Background:

The government has just constructed a bus$-$bus interchange facility at Tuen Mun Road. Passengers can take a bus route from anywhere to the facility $($i$.$e$.,1$st trip$),$ then interchange another bus route to reach their destination $($i$.$e$.,2$nd trip$).$

To encourage passengers interchanging routes that BNB operates in this facility, the company has set up the following discount scheme for passengers who pay both trips by Octopus card $($an e$-$payment method$)$:

$1.$ If the full fare of the $2$nd trip is more expensive than the $1$st trip, the fare passengers need to pay for the $2$nd trip will be the difference between the full fare of the two trips. Or else, passengers do not need to pay for the $2$nd trip.

$2.$ If the route name taken in the $1$st trip starts with $$P$,$ e$.$g$.,$ P$960,$ the $2$nd trip will be free regardless of the route the passenger takes.

$3.$ The above discount scheme does not apply in the following situations:

$($i$)$ The bus route taken in the $1$st trip is not operated by the Big Northwest Bus Company.

$($ii$)$ The route name taken in the $2$nd trip starts with $$A$,$ e$.$g$.,$ A$33$X$.$

$($iii$)$ The remaining balance in the passenger$$s Octopus card is less than HK$$1$ when paying for the $2$nd trip.

For situation $($i$)$ and $($ii$),$ full fare must be paid for the $2$nd trip.

For situation $($iii$),$ the payment fails and passenger has to pay the $2$nd trip by cash.

Task:

Write a program Question$1.$java that calculates the remaining balance of the passenger$$s Octopus card, after he$/$she uses it to conduct payment for the $2$nd trip on any BNB$$s bus routes.

The program should take in three lines of input with the following format:

The program should output the remaining balance of the passenger$$s Octopus card after paying for the $2$nd trip.

Assumptions:

$1.$ The company code of the Big Northwest Bus Company is $$BNB$.$

$2.$ Length of the route name and the operating company code will not be longer than $4$ characters. All English characters involved are capitalized.

$3.$ The remaining balance and full fares of the bus trips must be an integer.

$4.$ All passengers must take the $1$st bus trip to enter the interchange facility, and all of them pay the $1$st trip successfully by using their Octopus card.

$5.$ There is no other purchase paid by the Octopus card in$-$between the two trips.

$6.$ The three lines of input are always valid.

Sample Test Cases:

Test Case $1$

Input:

$8$

$58$M BNB $9$

$960$ BNB $14$

Output:

The remaining balance is $3.$

Test Case $2$

Input:

$2$

$962$X CTB $23$

$961$ BNB $14$

Output:

The remaining balance is $-12.$

Test Case $3$

Input:

$-3$

$59$M BNB $19$

$961$ BNB $24$

Output:

The remaining balance is $-3.$