pSort

Problem Source

Original problem: CF28B pSort | Luogu

Problem Description

There is a sequence $a_1, a_2, \dots, a_n$ of $n$ elements. Initially, every element satisfies $a_i = i$.

In one operation, you may swap the $i$-th and $j$-th elements if and only if $|i - j| = d_i$.

You are given the sequences $b_1, b_2, \dots, b_n$ and $d_1, d_2, \dots, d_n$. Determine whether, after several swaps, the sequence $a$ can be made exactly equal to $b$.

Input Format

The first line contains a positive integer $n$, as described above.

The second line contains $n$ positive integers giving $b_1, b_2, \dots, b_n$.

The third line contains $n$ positive integers giving $d_1, d_2, \dots, d_n$.

Output Format

If possible, output YES; otherwise output NO.

Sample Input 1

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

Sample Output 1

YES

Sample Input 2

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

Sample Output 2

NO

Constraints

$1 \le n, d_i \le 100$. The elements of $b$ are guaranteed to be distinct.