#include <bits/stdc++.h>
using namespace std;
void err(istream_iterator<string> it) { return; }
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << endl;
  err(++it, args...);
}
void solve() {
  int N;
  cin >> N;
  string status;
  cin >> status;
  vector<vector<int>> curr;
  for (int i = 0; i < N; ++i) {
    int x, y;
    cin >> x >> y;
    vector<int> temp = {};
    if (status[i] == '1') {
      for (int i = 1; i <= 500; ++i) {
        if (i <= y)
          temp.push_back(1);
        else {
          if (((i - y + x - 1) / x) & 1) {
            temp.push_back(0);
          } else {
            temp.push_back(1);
          }
        }
      }
      curr.push_back(temp);
    } else {
      for (int i = 1; i <= 500; ++i) {
        if (i <= y)
          temp.push_back(0);
        else {
          if (((i - y + x - 1) / x) & 1) {
            temp.push_back(1);
          } else {
            temp.push_back(0);
          }
        }
      }
      curr.push_back(temp);
    }
  }
  int ret = INT_MIN;
  for (int i = 0; i < 500; ++i) {
    int cnt = 0;
    for (int j = 0; j < N; ++j) {
      if (curr[j][i] == 1) {
        ++cnt;
      }
    }
    ret = max(ret, cnt);
  }
  cout << ret << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  auto start = chrono::high_resolution_clock::now();
  solve();
  auto end = chrono::high_resolution_clock::now();
  cerr << " Execution time : "
       << chrono::duration_cast<chrono::milliseconds>(end - start).count()
       << "ms" << endl;
  return 0;
}

### Prompt

Your task is to create a Cpp solution to 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;
void err(istream_iterator<string> it) { return; }
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << endl;
  err(++it, args...);
}
void solve() {
  int N;
  cin >> N;
  string status;
  cin >> status;
  vector<vector<int>> curr;
  for (int i = 0; i < N; ++i) {
    int x, y;
    cin >> x >> y;
    vector<int> temp = {};
    if (status[i] == '1') {
      for (int i = 1; i <= 500; ++i) {
        if (i <= y)
          temp.push_back(1);
        else {
          if (((i - y + x - 1) / x) & 1) {
            temp.push_back(0);
          } else {
            temp.push_back(1);
          }
        }
      }
      curr.push_back(temp);
    } else {
      for (int i = 1; i <= 500; ++i) {
        if (i <= y)
          temp.push_back(0);
        else {
          if (((i - y + x - 1) / x) & 1) {
            temp.push_back(1);
          } else {
            temp.push_back(0);
          }
        }
      }
      curr.push_back(temp);
    }
  }
  int ret = INT_MIN;
  for (int i = 0; i < 500; ++i) {
    int cnt = 0;
    for (int j = 0; j < N; ++j) {
      if (curr[j][i] == 1) {
        ++cnt;
      }
    }
    ret = max(ret, cnt);
  }
  cout << ret << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  auto start = chrono::high_resolution_clock::now();
  solve();
  auto end = chrono::high_resolution_clock::now();
  cerr << " Execution time : "
       << chrono::duration_cast<chrono::milliseconds>(end - start).count()
       << "ms" << endl;
  return 0;
}

```