#include <bits/stdc++.h>
using namespace std;
const int MAXN = 105;
const int MAX = 1005;
int n, a[MAXN], b[MAXN];
char s[MAXN];
bool flip[MAXN][MAX];
int main() {
  scanf("%d %s", &n, s);
  for (int i = 0; i < n; i++) {
    scanf("%d %d", &a[i], &b[i]);
    for (int j = b[i]; j < MAX; j += a[i]) flip[i][j] = true;
  }
  int res = 0;
  for (int i = 0; i < MAX; i++) {
    int cnt = 0;
    for (int j = 0; j < MAXN; j++) {
      if (flip[j][i]) {
        s[j] = '0' ^ '1' ^ s[j];
      }
      if (s[j] == '1') cnt++;
    }
    res = max(res, cnt);
  }
  printf("%d\n", res);
  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;
const int MAXN = 105;
const int MAX = 1005;
int n, a[MAXN], b[MAXN];
char s[MAXN];
bool flip[MAXN][MAX];
int main() {
  scanf("%d %s", &n, s);
  for (int i = 0; i < n; i++) {
    scanf("%d %d", &a[i], &b[i]);
    for (int j = b[i]; j < MAX; j += a[i]) flip[i][j] = true;
  }
  int res = 0;
  for (int i = 0; i < MAX; i++) {
    int cnt = 0;
    for (int j = 0; j < MAXN; j++) {
      if (flip[j][i]) {
        s[j] = '0' ^ '1' ^ s[j];
      }
      if (s[j] == '1') cnt++;
    }
    res = max(res, cnt);
  }
  printf("%d\n", res);
  return 0;
}

```