#include <bits/stdc++.h>
using namespace std;
template <class T>
inline void read(T &s) {
  s = 0;
  register char ch = getchar();
  register int w = 0;
  while (!isdigit(ch)) w |= ch == '-', ch = getchar();
  while (isdigit(ch)) s = (s << 1) + (s << 3) + (ch ^ 48), ch = getchar();
  if (w) s = -s;
}
namespace Sakii {
int n, x[110][200], ans, a[110], b[110];
string s;
int gcd(int m, int n) { return n == 0 ? m : gcd(n, m % n); }
inline void main() {
  read(n);
  cin >> s;
  int la = 1, mul, g;
  for (int i = 0; i < s.size(); i++) x[i][0] = s[i] - '0', ans += x[i][0];
  for (int i = 0; i < n; i++) {
    read(a[i]);
    read(b[i]);
  }
  la = 130;
  for (int i = 0; i < n; i++) {
    for (int j = 1; j < la; j++) {
      x[i][j] = x[i][0];
    }
  }
  for (int i = 0; i < n; i++) {
    int f = la / a[i];
    for (int j = 0; j < f; j++) {
      for (int k = b[i] + j * a[i]; k <= b[i] - 1 + (j + 1) * a[i]; k++) {
        if (j % 2 == 0) x[i][k] = (x[i][0]) ? 0 : 1;
      }
    }
  }
  for (int i = 0; i < la; i++) {
    int res = 0;
    for (int j = 0; j < n; j++) {
      res += x[j][i];
    }
    ans = max(res, ans);
  }
  printf("%d\n", ans);
  return;
}
}  // namespace Sakii
int main() {
  Sakii::main();
  return 0;
}

### Prompt

Create a solution in Cpp for 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;
template <class T>
inline void read(T &s) {
  s = 0;
  register char ch = getchar();
  register int w = 0;
  while (!isdigit(ch)) w |= ch == '-', ch = getchar();
  while (isdigit(ch)) s = (s << 1) + (s << 3) + (ch ^ 48), ch = getchar();
  if (w) s = -s;
}
namespace Sakii {
int n, x[110][200], ans, a[110], b[110];
string s;
int gcd(int m, int n) { return n == 0 ? m : gcd(n, m % n); }
inline void main() {
  read(n);
  cin >> s;
  int la = 1, mul, g;
  for (int i = 0; i < s.size(); i++) x[i][0] = s[i] - '0', ans += x[i][0];
  for (int i = 0; i < n; i++) {
    read(a[i]);
    read(b[i]);
  }
  la = 130;
  for (int i = 0; i < n; i++) {
    for (int j = 1; j < la; j++) {
      x[i][j] = x[i][0];
    }
  }
  for (int i = 0; i < n; i++) {
    int f = la / a[i];
    for (int j = 0; j < f; j++) {
      for (int k = b[i] + j * a[i]; k <= b[i] - 1 + (j + 1) * a[i]; k++) {
        if (j % 2 == 0) x[i][k] = (x[i][0]) ? 0 : 1;
      }
    }
  }
  for (int i = 0; i < la; i++) {
    int res = 0;
    for (int j = 0; j < n; j++) {
      res += x[j][i];
    }
    ans = max(res, ans);
  }
  printf("%d\n", ans);
  return;
}
}  // namespace Sakii
int main() {
  Sakii::main();
  return 0;
}

```