Long Number

You are given a long decimal number a consisting of n digits from 1 to 9. You also have a function f that maps every digit from 1 to 9 to some (possibly the same) digit from 1 to 9.

You can perform the following operation no more than once: choose a non-empty contiguous subsegment of digits in a, and replace each digit x from this segment with f(x). For example, if a = 1337, f(1) = 1, f(3) = 5, f(7) = 3, and you choose the segment consisting of three rightmost digits, you get 1553 as the result.

What is the maximum possible number you can obtain applying this operation no more than once?

Input

The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of digits in a.

The second line contains a string of n characters, denoting the number a. Each character is a decimal digit from 1 to 9.

The third line contains exactly 9 integers f(1), f(2), ..., f(9) (1 ≤ f(i) ≤ 9).

Output

Print the maximum number you can get after applying the operation described in the statement no more than once.

Examples

Input

4 1337 1 2 5 4 6 6 3 1 9

Output

1557

Input

5 11111 9 8 7 6 5 4 3 2 1

Output

99999

Input

2 33 1 1 1 1 1 1 1 1 1

Output

33

inputFormat

Input

The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of digits in a.

The second line contains a string of n characters, denoting the number a. Each character is a decimal digit from 1 to 9.

The third line contains exactly 9 integers f(1), f(2), ..., f(9) (1 ≤ f(i) ≤ 9).

outputFormat

Output

Print the maximum number you can get after applying the operation described in the statement no more than once.

Examples

Input

4 1337 1 2 5 4 6 6 3 1 9

Output

1557

Input

5 11111 9 8 7 6 5 4 3 2 1

Output

99999

Input

2 33 1 1 1 1 1 1 1 1 1

Output

33

样例

2
33
1 1 1 1 1 1 1 1 1

33