#include <bits/stdc++.h>
using namespace std;
int a[110], b[110];
int timer[110];
bool light[110];
int n;
int lights() {
  int ret = 0;
  for (int i = 0; i < n; ++i) ret += light[i];
  return ret;
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  string str;
  cin >> n >> str;
  for (int i = 0; i < n; ++i) light[i] = (str[i] == '1');
  for (int i = 0; i < n; ++i) {
    cin >> a[i] >> b[i];
    timer[i] = b[i];
  }
  int ans = lights();
  for (int i = 0; i < 100000; ++i) {
    for (int j = 0; j < n; ++j) {
      timer[j]--;
      if (timer[j] == 0) {
        light[j] = (light[j] ^ 1);
        timer[j] = a[j];
      }
    }
    ans = max(ans, lights());
  }
  cout << ans << endl;
}

### Prompt

In Cpp, your task is to solve the following problem:

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 a[110], b[110];
int timer[110];
bool light[110];
int n;
int lights() {
  int ret = 0;
  for (int i = 0; i < n; ++i) ret += light[i];
  return ret;
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  string str;
  cin >> n >> str;
  for (int i = 0; i < n; ++i) light[i] = (str[i] == '1');
  for (int i = 0; i < n; ++i) {
    cin >> a[i] >> b[i];
    timer[i] = b[i];
  }
  int ans = lights();
  for (int i = 0; i < 100000; ++i) {
    for (int j = 0; j < n; ++j) {
      timer[j]--;
      if (timer[j] == 0) {
        light[j] = (light[j] ^ 1);
        timer[j] = a[j];
      }
    }
    ans = max(ans, lights());
  }
  cout << ans << endl;
}

```