You have an array a consisting of n integers. Each integer from 1 to n appears exactly once in this array.
For some indices i (1 ≤ i ≤ n - 1) it is possible to swap i-th element with (i + 1)-th, for other indices it is not possible. You may perform any number of swapping operations any order. There is no limit on the number of times you swap i-th element with (i + 1)-th (if the position is not forbidden).
Can you make this array sorted in ascending order performing some sequence of swapping operations?
The first line contains one integer n (2 ≤ n ≤ 200000) — the number of elements in the array.
The second line contains n integers a 1, a 2, ..., 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.
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.
1 2 5 3 4 6
1 2 5 3 4 6
In the first example you may swap a 3 and a 4, and then swap a 4 and a 5.