Hacks are disabled on this problem. We are excited to introduce a new language for this Codeforces round: the Deranged Calculator language (DC). The DC language is a simplified programming language with some weird constraints. It only supports a single expression on one line and only has a single positive integer (n) as input. The syntax of the expression is similar to that of most programming languages (in fact, the expression is valid Python), but it is very limited: Expressions consist of the input parameter (n), parenthesized expressions, and calls to the round function. These are joined together by the operators + , - , * , and / . Grouping with parentheses () can be used to change the order of operations, as usual. The operators * and / have equal precedence and take precedence over + and - , which also have equal precedence. Operators of equal precedence are evaluated from left to right. The round function takes a single expression as its argument and rounds its value to the nearest integer, rounding up when the fractional part is exactly (0.5). (For example, round(n/(n-n-n-n)) will always evaluate to (0), because (x/(x-x-x-x)=-\frac{1}{2}) for a positive integer (x). The fractional part is (0.5), so it will be rounded up to (0).) Only the input value (n) can be used; no numeric constants are allowed in the program. All operations are performed using exact fractional arithmetic, so division does not round and can produce fractions. A derangement of (n) numbers is a permutation of those numbers in which none of the numbers appears in its original position. For example, the derangements of the sequence (1, 2, 3) are (2, 3, 1) and (3, 1, 2). You are given a single integer (k). Your job is to make a valid DC program that, for every integer (n) ((2 \le n \le k)), calculates the number of derangements of the sequence (1, 2, \ldots, n), when (n) is given as input to the DC prog