#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  vector<int> arr(n);
  vector<vector<int> > g(n, vector<int>(n, 1e9));
  vector<int> ord(n);
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
    arr[i]--;
  }
  int a, d;
  for (int i = 0; i < n; ++i) {
    cin >> d;
    a = i - d;
    if (a >= 0) {
      g[i][a] = 1;
      g[a][i] = 1;
    }
    a = i + d;
    if (a < n) {
      g[i][a] = 1;
      g[a][i] = 1;
    }
  }
  for (int k = 0; k < n; ++k) {
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        if (g[i][k] != 1e9 && g[k][j] != 1e9) {
          g[i][j] = min(g[i][j], g[i][k] + g[k][j]);
        }
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    if (arr[i] != i && g[i][arr[i]] == 1e9) {
      cout << "NO" << endl;
      return 0;
    }
  }
  cout << "YES" << endl;
  return 0;
}

### Prompt

Please create a solution in Cpp to the following problem:

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>
using namespace std;
int main() {
  int n;
  cin >> n;
  vector<int> arr(n);
  vector<vector<int> > g(n, vector<int>(n, 1e9));
  vector<int> ord(n);
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
    arr[i]--;
  }
  int a, d;
  for (int i = 0; i < n; ++i) {
    cin >> d;
    a = i - d;
    if (a >= 0) {
      g[i][a] = 1;
      g[a][i] = 1;
    }
    a = i + d;
    if (a < n) {
      g[i][a] = 1;
      g[a][i] = 1;
    }
  }
  for (int k = 0; k < n; ++k) {
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        if (g[i][k] != 1e9 && g[k][j] != 1e9) {
          g[i][j] = min(g[i][j], g[i][k] + g[k][j]);
        }
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    if (arr[i] != i && g[i][arr[i]] == 1e9) {
      cout << "NO" << endl;
      return 0;
    }
  }
  cout << "YES" << endl;
  return 0;
}

```