Let DP_i, j be the minimum cost of having i captains and j pilots. Let's number the pilots 1 to N, from youngest to oldest. If we are at a state (i, j), we're considering next pilot with index i + j + 1, and a state (i, j) is valid if i ≤ j (otherwise, we couldn't assign younger pilots to all the captains). From state (i, j), the valid transitions are to states (i, j + 1) and (i + 1, j).

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