acc + num, 0);
}