920_C. Swap Adjacent Elements
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?

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, ..., an (1 ≤ ai ≤ 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.

Examples

Input

6
1 2 5 3 4 6
01110


Output

YES


Input

6
1 2 5 3 4 6
01010


Output

NO

Note

In the first example you may swap a3 and a4, and then swap a4 and a5.
```python
n=int(input())
l=[int(i) for i in input().split()]
#canswap=[int(i) for i in input().split()]
canswap=input()
maxi=l[0]
for i in range(0,n-1,):
    maxi=max(maxi,l[i])
    if canswap[i]=='0' and i+1<maxi:
        print('NO')
        exit() 
print('YES')
```