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B. Koala and Lights

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIt 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.

Input

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.

Output

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

Examples

Input

3 101 3 3 3 2 3 1

Output

2

Input

4 1111 3 4 5 2 3 1 3 2

Output

4

Input

6 011100 5 3 5 5 2 4 3 5 4 2 1 5

Output

6

Note

For first example, the lamps' states are shown in the picture above. The largest number of simultaneously on lamps is $$$2$$$ (e.g. at the moment $$$2$$$).

In the second example, all lights are initially on. So the answer is $$$4$$$.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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