A12794 | Koala and Lights

It is a holiday season, and Koala is decorating his house with cool lights! He owns $n$ lights, all of which flash periodically.

After taking a quick glance at them, Koala realizes that each of his lights can be described with two parameters $a_i$ and $b_i$ . Light with parameters $a_i$ and $b_i$ will toggle (on to off, or off to on) every $a_i$ seconds starting from the $b_i$ -th second. In other words, it will toggle at the moments $b_i$ , $b_i + a_i$ , $b_i + 2 \cdot a_i$ and so on.

You know for each light whether it's initially on or off and its corresponding parameters $a_i$ and $b_i$ . Koala is wondering what is the maximum number of lights that will ever be on at the same time. So you need to find that out.

Here is a graphic for the first example.

The first line contains a single integer $n$ ( $1 \le n \le 100$ ), the number of lights.

The next line contains a string $s$ of $n$ characters. The $i$ -th character is "1", if the $i$ -th lamp is initially on. Otherwise, $i$ -th character is "0".

The $i$ -th of the following $n$ lines contains two integers $a_i$ and $b_i$ ( $1 \le a_i, b_i \le 5$ ) — the parameters of the $i$ -th light.

Print a single integer — the maximum number of lights that will ever be on at the same time.