William just finished his AP English reading comprehension test and is worried about his score. The test has $N$ questions and William remembers all of his answers, which he records in a string $S$. Each character in the string represents one of his answers: either A, B, C, or D.

Thankfully, his friend Kevin already took the test and got a perfect score. Eager to know how he did, William asks him for his answers so that he can compare.

However, Kevin has a very foggy memory, and only remembers the answers to some questions on the test. For each question, he writes ? if he forgot the answer or the correct answer otherwise, recording them in a string $T$. He also remembers the total number of questions on the test that have the answer A, B, C, and D, denoting them $N_A$, $N_B$, $N_C$, and $N_D$, respectively.

William recieves this information in a message from Kevin, but he's not sure what to do with it. As he's a chronic overthinker and a pessimist, he wants to determine the lowest mark he could possibly recieve. Can you write a program to help him?

Constraints

For all subtasks:

$N=N_A+N_B+N_C+N_D=|S|=|T|$

$1\le N\le {10}^6$

Subtask 1 [5%]

Kevin remembers the answer to every question.

Subtask 2 [60%]

Kevin remembers the answer to no questions.

Subtask 3 [35%]

No additional constraints.

Input Specification

The first line contains the integer $N$.

The second line contains the string $S$.

The third line contains the string $T$.

The fourth line contains the integers $N_A$, $N_B$, $N_C$, and $N_D$, separated by spaces.

Output Specification

The output contains one integer, the minimum number of questions that William could have gotten right.

Sample Input 1

9
DBCADDACB
D?C???BC?
1 1 2 5

Sample Output 1

4

Explanation for Sample 1

It can be proven that William will always get a minimum of 4 questions right.

The following is a possible answer key that would fulfill Kevin's data and lead to 4 correct answers:

Scantron:             DBCADDACB
Known Answer Key:     D?C???BC?
Possible Answer Key:  DDCDDABCD
Correct:              YNYNYNNYN

Sample Input 2

12
BBCCCBAABAAA
BBCCABCBBABA
3 6 3 0

Sample Output 2

8

Explanation for Sample 2

This case satisfies the conditions of Subtask 1.

William got questions 1, 2, 3, 4, 6, 9, 10, and 12 right, so he got a total of 8 questions right.