def min_cost_to_win(n):
    dp = [[0] * (n + 2) for _ in range(n + 2)]
    for length in range(2, n + 1):
        for i in range(1, n - length + 2):
            j = i + length - 1
            best = 10**9
            for p in range(i, j + 1):
                left = dp[i][p - 1] if p > i else 0
                right = dp[p + 1][j] if p < j else 0
                best = min(best, p + max(left, right))
            dp[i][j] = best
    return dp[1][n]


if __name__ == "__main__":
    print(min_cost_to_win(1))
    print(min_cost_to_win(2))
    print(min_cost_to_win(10))