#include <bits/stdc++.h>
using namespace std;
void solve() {
  long long ye_bhi_theek_hai, meri_jann_ho_tum, j, k, m;
  cin >> ye_bhi_theek_hai;
  string s;
  cin >> s;
  long long a[ye_bhi_theek_hai][10000];
  memset(a, 0, sizeof(a));
  for (meri_jann_ho_tum = 0; meri_jann_ho_tum < ye_bhi_theek_hai;
       meri_jann_ho_tum++) {
    long long x, y;
    cin >> x >> y;
    for (j = 0; j < y; j++) {
      a[meri_jann_ho_tum][j] = s[meri_jann_ho_tum] - '0';
    }
    for (j = y; j < 10000;) {
      long long p = 10000;
      for (k = j; k < min(j + x, p); k++) {
        if (a[meri_jann_ho_tum][j - 1] == 1) {
          a[meri_jann_ho_tum][k] = 0;
        } else {
          a[meri_jann_ho_tum][k] = 1;
        }
      }
      j = k;
    }
  }
  long long ans = -1;
  for (meri_jann_ho_tum = 0; meri_jann_ho_tum < 10000; meri_jann_ho_tum++) {
    long long x = 0;
    for (j = 0; j < ye_bhi_theek_hai; j++) {
      if (a[j][meri_jann_ho_tum]) x++;
    }
    ans = max(ans, x);
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t;
  t = 1;
  while (t--) {
    solve();
  }
}

### 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;
void solve() {
  long long ye_bhi_theek_hai, meri_jann_ho_tum, j, k, m;
  cin >> ye_bhi_theek_hai;
  string s;
  cin >> s;
  long long a[ye_bhi_theek_hai][10000];
  memset(a, 0, sizeof(a));
  for (meri_jann_ho_tum = 0; meri_jann_ho_tum < ye_bhi_theek_hai;
       meri_jann_ho_tum++) {
    long long x, y;
    cin >> x >> y;
    for (j = 0; j < y; j++) {
      a[meri_jann_ho_tum][j] = s[meri_jann_ho_tum] - '0';
    }
    for (j = y; j < 10000;) {
      long long p = 10000;
      for (k = j; k < min(j + x, p); k++) {
        if (a[meri_jann_ho_tum][j - 1] == 1) {
          a[meri_jann_ho_tum][k] = 0;
        } else {
          a[meri_jann_ho_tum][k] = 1;
        }
      }
      j = k;
    }
  }
  long long ans = -1;
  for (meri_jann_ho_tum = 0; meri_jann_ho_tum < 10000; meri_jann_ho_tum++) {
    long long x = 0;
    for (j = 0; j < ye_bhi_theek_hai; j++) {
      if (a[j][meri_jann_ho_tum]) x++;
    }
    ans = max(ans, x);
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t;
  t = 1;
  while (t--) {
    solve();
  }
}

```