Write a C program to maintain n counters indexed by 0 .. n-1. n will be the first input value and all counters are initially valued as zero. The following operations will then appear, one per line, in the input: a. 0 - terminate execution.

b. 1 - print the counters in ascending index value order as (index, count) pairs. (O(n) time)

c. 2 - print the counters in ascending counter value order as (index, count) pairs. (O(n) time)

d. 3 i - add one to the counter indexed by i. (O(log n) time)

e. 4 i - subtract one from the counter indexed by i. (O(log n) time)

f. 5 i j - determine the number of counters whose values are no smaller than i and no larger than j. (O(log n) time)

The input will be read from standard input (stdin) as either keyboard typing or as a shell redirect (<) from a file.

Prompts/menus are completely unnecessary!

Your program should dynamically allocate three tables - map, index, and count. (If you wish, the last two tables may be implemented as an array of structs.) index[i] indicates which of the n counters has its value presently stored as count[i]. map[i] is used to find the counter with index i, i.e. it is always true that index[map[i]]==i. Operation 2 may be coded as: for (i=0;i