In c$++$plz Problem $3-$ Filename: GameBase

Write a program that plays a math game using different bases. The game is simple: it has two steps:

convert and repeat. Given a number, convert it to base $10$ from the smallest base it could possibly be

read in until it can no longer be converted into a smaller number.

Input from the keyboard a positive integer in the range $[1,1000000000]$ to simulate the game

with. Assume proper input. Output to the screen first the original number in base ten, and then one per

line each reduction. After the number can no longer be reduced, print it$.$ Finally, the program should ask

if the user wants to run the program again $($Check case$).$ Refer to the sample output below.

Sample Run:

Enter integer: $457$

$51$ base $4$

$31$ base $6$

$13$ base $4$

$7$ base $4$

$7$

Run Again $(\frac{Y}{N})$ : Y

Enter integer: $718347628$

$718347628$ base $10$

$310570550$ base $9$

$52621672$ base $8$

$11215802$ base $8$

$5443364$ base $9$

$666299$ base $7$

$666299$

Run Again $(\frac{Y}{N})$ : n