#include <bits/stdc++.h>
using namespace std;
int main() {
  int tc = 1;
  while (tc--) {
    long long n;
    cin >> n;
    string x;
    cin >> x;
    pair<pair<long long, long long>, long long> p[n];
    long long a[n];
    for (int i = 0; i < n; i++)
      cin >> p[i].first.first >> p[i].first.second, p[i].second = i,
                                                    a[i] = x[i] - '0';
    sort(p, p + n);
    long long c = 0, ans = 0;
    string rep;
    for (int tim = 0; tim <= 1e5; tim++) {
      for (int i = 0; i < n; i++) {
        if (p[i].first.second == tim) c++;
        if (tim >= p[i].first.second &&
            (tim - p[i].first.second) % p[i].first.first == 0)
          a[p[i].second] = 1 - a[p[i].second];
      }
      long long cnt = 0;
      for (int i = 0; i < n; i++)
        if (a[i]) cnt++;
      ans = max(ans, cnt);
      if (c == n) rep = x;
    }
    cout << ans << endl;
  }
  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;
int main() {
  int tc = 1;
  while (tc--) {
    long long n;
    cin >> n;
    string x;
    cin >> x;
    pair<pair<long long, long long>, long long> p[n];
    long long a[n];
    for (int i = 0; i < n; i++)
      cin >> p[i].first.first >> p[i].first.second, p[i].second = i,
                                                    a[i] = x[i] - '0';
    sort(p, p + n);
    long long c = 0, ans = 0;
    string rep;
    for (int tim = 0; tim <= 1e5; tim++) {
      for (int i = 0; i < n; i++) {
        if (p[i].first.second == tim) c++;
        if (tim >= p[i].first.second &&
            (tim - p[i].first.second) % p[i].first.first == 0)
          a[p[i].second] = 1 - a[p[i].second];
      }
      long long cnt = 0;
      for (int i = 0; i < n; i++)
        if (a[i]) cnt++;
      ans = max(ans, cnt);
      if (c == n) rep = x;
    }
    cout << ans << endl;
  }
  return 0;
}

```