Dynamic Array

Do you know about dynamic arrays? If not, you have probably declared arrays with a fixed size. You may have run into a case where the array was too small and the judge returned an unwanted result. A dynamic array grows automatically when its declared size is not enough. The following explains how this works.

A dynamic array operates as follows.

1. Create a dynamic array with any initial size you want. The dynamic array starts empty.
2. When you need to store an element but the dynamic array is full, declare a new dynamic array whose size is $2$ times the current size.
3. Copy all elements of the existing dynamic array to the front of the new $2$-times-size array. Then delete the existing array and replace it with the new one. Store the element from step 2 after the copied elements.

To do this, a dynamic array manages two variables. $S$ is the current maximum size, and $U$ is the number of slots currently in use.

Given the initial size of a dynamic array and a series of store or delete commands, print the maximum size of the array after all commands are processed.

The first line contains three integers $S\_0$, $N$, and $M$, separated by spaces. $S\_0$ is the initial maximum size, $N$ is the number of store commands, and $M$ is the number of delete commands. $(1 \le S\_0 \le 10, \; 1 \le N \le 100\,000, \; 0 \le M \le N)$

From the second line through line $N + M + 1$, each line contains either 1 or 0. 1 stores an element in the array. 0 deletes an element from the end of the array.

A delete command is never given when the dynamic array has no elements.

Print the maximum size of the dynamic array after all commands are processed.

A well-known example of a dynamic array is the vector in C++.