#include <bits/stdc++.h>
using namespace std;
int LIGHT_SIZE;
bool light[101];
int start[101];
int cycle[101];
int ini_Lights(const string& s) {
  LIGHT_SIZE = s.size();
  int on = 0;
  for (int i = 0; i < s.size(); i++) {
    light[i] = s[i] == '1';
    if (light[i]) {
      on++;
    }
  }
  return on;
}
int simRound(int round, int lastOn) {
  int on = lastOn;
  for (int i = 0; i < LIGHT_SIZE; i++) {
    int begin = round - start[i];
    if (begin >= 0 && begin % cycle[i] == 0) {
      light[i] = !light[i];
      if (light[i]) {
        on++;
      } else {
        on--;
      }
    }
  }
  return on;
}
void coutSim() {
  for (int i = 0; i < LIGHT_SIZE; i++) {
    cout << (light[i]) ? '1' : '0';
  }
  cout << endl;
}
int main() {
  cin >> LIGHT_SIZE;
  string s;
  cin >> s;
  int max_on = ini_Lights(s);
  int last_on = max_on;
  for (int i = 0; i < LIGHT_SIZE; i++) {
    cin >> cycle[i] >> start[i];
  }
  for (int i = 1; i <= 100000; i++) {
    last_on = simRound(i, last_on);
    max_on = max(max_on, last_on);
    if (max_on == LIGHT_SIZE) {
      break;
    }
  }
  cout << max_on << endl;
}

### 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 LIGHT_SIZE;
bool light[101];
int start[101];
int cycle[101];
int ini_Lights(const string& s) {
  LIGHT_SIZE = s.size();
  int on = 0;
  for (int i = 0; i < s.size(); i++) {
    light[i] = s[i] == '1';
    if (light[i]) {
      on++;
    }
  }
  return on;
}
int simRound(int round, int lastOn) {
  int on = lastOn;
  for (int i = 0; i < LIGHT_SIZE; i++) {
    int begin = round - start[i];
    if (begin >= 0 && begin % cycle[i] == 0) {
      light[i] = !light[i];
      if (light[i]) {
        on++;
      } else {
        on--;
      }
    }
  }
  return on;
}
void coutSim() {
  for (int i = 0; i < LIGHT_SIZE; i++) {
    cout << (light[i]) ? '1' : '0';
  }
  cout << endl;
}
int main() {
  cin >> LIGHT_SIZE;
  string s;
  cin >> s;
  int max_on = ini_Lights(s);
  int last_on = max_on;
  for (int i = 0; i < LIGHT_SIZE; i++) {
    cin >> cycle[i] >> start[i];
  }
  for (int i = 1; i <= 100000; i++) {
    last_on = simRound(i, last_on);
    max_on = max(max_on, last_on);
    if (max_on == LIGHT_SIZE) {
      break;
    }
  }
  cout << max_on << endl;
}

```