library Arrays {
    /**
     * @dev Upper bound search function which is kind of binary search algorithm. It searches sorted
     * array to find index of the element value. If element is found then returns its index otherwise
     * it returns index of first element which is greater than searched value. If searched element is
     * bigger than any array element function then returns first index after last element (i.e. all
     * values inside the array are smaller than the target). Complexity O(log n).
     * @param array The array sorted in ascending order.
     * @param element The element's value to be found.
     * @return The calculated index value. Returns 0 for empty array.
     */
    function findUpperBound(uint256[] storage array, uint256 element) internal view returns (uint256) {
        if (array.length == 0) {
            return 0;
        }

        uint256 low = 0;
        uint256 high = array.length;

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds down (it does integer division with truncation).
            if (array[mid] > element) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }

        // At this point `low` is the exclusive upper bound. We will return the inclusive upper bound.
        if (low > 0 && array[low - 1] == element) {
            return low - 1;
        } else {
            return low;
        }
    }
}
/**
 * @title Arrays
 * @dev Utility library of inline array functions
 */
function findUpperBound(uint256[] storage array, uint256 element) internal view returns (uint256) {
    if (array.length == 0) {
        return 0;
    }

    uint256 low = 0;
    uint256 high = array.length;

    while (low < high) {
        uint256 mid = Math.average(low, high);

        // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
        // because Math.average rounds down (it does integer division with truncation).
        if (array[mid] > element) {
            high = mid;
        } else {
            low = mid + 1;
        }
    }

    // At this point `low` is the exclusive upper bound. We will return the inclusive upper bound.
    if (low > 0 && array[low - 1] == element) {
        return low - 1;
    } else {
        return low;
    }
}

/**
 * @dev Upper bound search function which is kind of binary search algorithm. It searches sorted
 * array to find index of the element value. If element is found then returns its index otherwise
 * it returns index of first element which is greater than searched value. If searched element is
 * bigger than any array element function then returns first index after last element (i.e. all
 * values inside the array are smaller than the target). Complexity O(log n).
 * @param array The array sorted in ascending order.
 * @param element The element's value to be found.
 * @return The calculated index value. Returns 0 for empty array.
 */