Missing Number

The list holds n distinct numbers taken from 0, 1, …, n, so exactly one number in that range is missing. Find it. (Hint: compare the expected total with the actual total.)

Implement missing_number(numbers).

Input

numbers: n distinct numbers from 0 to n.

Output

Return the missing number.

Constraints

0 ≤ n ≤ 100,000

Examples

Input:
numbers = [3, 0, 1]

Expected output:
expected = 2

Input:
std::vector<long long> numbers = {3, 0, 1};

Expected output:
long long expected = 2;

Input:
long[] numbers = new long[] {3, 0, 1};

Expected output:
long expected = 2;

Input:
numbers = [0]

Expected output:
expected = 1

Input:
std::vector<long long> numbers = {0};

Expected output:
long long expected = 1;

Input:
long[] numbers = new long[] {0};

Expected output:
long expected = 1;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• GWU CS1111 Introduction to Software Development - lab sequence