#include <bits/stdc++.h>
using namespace std;
bool a[105][100005];
vector<string> V;
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  string str;
  cin >> str;
  V.push_back(str);
  for (int i = 1; i <= n; i++) {
    int x, y;
    cin >> x >> y;
    for (int j = 0; y + j * x < 100005; j++) a[i][y + j * x] = true;
  }
  int ans = 0;
  for (int i = 0; i < str.size(); i++)
    if (str[i] == '1') ans++;
  for (int i = 1; i < 100005; i++) {
    string ss = V[i - 1];
    for (int j = 1; j <= n; j++)
      if (a[j][i]) {
        if (ss[j - 1] == '0')
          ss[j - 1] = '1';
        else
          ss[j - 1] = '0';
      }
    int tt = 0;
    for (int i = 0; i < ss.size(); i++)
      if (ss[i] == '1') tt++;
    ans = max(ans, tt);
    V.push_back(ss);
  }
  cout << ans;
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
bool a[105][100005];
vector<string> V;
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  string str;
  cin >> str;
  V.push_back(str);
  for (int i = 1; i <= n; i++) {
    int x, y;
    cin >> x >> y;
    for (int j = 0; y + j * x < 100005; j++) a[i][y + j * x] = true;
  }
  int ans = 0;
  for (int i = 0; i < str.size(); i++)
    if (str[i] == '1') ans++;
  for (int i = 1; i < 100005; i++) {
    string ss = V[i - 1];
    for (int j = 1; j <= n; j++)
      if (a[j][i]) {
        if (ss[j - 1] == '0')
          ss[j - 1] = '1';
        else
          ss[j - 1] = '0';
      }
    int tt = 0;
    for (int i = 0; i < ss.size(); i++)
      if (ss[i] == '1') tt++;
    ans = max(ans, tt);
    V.push_back(ss);
  }
  cout << ans;
  return 0;
}

```