#include <bits/stdc++.h>
using namespace std;
int n, ans, a[105], b[105], cnt[500005], r[105];
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    char c;
    cin >> c;
    r[i] = c == '1';
  }
  for (int i = 1; i <= n; i++) cin >> a[i] >> b[i];
  for (int i = 1; i <= n; i++)
    for (int j = 0; j <= 500000; j++) {
      if (j >= b[i] && (j - b[i]) % a[i] == 0) r[i] = 1 - r[i];
      if (r[i]) cnt[j]++;
    }
  for (int j = 0; j <= 500000; j++) ans = max(ans, cnt[j]);
  cout << ans << endl;
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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 ⋅ 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.

<image> Here is a graphic for the first example.

Input

The first line contains a single integer n (1 ≤ n ≤ 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 ≤ a_i, b_i ≤ 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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n, ans, a[105], b[105], cnt[500005], r[105];
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    char c;
    cin >> c;
    r[i] = c == '1';
  }
  for (int i = 1; i <= n; i++) cin >> a[i] >> b[i];
  for (int i = 1; i <= n; i++)
    for (int j = 0; j <= 500000; j++) {
      if (j >= b[i] && (j - b[i]) % a[i] == 0) r[i] = 1 - r[i];
      if (r[i]) cnt[j]++;
    }
  for (int j = 0; j <= 500000; j++) ans = max(ans, cnt[j]);
  cout << ans << endl;
  return 0;
}

```