Please,I need CORRECT answer!!!Problem $3(15\%)$ Consider a data structure that stores a binary number. The initial value of the binary

number is $0.$ Two operations can be performed arbitrarily. The first operation increases the number by

$1,$ and the second operation resets the number to $0.$ The cost of increasing the number is the number of

bits changed. The cost of resetting the number is the number itself. For example, increasing the number

from $111$ to $1000$ has a cost of $4,$ and decreasing the number from $1001$ to $0000$ has a cost of $9.$ Prove a

Theta$(1)$ amortized cost for these two operations.