Consider the following grammar and the semantic actions to support the inherited type declaration attributes. Let $X_1, X_2, X_3, X_4, X_5$, and $X_6$ be the placeholders for the nonterminals $\mathrm{D}, \mathrm{T}, \mathrm{L}$ or $\mathrm{L}_1$ in the following table :

Production rule	Semantic action
D → T L	X1.type = X2.type
T → int	T.type = int
T → float	T.type = float
L → L1, id	X3.type = X4.type addType(id.entry, X5.type)
L → id	addType(id.entry, X6.type)

Which one of the following are the appropriate choices for $X_1, X_2, X_3$ and $X_4$ ?

The value of 3⁵¹ mod 5 is_________.

In an RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also known that $$\varphi $$(n) = 2880, where $$\varphi $$() denotes Euler's Totient Function, then the prime factor of n which is greater than 50 is ______.

Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches. Assume that these switches do not have any separate uplink ports. The minimum number of switches needed is _____.