B"Logical quantifiers are very useful tools for expressing claims about a set. For this problem, let's focus on the set of real numbers specifically. The set of real numbers includes zero and negatives. There are two kinds of quantifiers: universal ( forall ) and existential ( exists ). You can read more about them here. The universal quantifier is used to make a claim that a statement holds for all real numbers. For example: The existential quantifier is used to make a claim that there exists some real number for which the statement holds. For example: Moreover, these quantifiers can be nested. For example: Note that the order of variables and quantifiers is important for the meaning and veracity of a statement. There are n variables x_1,x_2, ldots,x_n , and you are given some formula of the form f(x_1, ... ,x_n):=(x_{j_1}<x_{k_1}) land (x_{j_2}<x_{k_2}) land cdots land (x_{j_m}<x_{k_m}), where land denotes logical AND. That is, f(x_1, ldots, x_n) is true if every inequality x_{j_i}<x_{k_i} holds. Otherwise, if at least one inequality does not hold, then f(x_1, ldots,x_n) is false. Your task is to assign quantifiers Q_1, ldots,Q_n to either universal ( forall ) or existential ( exists ) so that the statement Q_1 x_1, Q_2 x_2, ldots, Q_n x_n, f(x_1, ldots, x_n) is true, and the number of universal quantifiers is maximized, or determine that the statement is false for every possible assignment of quantifiers. Note that the order the variables appear in the statement is fixed. For example, if f(x_1,x_2):=(x_1<x_2) then you are not allowed to make x_2 appear first and use the statement forall x_2, exists x_1, x_1<x_2 . If you assign Q_1= exists and Q_2= forall , it will only be interpreted as exists x_1, forall x_2,x_1<x_2 . The first line contains two integers n and m ( 2 <= n <= 2 cdot 10^5 ; 1 <= m <= 2 cdot 10^5$$"...