Write a program (C/ C++) to construct a graph with three types of nodes organized into three layers as follows:

a) Number of nodes in Layer_1 = 10

b) Number of nodes in Layer_2 = 20

c) Number of nodes in Layer_3 = 40

a) Each node in Layer_3 connects to exactly 2 nodes in Layer_2

b) Each node in Layer_2 connects 3 to 5 nodes in Layer_3

c) Each node in Layer_2 connects to exactly 2 nodes in Layer_1

d) Each node in Layer_1 connects 3 to 5 nodes in Layer_2

Note: There is no direct connection between Layer_1 and Layer_3.

Sample Output:

Consider the number of nodes in Layer 1, 2 and 3 are 3, 5, 8 (with same connection constraints).

Layer 1 to Layer 2:

A1 -> B1, B2, B3 A2 -> B1, B2, B3, B4

A3 -> B2, B3, B4, B5

Layer 2 to Layer 1:

B1 -> A1, A2 B2 -> A2, A3 B3 -> A1, A2

B4 -> A1, A3

B5 -> A2, A3

Layer 2 to Layer 3: B1 -> C1, C2, C3, C4, C5

B2 -> C1, C2, C3, C4, C5

B3 -> C3, C4, C5, C6, C7

B4 -> C3, C4, C5, C7, C8

B5 -> C1, C2, C6, C7, C8

Layer 3 to Layer 1:

C1 ->B1, B3