#include <bits/stdc++.h>
const double Pi = acos(-1.0);
using namespace std;
vector<int> edges[1005];
vector<int> gmembers[1005];
int recurse(int pos, int groups[1005], int group) {
  if (groups[pos] != -1) return 0;
  groups[pos] = group;
  gmembers[group].push_back(pos);
  for (int i = 0; i < edges[pos].size(); i++) {
    int next = edges[pos][i];
    recurse(next, groups, group);
  }
  return 0;
}
int main(int argc, char** argv) {
  int num;
  int perm[1005];
  int favs[1005];
  cin >> num;
  for (int i = 0; i < num; i++) {
    cin >> perm[i];
    perm[i]--;
  }
  for (int i = 0; i < num; i++) cin >> favs[i];
  for (int i = 0; i < num; i++) {
    int back = i - favs[i];
    int front = i + favs[i];
    if (back >= 0) {
      edges[i].push_back(back);
      edges[back].push_back(i);
    }
    if (front < num) {
      edges[i].push_back(front);
      edges[front].push_back(i);
    }
  }
  int groups[1005];
  for (int i = 0; i < num; i++) groups[i] = -1;
  int currgroup = 0;
  for (int i = 0; i < num; i++) {
    if (groups[i] == -1) {
      recurse(i, groups, currgroup);
      currgroup++;
    }
  };
  for (int i = 0; i < currgroup; i++) {
    vector<int> ids = gmembers[i];
    vector<int> values;
    for (int j = 0; j < ids.size(); j++) {
      int id = ids[j];
      values.push_back(perm[id]);
    }
    sort(ids.begin(), ids.end());
    sort(values.begin(), values.end());
    if (ids != values) {
      cout << "NO\n";
      return 0;
    }
  }
  cout << "YES\n";
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

One day n cells of some array decided to play the following game. Initially each cell contains a number which is equal to it's ordinal number (starting from 1). Also each cell determined it's favourite number. On it's move i-th cell can exchange it's value with the value of some other j-th cell, if |i - j| = di, where di is a favourite number of i-th cell. Cells make moves in any order, the number of moves is unlimited.

The favourite number of each cell will be given to you. You will also be given a permutation of numbers from 1 to n. You are to determine whether the game could move to this state.

Input

The first line contains positive integer n (1 ≤ n ≤ 100) — the number of cells in the array. The second line contains n distinct integers from 1 to n — permutation. The last line contains n integers from 1 to n — favourite numbers of the cells.

Output

If the given state is reachable in the described game, output YES, otherwise NO.

Examples

Input

5
5 4 3 2 1
1 1 1 1 1


Output

YES


Input

7
4 3 5 1 2 7 6
4 6 6 1 6 6 1


Output

NO


Input

7
4 2 5 1 3 7 6
4 6 6 1 6 6 1


Output

YES

### Response

```cpp
#include <bits/stdc++.h>
const double Pi = acos(-1.0);
using namespace std;
vector<int> edges[1005];
vector<int> gmembers[1005];
int recurse(int pos, int groups[1005], int group) {
  if (groups[pos] != -1) return 0;
  groups[pos] = group;
  gmembers[group].push_back(pos);
  for (int i = 0; i < edges[pos].size(); i++) {
    int next = edges[pos][i];
    recurse(next, groups, group);
  }
  return 0;
}
int main(int argc, char** argv) {
  int num;
  int perm[1005];
  int favs[1005];
  cin >> num;
  for (int i = 0; i < num; i++) {
    cin >> perm[i];
    perm[i]--;
  }
  for (int i = 0; i < num; i++) cin >> favs[i];
  for (int i = 0; i < num; i++) {
    int back = i - favs[i];
    int front = i + favs[i];
    if (back >= 0) {
      edges[i].push_back(back);
      edges[back].push_back(i);
    }
    if (front < num) {
      edges[i].push_back(front);
      edges[front].push_back(i);
    }
  }
  int groups[1005];
  for (int i = 0; i < num; i++) groups[i] = -1;
  int currgroup = 0;
  for (int i = 0; i < num; i++) {
    if (groups[i] == -1) {
      recurse(i, groups, currgroup);
      currgroup++;
    }
  };
  for (int i = 0; i < currgroup; i++) {
    vector<int> ids = gmembers[i];
    vector<int> values;
    for (int j = 0; j < ids.size(); j++) {
      int id = ids[j];
      values.push_back(perm[id]);
    }
    sort(ids.begin(), ids.end());
    sort(values.begin(), values.end());
    if (ids != values) {
      cout << "NO\n";
      return 0;
    }
  }
  cout << "YES\n";
  return 0;
}

```