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B. Long Number

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — 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 $$$f(1)$$$, $$$f(2)$$$, ..., $$$f(9)$$$ ($$$1 \le f(i) \le 9$$$).

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

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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