#include <bits/stdc++.h>
using namespace std;
vector<vector<long long int> > co(105);
long long int v[105] = {0}, k = 0;
void dfs(long long int x) {
  v[x] = k;
  for (long long int i = 0; i < co[x].size(); i++) {
    if (v[co[x][i]] == 0) {
      dfs(co[x][i]);
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n, a[105], b[105], i, j;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> b[i];
  }
  for (i = 1; i <= n; i++) {
    cin >> a[i];
    if (a[i] < i) {
      co[i].push_back(i - a[i]);
      co[i - a[i]].push_back(i);
    }
    if (n >= a[i] + i) {
      co[i].push_back(a[i] + i);
      co[i + a[i]].push_back(i);
    }
  }
  for (i = 1; i <= n; i++) {
    if (v[i] == 0) {
      k++;
      dfs(i);
    }
  }
  for (i = 1; i <= n; i++) {
    if (v[i] != v[b[i]]) {
      cout << "NO";
      return 0;
    }
  }
  cout << "YES";
  return 0;
}

### Prompt

In Cpp, your task is to solve 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;
vector<vector<long long int> > co(105);
long long int v[105] = {0}, k = 0;
void dfs(long long int x) {
  v[x] = k;
  for (long long int i = 0; i < co[x].size(); i++) {
    if (v[co[x][i]] == 0) {
      dfs(co[x][i]);
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n, a[105], b[105], i, j;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> b[i];
  }
  for (i = 1; i <= n; i++) {
    cin >> a[i];
    if (a[i] < i) {
      co[i].push_back(i - a[i]);
      co[i - a[i]].push_back(i);
    }
    if (n >= a[i] + i) {
      co[i].push_back(a[i] + i);
      co[i + a[i]].push_back(i);
    }
  }
  for (i = 1; i <= n; i++) {
    if (v[i] == 0) {
      k++;
      dfs(i);
    }
  }
  for (i = 1; i <= n; i++) {
    if (v[i] != v[b[i]]) {
      cout << "NO";
      return 0;
    }
  }
  cout << "YES";
  return 0;
}

```