Minimize coins with overpay and change

You have an unlimited number of coins with denominations: - `1, 5, 10, 50, 100, 200` You need to pay exactly `n` units to another person. You are allowed to **overpay**, and the other person will always be able to give you **exact change** (they also have unlimited coins). Define the **total coins used** as: - the number of coins you give to pay, **plus** - the number of coins you receive back as change. Return the **minimum possible total number of coins** needed to complete the transaction. ### Input - A single integer `n`. ### Output - A single integer: the minimum total number of coins exchanged. ### Example **Input:** ``` 41 ``` **Output:** ``` 3 ``` **Explanation:** Pay `50 + 1` (2 coins) and receive `10` as change (1 coin), total `2 + 1 = 3`. ### Constraints - Assume `0 ≤ n ≤ 10^9`. - Both payer and receiver have unlimited coins of each denomination.