#include <bits/stdc++.h>
using namespace std;
template <class T>
void dbs(string str, T t) {
  cerr << str << " : " << t << "\n";
}
template <class T, class... S>
void dbs(string str, T t, S... s) {
  int idx = str.find(',');
  cerr << str.substr(0, idx) << " : " << t << ",";
  dbs(str.substr(idx + 1), s...);
}
template <class S, class T>
ostream& operator<<(ostream& os, const pair<S, T>& p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class T>
ostream& operator<<(ostream& os, const multiset<T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class S, class T>
ostream& operator<<(ostream& os, const map<S, T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class T>
void prc(T a, T b) {
  cerr << "[";
  for (T i = a; i != b; ++i) {
    if (i != a) cerr << ", ";
    cerr << *i;
  }
  cerr << "]\n";
}
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long findlcm(vector<int> arr, int n) {
  long long ans = arr[0];
  for (int i = 1; i < n; i++) ans = (((arr[i] * ans)) / (gcd(arr[i], ans)));
  return ans;
}
int main() {
  int n;
  cin >> n;
  string s;
  cin >> s;
  vector<int> a(n), b(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i] >> b[i];
  }
  vector<int> state(n);
  for (int i = 0; i < n; i++) {
    state[i] = (s[i] - '0');
  }
  long long int lcm = findlcm(a, n);
  int maxB = -1;
  for (int i = 0; i < n; i++) {
    maxB = max(maxB, b[i]);
  }
  int maxTime = maxB + 2 * lcm;
  int countMax = 0;
  for (int i = 0; i < n; i++) {
    if (state[i]) countMax++;
  }
  for (long long i = 1; i <= maxTime; i++) {
    int count = 0;
    for (int j = 0; j < n; j++) {
      if (i < b[j]) {
        if (state[j]) count++;
      } else {
        if ((i - b[j]) % a[j] == 0) {
          state[j] = !state[j];
        }
        if (state[j]) {
          count++;
        }
      }
      countMax = max(count, countMax);
    }
  }
  cout << countMax << "\n";
  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>
using namespace std;
template <class T>
void dbs(string str, T t) {
  cerr << str << " : " << t << "\n";
}
template <class T, class... S>
void dbs(string str, T t, S... s) {
  int idx = str.find(',');
  cerr << str.substr(0, idx) << " : " << t << ",";
  dbs(str.substr(idx + 1), s...);
}
template <class S, class T>
ostream& operator<<(ostream& os, const pair<S, T>& p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class T>
ostream& operator<<(ostream& os, const multiset<T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class S, class T>
ostream& operator<<(ostream& os, const map<S, T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class T>
void prc(T a, T b) {
  cerr << "[";
  for (T i = a; i != b; ++i) {
    if (i != a) cerr << ", ";
    cerr << *i;
  }
  cerr << "]\n";
}
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long findlcm(vector<int> arr, int n) {
  long long ans = arr[0];
  for (int i = 1; i < n; i++) ans = (((arr[i] * ans)) / (gcd(arr[i], ans)));
  return ans;
}
int main() {
  int n;
  cin >> n;
  string s;
  cin >> s;
  vector<int> a(n), b(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i] >> b[i];
  }
  vector<int> state(n);
  for (int i = 0; i < n; i++) {
    state[i] = (s[i] - '0');
  }
  long long int lcm = findlcm(a, n);
  int maxB = -1;
  for (int i = 0; i < n; i++) {
    maxB = max(maxB, b[i]);
  }
  int maxTime = maxB + 2 * lcm;
  int countMax = 0;
  for (int i = 0; i < n; i++) {
    if (state[i]) countMax++;
  }
  for (long long i = 1; i <= maxTime; i++) {
    int count = 0;
    for (int j = 0; j < n; j++) {
      if (i < b[j]) {
        if (state[j]) count++;
      } else {
        if ((i - b[j]) % a[j] == 0) {
          state[j] = !state[j];
        }
        if (state[j]) {
          count++;
        }
      }
      countMax = max(count, countMax);
    }
  }
  cout << countMax << "\n";
  return 0;
}

```