#include <bits/stdc++.h>
using namespace std;
long long read() {
  long long ans = 0;
  char c = getchar();
  while (c < '0' || c > '9') c = getchar();
  while (c >= '0' && c <= '9') ans = ans * 10 + c - 48, c = getchar();
  return ans;
}
int n;
int a[211], b[211];
char s[211];
int maxn = 0;
int main() {
  n = read();
  scanf("%s", s + 1);
  for (int i = 1; i <= n; ++i) a[i] = read(), b[i] = read();
  for (int t = 0; t <= 100000; ++t) {
    int num = 0;
    for (int i = 1; i <= n; ++i) {
      int x = s[i] - '0';
      if (b[i] > t)
        num += x;
      else {
        int y = (t - b[i]) / a[i] + 1;
        if ((y & 1) == 0)
          num += x;
        else
          num += (x ^ 1);
      }
    }
    maxn = max(num, maxn);
  }
  printf("%d\n", maxn);
  return 0;
}

### Prompt

Generate 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;
long long read() {
  long long ans = 0;
  char c = getchar();
  while (c < '0' || c > '9') c = getchar();
  while (c >= '0' && c <= '9') ans = ans * 10 + c - 48, c = getchar();
  return ans;
}
int n;
int a[211], b[211];
char s[211];
int maxn = 0;
int main() {
  n = read();
  scanf("%s", s + 1);
  for (int i = 1; i <= n; ++i) a[i] = read(), b[i] = read();
  for (int t = 0; t <= 100000; ++t) {
    int num = 0;
    for (int i = 1; i <= n; ++i) {
      int x = s[i] - '0';
      if (b[i] > t)
        num += x;
      else {
        int y = (t - b[i]) / a[i] + 1;
        if ((y & 1) == 0)
          num += x;
        else
          num += (x ^ 1);
      }
    }
    maxn = max(num, maxn);
  }
  printf("%d\n", maxn);
  return 0;
}

```