$1.$ 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!

$2.$ Submit your C program on Canvas by $5$:$00$ pm on September $10.$ Comments at the beginning of the source file should

include: your name, your ID number, and the command used to compile your code on Omega $(5$ point penalty for noncompliance$).$