#include <bits/stdc++.h>
int dr[] = {2, 2, -2, -2, 1, -1, 1, -1};
int dc[] = {1, -1, 1, -1, 2, 2, -2, -2};
int dr1[] = {0, 0, 0, 1, 1, 1, -1, -1, -1};
int dc1[] = {-1, 0, 1, -1, 0, 1, -1, 0, 1};
int dr2[] = {0, 0, 1, -1};
int dc2[] = {1, -1, 0, 0};
using namespace std;
long long int mark[10002];
int main() {
  string t;
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int n, i, j, a, b;
  cin >> n;
  cin >> t;
  for (i = 0; i < n; i++) {
    cin >> a >> b;
    long long int f = t[i] - '0';
    for (j = 0; j < b; j++) mark[j] += f;
    for (j = b; j + a <= 10000; j += a) {
      f ^= 1;
      for (long long int k = j; k < j + a && k <= 10000; k++) mark[k] += f;
    }
  }
  long long int max1 = 0;
  for (i = 0; i <= 10000; i++) max1 = max(max1, mark[i]);
  cout << max1 << endl;
}

### 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>
int dr[] = {2, 2, -2, -2, 1, -1, 1, -1};
int dc[] = {1, -1, 1, -1, 2, 2, -2, -2};
int dr1[] = {0, 0, 0, 1, 1, 1, -1, -1, -1};
int dc1[] = {-1, 0, 1, -1, 0, 1, -1, 0, 1};
int dr2[] = {0, 0, 1, -1};
int dc2[] = {1, -1, 0, 0};
using namespace std;
long long int mark[10002];
int main() {
  string t;
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int n, i, j, a, b;
  cin >> n;
  cin >> t;
  for (i = 0; i < n; i++) {
    cin >> a >> b;
    long long int f = t[i] - '0';
    for (j = 0; j < b; j++) mark[j] += f;
    for (j = b; j + a <= 10000; j += a) {
      f ^= 1;
      for (long long int k = j; k < j + a && k <= 10000; k++) mark[k] += f;
    }
  }
  long long int max1 = 0;
  for (i = 0; i <= 10000; i++) max1 = max(max1, mark[i]);
  cout << max1 << endl;
}

```