In thePeople’s Republic of Granadia (P. R.O. G.), there are only6,9, and20- cent coins. Usingstrong induction, prove that every amount of Granadian moneyequal to44cents or more can beexclusivelypaid for via procuring or disposing of 6-cent,9-cent and 20-cent coins. No weak induction proofs will be accepted for credit. Hint: If this were weak induction, you would likely try to prove that you can at leastpay 44 cents in the base, make your inductive hypothesis, and then at the step you wouldthink how you might be able to addjust onemore cent by combining the appropriatedenominations. With strong induction, you will have to makebigger"jumps". How canyou ensure that the "jump" doesn’t "jump over" amounts of money that are actually payableby our coin denominations?