Missing order numbers

Problem

Orders are numbered from 1 to n. A report lists the order numbers that were received, in any order and possibly with repeats.

Print the order numbers from 1 to n that are missing from the report, in increasing order, separated by spaces. If none is missing, print None.

Input: The first line is n. The second line holds the received order numbers separated by spaces (at least one).
Output: The missing numbers in increasing order, separated by spaces, or None.
Constraints: 1 ≤ n ≤ 100000
Every received number is between 1 and n

Example

Input

6
1 2 4 6 2

Output

3 5

Orders 3 and 5 are missing.

Try the problem first. Open one hint at a time.

Hint 1

Put the received numbers in a set so checking one is fast.

Hint 2

Go through 1 to n and keep the numbers that are not in the set.

Write your Python code, run it on the examples and submit it to hidden tests.