Problem Statement

You are given two arrays:

• departing which represents the cost of departing flights at each time index.
• returning which represents the cost of returning flights at each time index.

The index represents the time of departure or return. The goal is to find the minimum round-trip cost, where a returning flight can only be taken at a time later than the departing flight (i.e., if departing at time i, the return flight must be from time (i+1) onwards).

Example

Input

departing = [1, 2, 3, 4]
returning = [4, 3, 2, 1]

Output

2

Explanation

• If we depart at time 0 (cost 1), we must return at time ≥ 1. The available return costs are [3, 2, 1], and the best option is at time 3 with cost 1.
• Round-trip cost = 1 (depart) + 1 (return) = 2.
• This is the minimum possible cost.

Constraints

• Solve the problem in O(n) time complexity.

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