Description

In a certain mode of the calculator, pressing a key, for example 1, will produce the middle pitch Do.

Here is the key-to-pitch table.

+ 低音Fa
< 低音So
* 低音La
/ 低音Xi
1 中音Do
2 中音Re
3 中音Mi
4 中音Fa
5 中音So
6 中音La
7 高音Xi
8 高音Do
9 高音Re
= 高音Mi
% 高音Fa
C 高音So
M 高音La

Now Xiao A has obtained a piece of sheet music — we call it calculator notation, a variant of numbered musical notation (jianpu).

Durations (i.e., how long you press) are recorded as follows, for example:

1 is a quarter note, taking $1$ beat.

1- is a half note, taking $2$ beats.

1--- is a whole note, taking $4$ beats.

For notes shorter than a quarter note, we use nested parentheses, for example:

(1(34(56))2)

1 and 2 are inside one layer of parentheses, so they are eighth notes, taking $0.5$ beat.

3 and 4 are inside two layers of parentheses, so they are sixteenth notes, taking $0.25$ beat.

5 and 6 are inside three layers of parentheses, so they are thirty-second notes, taking $\dfrac{1}{8}$ beat.

At most thirty-second notes will appear in the testdata; there are no shorter notes.

The symbol - will not appear inside parentheses.

Adding a dot . after a note means the note is extended by $1/2$ of its original duration.

For example, 1-. is $3$ beats, 1. is $1.5$ beats, and in (3.(45.)), 3 is $\dfrac{3}{4}$ beat, 4 is $\dfrac{1}{4}$ beat, and 5 is $\dfrac{3}{8}$ beat.

There will not be two or more consecutive dots. A whole note will not be dotted.

Ignore other musical symbols.

In addition, the entire score provides an integer $T$, the number of beats per minute.

For readability, the score may contain arbitrary line breaks and spaces. They can be ignored when reading the input.

Now Xiao A wants to know how many seconds it takes to finish playing this score.

Input Format

The first line contains two integers $n, T$, the number of lines of the score and the beats per minute.

The next $n$ lines contain the score.

Output Format

Output a single integer: the total time in seconds needed to perform the score. If the exact time is fractional, round down to an integer.

2 60
3345 5432 1123 322-
3345 5432 1123 211-

32

5 120
3(1.(3))55 8(7.(6))65 655(3.(1)) (4.(4))32- 
3(1.(2))35 8(7.(6))65 655(4.(3)) (2.(3))21- 
2.(3)44 6(6.(6))(5.(4))3 3.(5)88 (9.(8)7.(6))5-
=.(=)(9.(8))7 9.(8)(7.(6))5  8(856543) (2.(3))43- 
=.(=)(9.(8))7 9.(8)(7.(6))5  8(857654) (3.(4))21- 

40

Hint

• Sample Explanation

For the first sample, there are $28$ quarter notes and $2$ half notes, totaling $32$ beats. With $60$ beats per minute, the total time is $32$ seconds.

• Constraints

For $40\%$ of the testdata, the characters (, ), and . do not appear.

For $100\%$ of the testdata, $1 \le n \le 100,\ 50 \le T \le 200$, and each line contains at most $100$ characters.

Translated by ChatGPT 5