#include <bits/stdc++.h>
#pragma warning(disable : 4996)
using namespace std;
clock_t start_time, end_time;
void open() {
  ((void)0);
  ((void)0);
}
void close() {
  ((void)0);
  ((void)0);
  ((void)0);
}
const int MAX = 2e5 + 1;
const int MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const long long LL_INF = 0x3f3f3f3f3f3f3f3fLL;
const double PI = acos(-1);
const long double ERR = 1e-10;
const int move_r[] = {-1, 0, 1, 0, -1, -1, 1, 1};
const int move_c[] = {0, -1, 0, 1, -1, 1, -1, 1};
int t, n, a[105], b[105];
char in[105];
int main(int argc, char *argv[]) {
  open();
  scanf("%d %s", &n, in);
  for (int i = 0; i < n; ++i) scanf("%d %d", a + i, b + i);
  int cnt = 0, ans = 0;
  for (int i = 0; i < n; ++i)
    if (in[i] == '1') cnt++;
  ans = cnt;
  for (int i = 1; i <= 500; ++i) {
    for (int j = 0; j < n; ++j) {
      if (i >= b[j] && (i - b[j]) % a[j] == 0) {
        if (in[j] == '1') {
          in[j] = '0';
          cnt--;
        } else {
          in[j] = '1';
          cnt++;
        }
      }
    }
    ans = max(ans, cnt);
  }
  printf("%d\n", ans);
  close();
  return 0;
}

### Prompt

Your task is to create 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>
#pragma warning(disable : 4996)
using namespace std;
clock_t start_time, end_time;
void open() {
  ((void)0);
  ((void)0);
}
void close() {
  ((void)0);
  ((void)0);
  ((void)0);
}
const int MAX = 2e5 + 1;
const int MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const long long LL_INF = 0x3f3f3f3f3f3f3f3fLL;
const double PI = acos(-1);
const long double ERR = 1e-10;
const int move_r[] = {-1, 0, 1, 0, -1, -1, 1, 1};
const int move_c[] = {0, -1, 0, 1, -1, 1, -1, 1};
int t, n, a[105], b[105];
char in[105];
int main(int argc, char *argv[]) {
  open();
  scanf("%d %s", &n, in);
  for (int i = 0; i < n; ++i) scanf("%d %d", a + i, b + i);
  int cnt = 0, ans = 0;
  for (int i = 0; i < n; ++i)
    if (in[i] == '1') cnt++;
  ans = cnt;
  for (int i = 1; i <= 500; ++i) {
    for (int j = 0; j < n; ++j) {
      if (i >= b[j] && (i - b[j]) % a[j] == 0) {
        if (in[j] == '1') {
          in[j] = '0';
          cnt--;
        } else {
          in[j] = '1';
          cnt++;
        }
      }
    }
    ans = max(ans, cnt);
  }
  printf("%d\n", ans);
  close();
  return 0;
}

```