#include <bits/stdc++.h>
using namespace std;
const long long inf = 1e16;
const long long _inf = -1e16;
long long dx[] = {1, -1, 0, 0};
long long dy[] = {0, 0, 1, -1};
long long addmod(long long& a, long long b) {
  a += b;
  if (a >= 1000000007) a -= 1000000007;
}
long long submod(long long& a, long long b) {
  a -= b;
  if (a < 0) a += 1000000007;
}
long long a[1000];
long long b[1000];
long long res[110][100010];
int main() {
  long long n, i, j, fl, k, ans, mx;
  string s;
  cin >> n;
  cin >> s;
  for (i = 0; i < n; i++) cin >> a[i] >> b[i];
  for (i = 0; i < n; i++) {
    for (j = 0; j < b[i]; j++) res[i][j] = s[i] - '0';
    if (s[i] == '0')
      fl = 1;
    else
      fl = 0;
    while (j <= 100000) {
      for (k = j; k < j + a[i]; k++) {
        res[i][k] = fl;
      }
      if (fl == 0)
        fl = 1;
      else
        fl = 0;
      j += a[i];
    }
  }
  mx = 1;
  for (i = 0; i < 100000; i++) {
    ans = 0;
    for (j = 0; j < n; j++) {
      if (res[j][i] == 1) ans++;
    }
    mx = max(mx, ans);
  }
  cout << mx << endl;
  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;
const long long inf = 1e16;
const long long _inf = -1e16;
long long dx[] = {1, -1, 0, 0};
long long dy[] = {0, 0, 1, -1};
long long addmod(long long& a, long long b) {
  a += b;
  if (a >= 1000000007) a -= 1000000007;
}
long long submod(long long& a, long long b) {
  a -= b;
  if (a < 0) a += 1000000007;
}
long long a[1000];
long long b[1000];
long long res[110][100010];
int main() {
  long long n, i, j, fl, k, ans, mx;
  string s;
  cin >> n;
  cin >> s;
  for (i = 0; i < n; i++) cin >> a[i] >> b[i];
  for (i = 0; i < n; i++) {
    for (j = 0; j < b[i]; j++) res[i][j] = s[i] - '0';
    if (s[i] == '0')
      fl = 1;
    else
      fl = 0;
    while (j <= 100000) {
      for (k = j; k < j + a[i]; k++) {
        res[i][k] = fl;
      }
      if (fl == 0)
        fl = 1;
      else
        fl = 0;
      j += a[i];
    }
  }
  mx = 1;
  for (i = 0; i < 100000; i++) {
    ans = 0;
    for (j = 0; j < n; j++) {
      if (res[j][i] == 1) ans++;
    }
    mx = max(mx, ans);
  }
  cout << mx << endl;
  return 0;
}

```