Swap Adjacent Elements

Description:

Input:

The first line contains one integer n (2 ≤ n ≤ 200000) — the number of elements in the array.

The second line contains n integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 200000) — the elements of the array. Each integer from 1 to n appears exactly once.

The third line contains a string of n - 1 characters, each character is either 0 or 1. If i-th character is 1, then you can swap i-th element with (i + 1)-th any number of times, otherwise it is forbidden to swap i-th element with (i + 1)-th.

Output:

If it is possible to sort the array in ascending order using any sequence of swaps you are allowed to make, print YES. Otherwise, print NO.

Sample Input:

6
1 2 5 3 4 6
01110

Sample Output:

YES

Sample Input:

6
1 2 5 3 4 6
01010

Sample Output:

NO

Note:

In the first example you may swap a₃ and a₄, and then swap a₄ and a₅.