AT_past20_g ご飯とパン

There are $ N $ bowls of rice and $ M $ slices of bread. The $ i $ -th bowl of rice has a deliciousness of $ R_i $ , and the $ i $ -th slice of bread has a deliciousness of $ P_i $ . For the next $ K $ days, you will choose to eat either rice or bread. You will get tired of it if you eat the same dish in a row, so you will never eat rice two days in a row, or eat bread two days in a row. Determine if this plan is feasible. If it is, find the maximum possible total deliciousness.

The input is given from Standard Input in the following format: > $ N $ $ M $ $ K $ $ R_1 $ $ \ldots $ $ R_N $ $ P_1 $ $ \ldots $ $ P_M $

Print `-1` if the plan is infeasible. Otherwise, print the maximum possible total deliciousness of the dishes that you eat.

### Sample Explanation 1 By eating the third bowl of rice on day $ 1 $ , the second slice of bread on day $ 2 $ , and the second bowl of rice on day $ 3 $ , the total deliciousness will be $ 15 $ . ### Sample Explanation 2 The meal plan for the next $ K $ days is infeasible. ### Constraints - $ 1\leq N,M \leq 1000 $ - $ 1\leq K \leq N+M $ - $ 1\leq R_i, P_i \leq 1000 $ - All input values are integers.