#include <bits/stdc++.h>
using namespace std;
using LL = long long;
template <typename Container>
inline int ssize(Container& x) {
  return x.size();
}
int read() {
  register char c = '?';
  while (!isdigit(c)) c = getchar();
  register int ans = 0;
  for (; isdigit(c); c = getchar()) ans = ans * 10 + c - '0';
  return ans;
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  constexpr char endl = '\n';
  int n;
  char s[105];
  cin >> n >> &s[1];
  int a[105], b[105];
  for (register auto i = (1), __r = decltype(i)(n); i <= __r; ++i)
    cin >> a[i] >> b[i];
  int ans = count(&s[1], &s[n] + 1, '1');
  for (register auto t = (1), __r = decltype(t)(1e6); t <= __r; ++t) {
    for (register auto i = (1), __r = decltype(i)(n); i <= __r; ++i)
      if (t >= b[i] && (t - b[i]) % a[i] == 0) s[i] = '0' + '1' - s[i];
    ans = max(ans, (int)count(&s[1], &s[n] + 1, '1'));
  }
  cout << ans;
}

### Prompt

Please formulate 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;
using LL = long long;
template <typename Container>
inline int ssize(Container& x) {
  return x.size();
}
int read() {
  register char c = '?';
  while (!isdigit(c)) c = getchar();
  register int ans = 0;
  for (; isdigit(c); c = getchar()) ans = ans * 10 + c - '0';
  return ans;
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  constexpr char endl = '\n';
  int n;
  char s[105];
  cin >> n >> &s[1];
  int a[105], b[105];
  for (register auto i = (1), __r = decltype(i)(n); i <= __r; ++i)
    cin >> a[i] >> b[i];
  int ans = count(&s[1], &s[n] + 1, '1');
  for (register auto t = (1), __r = decltype(t)(1e6); t <= __r; ++t) {
    for (register auto i = (1), __r = decltype(i)(n); i <= __r; ++i)
      if (t >= b[i] && (t - b[i]) % a[i] == 0) s[i] = '0' + '1' - s[i];
    ans = max(ans, (int)count(&s[1], &s[n] + 1, '1'));
  }
  cout << ans;
}

```